GECCO '25 Companion: Proceedings of the Genetic and Evolutionary Computation Conference Companion

We introduce Neighborhood Adaptive DE, an automatically designed variant of Differential Evolution (DE) tuned specifically for Many Affine Black-Box Optimization benchmark functions. The algorithm was generated by the Large Language Model Evolutionary Algorithm LLaMEA approach, which employed a (4,12) Evolution Strategy in combination with the large language model Gemini-2.0-Flash to generate new optimization algorithms. Key features of Neighborhood Adaptive DE include sampling a small, randomly chosen subset of 'neighbors' for each individual and using the best among those as the base vector in mutation (instead of the global best). This neighborhood-based strategy, along with adaptive tuning of scale factor F and crossover rate CR, leads to greater diversity and mitigates premature convergence. Additionally, an automatic restart mechanism re-initializes the population upon detecting stagnation. Experimental benchmarking indicates that Neighborhood Adaptive DE outperforms other algorithms on the benchmark, including the winner of last-years Many Affine competition, suggesting that automated design with LLaMEA can yield novel, high-performance algorithms for challenging black-box optimization tasks.

This paper is devoted to the implementation of the LLM Designed Evolutionary Algorithms, using a GNBG-generated Test Suite. Traditional metaheuristics face challenges in maintaining efficiency and effectiveness as complexity increases. Our research addresses these issues by focusing on enhancing individual methods within a class rather than reorganizing entire classes - a relatively unexplored strategy in black-box continuous optimization. By integrating Large-Language Models (LLMs), we evolve specific functions or components, offering novel insights into improving metaheuristic performance.

This paper presents an extended abstract, designed as a competition entry on LLM-designed Evolutionary Algorithms. We present DEuLLM, a differential evolution (DE) constructed entirely through prompt engineering with the help of a large language model (LLM). DEuLLM integrates key advances in DE, such as success-history-based parameter adaptations, distance-based feedback, linear population size reduction, and careful boundary control, without any code design outside the LLM-driven dialogue. The development process demonstrates how iterative prompting can guide the design of a competitive optimizer from scratch through natural language interaction. The results show that our proposed DEuLLM is able to locate the global optimum for 15 out of 24 test problems.

This paper presents an extended abstract describing an entry into the LLM for evolutionary algorithms tailored benchmarking competition using a GNBG-generated test suite. This study explores the generative design of optimization algorithms using large language models (LLMs) within the EASE modular framework, which supports iterative prompting and feedback-driven refinement. Across five successive generations, we observed a progressive transformation in algorithmic structure. The findings suggest opportunities for further research into the role of prompt design, feedback phrasing, and framework architecture in guiding the emergence of more task-adaptive, domain-specialized algorithmic behavior.

This paper presents an extended abstract describing an entry into the GNBG-II benchmarking competition. We propose a hybrid variant of the differential evolution (DE) algorithm based on the added properties of ALSHADE and jSO, named ALSHADE-jSO. This algorithm uses the current-to-Amean/1 mutation strategy inspired by ALSHADE and the weighted mean strategy inspired by jSO to generate new solutions. A selection strategy inspired by ALSHADE, SHADE-based parameter adjustments, and linear population size reduction (LPSR) mechanism of LSHADE are added for better exploration and exploitation operations. The results show that for 9 out of 24 problem instances, ALSHADE-jSO gives a success rate of 100% and is capable of achieving a global solution for 15 problems.

The mathematical runtime analysis of evolutionary algorithms traditionally regards the time an algorithm needs to find a solution of a certain quality when initialized with a random population. In practical applications it may be possible to guess solutions that are better than random ones. We start a mathematical runtime analysis for such situations. We observe that different algorithms profit to a very different degree from a better initialization. We also show that the optimal parameterization of an algorithm can depend strongly on the quality of the initial solutions. To overcome this difficulty, self-adjusting and randomized heavy-tailed parameter choices can be profitable. Finally, we observe a larger gap between the performance of the best evolutionary algorithm we found and the corresponding black-box complexity. This could suggest that evolutionary algorithms better exploiting good initial solutions are still to be found. These first findings stem from analyzing the performance of the (1 + 1) evolutionary algorithm and the static, self-adjusting, and heavy-tailed (1 + (λ,λ)) genetic algorithms on the OneMax benchmark. We are optimistic that the question of how to profit from good initial solutions is interesting beyond these first examples.

This paper for the hot-off-the-press track at GECCO 2025 summarizes the work [1].

In the area of multi-objective evolutionary algorithms (MOEAs), there is a trend of using an archive to store non-dominated solutions generated during the search. This is because 1) MOEAs may easily end up with the final population containing inferior solutions that are dominated by other solutions discarded during the search process and 2) the population that has a commensurable size of the problem's Pareto front is often not practical. In this paper, we theoretically show, for the first time, that using an archive can guarantee speed-ups for MOEAs. Specifically, we prove that for two well-established MOEAs (NSGA-II and SMS-EMOA) on two commonly studied problems (OneMinMax and LeadingOnesTrailingZeroes), using an archive brings a polynomial acceleration on the expected running time. The reason is that with an archive, the size of the population can reduce to a small constant; there is no need for the population to keep all the Pareto optimal solutions found. This contrasts existing theoretical studies for MOEAs where a population with a commensurable size of the problem's Pareto front is needed. The findings in this paper not only provide a theoretical confirmation for an increasingly popular practice in the design of MOEAs, but can also be beneficial to the theory community towards studying more practical MOEAs.

This paper for the Hot-off-the-Press track at GECCO 2025 summarizes the work Chao Bian, Shengjie Ren, Miqing Li, and Chao Qian. An Archive Can Bring Provable Speed-ups in Multi-Objective Evolutionary Algorithms (IJCAI'24). [4]

The compact genetic algorithm (cGA) is one of the simplest estimation-of-distribution algorithms (EDAs). Next to the univariate marginal distribution algorithm (UMDA)—another simple EDA—, the cGA has been subject to extensive mathematical runtime analyses, often showcasing a similar or even superior performance to competing approaches. Surprisingly though, up to date and in contrast to the UMDA and many other heuristics, we lack a rigorous runtime analysis of the cGA on the LeadingOnes benchmark—one of the most studied theory benchmarks in the domain of evolutionary computation.

We fill this gap in the literature by conducting a formal runtime analysis of the cGA on LeadingOnes of problem size n. For the cGA's single parameter μ = Ω(n log² n), we prove that the cGA samples the optimum of LeadingOnes with high probability within O(μn log n) function evaluations. For the best choice of μ, our result matches, up to polylogarithmic factors, the typical O(n²) runtime that many randomized search heuristics exhibit on LeadingOnes.

This paper for the hot-off-the-press track at GECCO 2025 summarizes the work Marcel Chwiałkowski, Benjamin Doerr, and Martin S. Krejca: Runtime analysis of the compact genetic algorithm on the LeadingOnes benchmark. IEEE Transactions on Evolutionary Computation 2025. Early access. DOI: 10.1109/TEVC.2025.3549929 [3].

In the last few years, the mathematical runtime analysis of randomized search heuristics has made a huge step forward by analyzing the most prominent multi-objective evolutionary algorithms (MOEAs). These results confirmed that many previous results for synthetic MOEAs extend to state-of-the-art MOEAs, but also exhibited some unexpected difficulties not seen with simple MOEAs. We continue this line of research by analyzing how the NSGA-II and the SMS-EMOA (also with a recently proposed stochastic population update) solve the NP-hard subset selection problem. For these two state-of-the-art algorithms, we prove performance guarantees that agree with those previously shown for the POSS algorithm, a variant of the simplistic GSEMO, namely that they compute (1 - e^-γ)-approximate solutions in expected time O(k²n). Our experiments confirm these findings. This work is the first runtime analysis of state-of-the-art MOEAs for the subset selection problem, and also the first runtime analysis of SMS-EMOA on a combinatorial problem.

This paper for the hot-off-the-press track at GECCO 2025 summarizes the work Renzhong Deng, Weijie Zheng, Mingfeng Li, Jie Liu, and Benjamin Doerr: Runtime analysis for state-of-the-art multi-objective evolutionary algorithms on the subset selection problem. Parallel Problem Solving from Nature, PPSN 2024. Springer, 264–279. 10.1007/978-3-031-70071-2_17 [8].

Deploying deep neural networks (DNNs) on microcontroller units (MCUs) is a common trend to process the increasing amount of sensor data generated at the edge, but it is challenging due to resource and latency constraints. Neural architecture search (NAS) helps automate the search for suitable DNNs. In our original work "Combining Multi-Objective Bayesian Optimization with Reinforcement Learning for TinyML" [3], we present a novel NAS strategy for edge deployment using multi-objective Bayesian optimization (MOBOpt) and reinforcement learning (RL). Our approach efficiently balances accuracy, memory, and computational complexity, outperforming existing methods on multiple datasets and architectures such as ResNet-18 and MobileNetV3.

The decomposition-based multi-objective evolutionary algorithm (MOEA/D) does not directly optimize a given multi-objective function f but instead optimizes N + 1 single-objective subproblems of f. We analyze for the first time how the MOEA/D with only standard mutation operators computes the whole Pareto front of the OneMinMax benchmark when the g-optima are a strict subset of the Pareto front. For standard bit mutation, we prove an expected runtime of O(nN log n + n^n/(2N)N log n) function evaluations. For the second phase, when the algorithm start with all g-optima, we prove an [EQUATION] expected runtime.

For power-law mutation with exponent β ∈ (1, 2), we prove an expected runtime of O(nN log n + n^β log n) function evaluations. The O(n^β log n) term from the second phase is independent of the number of subproblems N, leading to a huge speedup over standard bit mutation. In general, our bound for power-law suggests that the MOEA/D performs best for N = O(n^β-1), resulting in an O(n^β log n) bound.

This paper for the hot-off-the-press track at GECCO 2025 summarizes the work Benjamin Doerr, Martin S. Krejca, and Noé Weeks: Proven runtime guarantees for how the MOEA/D computes the Pareto front from the subproblem solutions. Parallel Problem Solving from Nature, PPSN 2024. Springer, 197–212. 10.1007/978-3-031-70071-2_13 [2].

We start the runtime analysis of multi-objective evolutionary algorithms for unbounded integer search spaces. We analyze single-and full-dimensional mutation operators with three different mutation strengths: changes by plus/minus one (unit strength), random changes following a law with exponential tails, and random changes following a power-law. We rigorously prove on a recently proposed benchmark that unit mutation can be slow when the initial solutions are far from the Pareto front. When setting the expected change right, exponential-tail mutation yields the best runtime guarantees in our results—however, with a wrong choice of this expectation, the performance guarantees quickly become uninteresting. With power-law mutation, we obtain good results uniformly over all problem parameters and starting points. We complement our mathematical findings with experimental results that suggest that our bounds are not always tight. Most prominently, power-law mutation outperforms the exponential-tail mutation even when the latter uses a near-optimal parametrization. Hence, we suggest to favor power-law mutation for unknown problems in integer spaces.

This paper for the hot-off-the-press track at GECCO 2025 summarizes the work Benjamin Doerr, Martin S. Krejca, and Günter Rudolph: Runtime Analysis for Multi-Objective Evolutionary Algorithms in Unbounded Integer Spaces. Conference on Artificial Intelligence, AAAI 2025. AAAI Press. 26955–26963. [11].

The non-dominated sorting genetic algorithm II (NSGA-II) is the most popular multi-objective optimization heuristic. Recent mathematical runtime analyses have detected two shortcomings in discrete search spaces, namely, that the NSGA-II has difficulties with more than two objectives and that it is very sensitive to the choice of the population size. To overcome these difficulties, we analyze a simple tie-breaking rule in the selection of the next population. Similar rules have been proposed before, but have found only little acceptance. We prove the effectiveness of our tie-breaking rule via mathematical runtime analyses on the classic OneMinMax, LeadingOnesTrailingZeros, and OneJump-ZeroJump benchmarks. We prove that this modified NSGA-II can optimize the three benchmarks efficiently also for many objectives, in contrast to the exponential lower runtime bound previously shown for OneMinMax with three or more objectives. For the bi-objective problems, we show runtime guarantees that do not increase when moderately increasing the population size over the minimum admissible size.

This paper for the hot-off-the-press track at GECCO 2025 summarizes the work Benjamin Doerr, Tudor Ivan, and Martin S. Krejca. Speeding up the NSGA-II with a simple tie-breaking rule. Conference on Artificial Intelligence, AAAI 2025. AAAI Press. 26964–26972 [8].

We study structural properties of the buffer allocation problem from the fitness landscape perspective. We consider manufacturing flow lines with series-parallel network structure. The machines are supposed to be unreliable, their time to failure and repair time are exponentially distributed. We carry out computational experiments with local search and genetic algorithms in order to evaluate the fitness landscape properties of previously published instances and their modifications. We show that in many problem instances, several clusters of local optima can be identified. Besides that, the so-called 'massif central' or 'big valley' structure of the fitness landscape is present only partially.

The performance of genetic algorithms is discussed with respect to population clustering. The crossover operator is shown to be useful on those problem instances, where the population clustering was observed and the permanent usage of crossover is recommended.

This abstract for the Hot-off-the-Press track of GECCO 2025 summarizes work that has appeared in [6].

This work introduces Multi-Level Symbolic Regression (MSR), a novel algorithm that leverages the inherent grouping in multi-level (MuL) datasets to learn a single, interpretable function structure shared across groups while adapting numerical parameters to capture group-specific variations. MSR runs parallel symbolic regression processes on each group in MuL datasets, fuses their outputs and balances performance across groups even in the presence of noise or unequal group sizes. To extend the applicability of our approach to standard tabular datasets lacking an explicit grouping variable, we also propose the Mean Local Intraclass Correlation Coefficient (MLICC). MLICC effectively identifies the most suitable feature to act as a level by partitioning data into local regions and quantifying intra-group similarity, thus facilitating implicit MuL analysis. Extensive experiments on both synthetic benchmarks and diverse real-world datasets ranging from educational and medical data to financial time series, which we collate and term as MSR-Bench, demonstrate that MSR achieves higher recovery rates of the true function structure and lower prediction errors compared to state-of-the-art symbolic regression methods and traditional MuL models. This Hot-of-the-Press paper summarizes the work K.S. Fong and M. Motani, "Multi-Level Symbolic Regression: Function Structure Learning for Multi-Level Data", International Conference on Artificial Intelligence and Statistics (AISTATS'24).

This short paper summarizes the main results of our work A Performance Analysis of Lexicase-Based and Traditional Selection Methods in GP for Symbolic Regression that has been recently accepted for publication in the ACM journal Transactions on Evolutionary Learning and Optimization. In this paper, we analyze the performance of several relevant lexicase variants and two traditional selection methods in combination with down-sampling strategies on a wide range of symbolic regression benchmark problems. We perform experiments not only for a given evaluation budget, but also for different time budgets as the time complexity of the selection methods varies greatly. We find that the performance ranking of the selection methods depends on the given setting. For example, for a given evaluation budget, the best performing method is ϵ-lexicase selection combined with a down-sampling strategy, while for a short runtime, selection methods using batches of training cases perform best. Further, we find that tournament selection combined with informed down-sampling performs relatively well overall.

This Hot Off the Press paper summarizes the work of Yuma Horaguchi, Kei Nishihara, and Masaya Nakata, entitled "Evolutionary multiobjective optimization assisted by scalarization function approximation for high-dimensional expensive problems", published in Swarm and Evolutionary Computation, 2024 [5].

This paper introduces a scalarization function approximation-based surrogate-assisted multiobjective evolutionary algorithm (SAMOEA) to solve high-dimensional expensive multiobjective optimization problems (EMOPs). Our algorithm, called SFA/DE¹, constructs an approximation model for each scalarization function in the framework of decomposition-based MOEAs to enhance the robustness of the degradation of the accuracy of surrogate models in high-dimensional space. Different from typical SAMOEAs, which approximate each objective function, this strategy uses a single approximation model to estimate the quality of candidate solutions, and thus it can hedge the risk of the accumulation of approximation errors caused by multiple approximation models. The experimental results show that SFA/DE outperforms the state-of-the-art SAMOEAs designed for high-dimensional EMOPs.

Bayesian optimisation (BO) is an efficient approach for solving expensive optimisation problems, where acquisition functions play a major role in achieving the tradeoff between exploitation and exploration. The exploitation-exploration tradeoff is challenging; excessive focus on exploitation can stagnate the search, while too much exploration can slow convergence. Multi-objectivisation has been explored as an effective approach to mitigate the exploitation-exploration tradeoff problem. Along this line, in this paper, we propose a Multi-Objectivisation-based adaptive Exploitation-Exploration tradeoff framework (MOEE) to balance exploitation and exploration in BO. MOEE considers the nondominated front formed by the exploitation and exploration objectives and adaptively switches the focus on exploration and exploitation on the basis of the search status. We verify our method on the 19 synthetic and practical problem instances with up to 20 dimensions, and the results show that our proposed multi-objectivisation framework can achieve a good balance between exploitation and exploration.

This paper for the Hot-off-the-Press track at GECCO'25 summarises the work [4]: Chao Jiang and Miqing Li. "Multi-objectivising acquisition functions in Bayesian optimisation." ACM Transactions on Evolutionary Learning and Optimization (2025).

Black-box optimisation is a central topic in optimisation theory, with the original No Free Lunch (NFL) theorems revealing fundamental limits of general-purpose algorithms. Understanding the implications of NFL in adversarial (maximin) optimisation has remained an open challenge [15, 16]. This paper establishes a rigorous NFL theorem for black-box adversarial optimisation under the Pure Strategy Nash Equilibrium (NE) solution concept. We highlight the role of the solution concept in defining optimality and show that, when performance is measured by the number of rows and columns queried in the payoff matrix, the average performance of all black-box adversarial optimisation algorithms is the same. We further develop a black-box complexity framework to analyse adversarial optimisation. By combining Yao's Principle with our NFL theorem, we derive general lower bounds on the query complexity for computing Nash Equilibria.

This paper, submitted to the Hot-off-the-Press track at GECCO 2025, summarises the work by Per Kristian Lehre and Shishen Lin: No Free Lunch Theorem and Black-Box Complexity Analysis for Adversarial Optimisation, NeurIPS 2024 (in press), https://openreview.net/forum?id=NkuySm8qVs [9].

This Hot Off the Press paper provides a brief summary of our recent work "Bayesian Inverse Transfer in Evolutionary Multiobjective Optimization". In this paper, we propose a novel concept termed inverse transfer for multiobjective optimization. Unlike conventional transfer approaches, inverse transfer leverages the shared objective functions commonly found across diverse application domains, even when the corresponding decision spaces are misaligned. This capability enables the effective integration of knowledge from heterogeneous source tasks. Furthermore, a key byproduct of inverse transfer is the construction of high-precision inverse models, which can not only enhance diversity by querying previously unexplored regions of the solution space but also facilitate the on-demand generation of customized solutions tailored to user preferences. Building upon this idea, we introduce the first Inverse Transfer Evolutionary Multiobjective Optimizer (invTrEMO). The source code of the invTrEMO is made available at https://github.com/LiuJ-2023/invTrEMO.

This paper serves as an extended abstract for the Hot-off-the-Press track at GECCO 2025, building upon the paper Liu, J., Gupta, A., Ong, Y. S. (2025). Bayesian Inverse Transfer in Evolutionary Multi-objective Optimization. ACM Transactions on Evolutionary Learning, 4(4), 1–27 [10].

Evolutionary algorithms (EAs) are widely used for multi-objective optimization due to their population-based nature. Traditional multi-objective EAs (MOEAs) generate a set of solutions to approximate the Pareto front, leaving a decision maker (DM) with the task of selecting a preferred solution. However, this process can be inefficient and time-consuming, especially when there are many objectives or the subjective preference of DM is known. To address this issue, interactive MOEAs (iMOEAs) integrate decision making into the optimization process, i.e., update the population with the help of the DM. In contrast to their wide applications, there have existed only two pieces of theoretical works on iMOEAs, which considered interactive variants of the two simple single-objective algorithms, RLS and (1+1)-EA. This paper provides the first running time analysis for practical iMOEAs. Specifically, we prove that the expected running time of the well-developed interactive NSGA-II (R-NSGA-II) for solving the OneMinMax and OneJumpZeroJump problems are all asymptotically faster than the traditional NSGA-II. Meanwhile, we present a variant of OneMinMax, and prove that R-NSGA-II can be exponentially slower than NSGA-II. These results provide theoretical justification for the effectiveness of iMOEAs while identifying situations where they may fail. Experiments are also conducted to validate the theoretical results.

This paper for the Hot-off-the-Press track at GECCO 2025 summarizes the work Tianhao Lu, Chao Bian, and Chao Qian. Towards Running Time Analysis of Interactive Multi-objective Evolutionary Algorithms. In: Proceedings of the AAAI Conference on Artificial Intelligence (AAAI'24), Vancouver, Canada, 2024, pp. 20777–85. [24]

A widely accepted way to assess the performance of iterative blackbox optimizers is to analyze their empirical cumulative distribution function (ECDF) of pre-defined quality targets achieved not later than a given runtime. In this work, we consider an alternative approach, based on the empirical attainment function (EAF) and we show that the target-based ECDF is an approximation of the EAF. We argue that the EAF has several advantages over the target-based ECDF. In particular, it does not require defining a priori quality targets per function, captures performance differences more precisely, and enables the use of additional summary statistics that enrich the analysis. We also show that the average area over the convergence curves is a simpler-to-calculate, but equivalent, measure of anytime performance. These analyses are available in the IOHanalyzer platform.

This manuscript for the Hot-off-the-Press track at GECCO 2025 is based on the paper "Using the Empirical Attainment Function for Analyzing Single-objective Black-box Optimization Algorithms" published by IEEE Transactions on Evolutionary Computation, 2025. doi: 10.1109/TEVC.2024.3462758 [10].

Geometric Semantic Genetic Programming (GSGP) enhances traditional GP by using search operators that act on the syntax of solutions with bounded effects on semantics, transforming symbolic regression into a uni-modal search problem. CPU and GPU implementations of GSGP have demonstrated efficiency by eliminating the need to evaluate variable-length syntactic models, but they remain unsuitable for real-time or resource-constrained scenarios. This paper presents GSGP-Hardware, a fully pipelined and parallel FPGA implementation developed using VHDL. Our solution features a custom fixed-point arithmetic division algorithm, concurrent individual evaluation, and optimal mutation step computation. Validated on five real-world benchmarks and synthesized using Vivado AMD-Xilinx, GSGP-Hardware achieves competitive predictive accuracy while delivering unprecedented performance gains; three orders of magnitude in runtime and four orders of magnitude in GPops/s compared to state-of-the-art GPU implementations. This work enables instantaneous symbolic regression with significantly lower power consumption, opening new possibilities for evolutionary algorithms in domains where computational resources and energy efficiency are limited.

The paper "Knowledge-based Optimization in Epidemics Prevention" proposes a knowledge-based method for optimization of vaccination assignments using epidemic modelling on graphs. A multiobjective evolutionary algorithm is used as the global optimizer with a local search procedure performing solution improvement based on counter-epidemic strategies known from epidemiology. The proposed method allows prioritizing the vaccinations according to the age of the individual or the node degree, which represents the number of contacts. With the aim of bringing this study closer to real-life applications, infection costs are calculated using real-life cost estimates found in the literature regarding the COVID-19 epidemic. Also, graph nodes have the "age" attribute assigned, which affects hospitalization probability and thus the infection costs.

This paper addresses theory in evolutionary multiobjective optimisation (EMO) and focuses on the role of crossover operators in many-objective optimisation. The advantages of using crossover are hardly understood and rigorous runtime analyses with crossover are lagging far behind its use in practice, specifically in the case of more than two objectives. We present a many-objective problem class together with a theoretical runtime analysis of the widely used NSGA-III to demonstrate that crossover can yield an exponential speedup on the runtime. In particular, this algorithm can find the Pareto set in expected polynomial time when using crossover, while without crossover it requires exponential time to even find a single Pareto-optimal point. To our knowledge, this is the first rigorous runtime analysis in many-objective optimisation demonstrating an exponential performance gap when using crossover for more than two objectives. This Hot-off-the-Press paper summarises the work Andre Opris, A Many-Objective Problem Where Crossover is Provably Indispensable, To appear at The 39th Annual AAAI Conference on Artificial Intelligence, 2025.

This paper, originally published in Evolutionary Computation Journal [11], investigates the interplay between surrogate model performance, model settings, and black-box landscape features within the context of Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Our focus is on understanding how landscape characteristics influence surrogate model accuracy during evolutionary optimization, aiming to inform the automated selection and tuning of surrogate models. We perform a comprehensive feature analysis, identifying robust and informative landscape features relevant to surrogate modeling. The analysis explores the error dependencies of four models across 39 settings, utilizing three methods for input data selection, drawn from surrogate-assisted CMA-ES runs on noiseless benchmarks within the Comparing Continuous Optimizers framework. The insights gained can help in the development of adaptive surrogate modeling strategies and metalearning approaches for evolutionary computation.

Effective and efficient optimization of real-world problems using Genetic Algorithms depends on the quality of masks used by variation operators. A high-quality variation mask groups variables which have a joint non-linear or non-monotonical influence on function value. In gray-box optimization, the dependencies are known a priori, while in black-box, they are discovered as a part of the optimization process. For both, variable dependency is typically considered as a symmetric relation, i.e., if variable a depends on b, then it is assumed that b depends on a. However, a thorough analysis of large-scale instances of an NP-complete real-world optimization problem shows that a variable dependency relation does not have to be symmetrical. Therefore, we present the concept of directional dependencies and the Directional Direct Linkage Empirical Discovery (2DLED). 2DLED discovers both dependency types (symmetrical and non-symmetrical) and tells them from each other. More details concerning 2DLED, directional dependencies and their utilization can be found in the original work [7].

Clustering is a fundamental problem in many areas, which aims to partition a given data set into groups (clusters) based on some distance measure, such that the data points in the same group are similar while that in different groups are dissimilar. Due to its importance and NP-hardness, a lot of methods have been proposed, among which Evolutionary Algorithms (EAs) are a class of popular ones. Evolutionary clustering has found many successful applications, but all the results are empirical, lacking theoretical support. This paper fills this gap by proving that the approximation performance of the GSEMO (a simple multi-objective EA (MOEA)) for solving four formulations of clustering, i.e., k-tMM, k-center, discrete k-median and k-means, can be theoretically guaranteed. Furthermore, we consider clustering under fairness, which tries to avoid algorithmic bias, and has recently been an important research topic in machine learning. We prove that for discrete k-median clustering under individual fairness, the approximation performance of the GSEMO can be theoretically guaranteed with respect to both the objective function and the fairness constraint.

This paper for the Hot-off-the-Press track at GECCO 2025 summarizes the work Chao Qian. Can Evolutionary Clustering Have Theoretical Guarantees? IEEE Transactions on Evolutionary Computation, 2024, 28(5): 1220–1234. [24]

Quality-Diversity (QD) algorithms are a new type of Evolutionary Algorithms (EAs), aiming to find a set of high-performing, yet diverse solutions. They have many successful applications in reinforcement learning and robotics, helping improve the robustness in complex environments. Furthermore, they often empirically find a better overall solution than traditional search algorithms which explicitly search for a single highest-performing solution. However, their theoretical analysis is far behind. In this paper, we try to shed some light on the optimization ability of QD algorithms theoretically. By comparing the popular QD algorithm MAP-Elites with (μ + 1)-EA (a typical EA focusing on finding better objective values only), we prove that on two NP-hard problems, i.e., monotone approximately submodular maximization and set cover, MAP-Elites can achieve the (asymptotically) optimal polynomial-time approximation ratio, while (μ + 1)-EA requires exponential expected time on some instances. This provides theoretical justification for that QD algorithms can be helpful for optimization, and discloses that the simultaneous search for high-performing solutions with diverse behaviors can provide stepping stones to good overall solutions and help avoid local optima.

This paper for the Hot-off-the-Press track at GECCO'25 summarizes the work C. Qian, K. Xue, and R.-J. Wang. Quality-Diversity Algorithms Can Provably Be Helpful for Optimization (IJCAI'24). [20]

In the real world, there exist a class of optimization problems that multiple (local) optimal solutions in the solution space correspond to a single point in the objective space. In this paper, we theoretically show that for such multimodal problems, a simple method that considers the diversity of solutions in the solution space can benefit the search in evolutionary algorithms (EAs). Specifically, we prove that the proposed method, working with crossover, can help enhance the exploration, leading to exponential acceleration on the expected running time. This result is derived by rigorous running time analysis in both single-objective and multi-objective scenarios, including (μ + 1)-GA solving the widely studied single-objective problem, Jump, and NSGA-II and SMS-EMOA (two well-established multi-objective EAs) solving the widely studied bi-objective problem, OneJumpZeroJump. Experiments are also conducted to validate the theoretical results. We hope that our results may encourage the exploration of diversity maintenance in the solution space for multi-objective optimization, where existing EAs usually only consider the diversity in the objective space and can easily be trapped in local optima.

This paper for the Hot-off-the-Press track at GECCO 2025 summarizes the work Shengjie Ren, Zhijia Qiu, Chao Bian, Miqing Li, and Chao Qian. Maintaining Diversity Provably Helps in Evolutionary Multimodal Optimization. In: Proceedings of the 33rd International Joint Conference on Artificial Intelligence, Jeju Island, South Korea, 2024, pp.7012–7020. [27]

Here we briefly summarize the main findings of the above mentioned paper by Rodriguez-Fernandez et al., 2024 [4]. In this work, the authors address the problem of computing all locally optimal solutions of a given multi-objective problem whose images are sufficiently close to the Pareto front. Such ϵ-locally optimal solutions are particularly interesting in the context of multi-objective multimodal optimization (MMO). To this end, first a new set of interest, L_Q,ϵ, is defined. Second, a new unbounded archiver, ArchiveUpdateL_Q,ϵ, is proposed that aims to capture this set in the limit. Third, several MOEAs are equipped with ArchiveUpdateL_Q,ϵ as external archiver and compared to their archive-free counterparts on selected benchmark problems. Finally, in order to make a fair comparison of the outcomes in particular for MOPs with a larger number of decision variables, a new performance indicator, I_EDR, is proposed and used.

This work explores the use of doubly stochastic matrices within Estimation of Distribution Algorithms to solve permutation-based problems, focusing on the Quadratic Assignment Problem (QAP). Experiments show DSMs outperform other models in both efficiency and effectiveness, with potential applicability to ordering problems like and other optimization methods.

Here we briefly summarize the main findings of the above mentioned paper by Schütze et al., 2024. In this work, the authors argue that the entire set of nearly optimal solutions of a given multi-objective optimization problem (MOP) is of potential interest for the decision maker (DM) to realize his/her project. To be more precise, in this work, first, a new set of interest, N_Q,ϵ, is proposed. Next, an unbounded archiver that aims to capture this set is proposed and analyzed. Further, four different subset selection strategies and a new performance indicator tailored to the problem at hand are proposed and discussed. Finally, the behavior of the archiver as external archiver within several multi-objective evolutionary algorithms (MOEAs) is presented indicating the benefit of the novel approach.

EVOTER is a framework for evolving transparent, interpretable rule sets that combine predictive accuracy with human readability. Unlike post-hoc explainers, EVOTER constructs intrinsically interpretable models through list-based grammatical evolution. The framework introduces three innovations: time-lag operators, feature-feature comparisons, and nonlinear transformations. It demonstrates strong performance across diverse domains including classification, time-series forecasting, and policy learning. By enabling models that are both effective and auditable, EVOTER advances the state of explainable artificial intelligence.

Learning Fuzzy-Classifier Systems (LFCSs), also known as evolutionary fuzzy rule-based machine learning, combine evolutionary algorithms with fuzzy rules to create interpretable models. However, traditional inference schemes lack mechanisms to quantify uncertainty in predictions. This paper introduces a novel class inference scheme based on the Dempster-Shafer Theory of Evidence that explicitly models epistemic uncertainty through an "I don't know" state. By calculating belief masses for each class hypothesis and uncertainty, our approach enhances robustness in real-world applications. Experiments on real-world datasets demonstrate statistically significant improvements in classification performance compared to conventional approaches. Our method forms smoother decision boundaries and provides quantitative measures of prediction confidence, addressing a critical gap in reliable decision-making for fuzzy rule-based machine learning.

This paper summarizes the ACM TELO article: Hiroki Shiraishi, Hisao Ishibuchi, and Masaya Nakata. 2025. A Class Inference Scheme With Dempster-Shafer Theory for Learning Fuzzy-Classifier Systems. ACM Transactions on Evolutionary Learning and Optimization. https://doi.org/10.1145/3717613 [7]. Our implementation is available at https://github.com/YNU-NakataLab/jUCS.

Rule-based machine learning systems face a fundamental representation challenge: traditional approaches require a priori selection between crisp intervals and/or fuzzy membership functions. This can result in either overly complex fuzzy rule sets or insufficiently expressive crisp rule sets. To address this limitation, we introduce a novel evolutionary approach for learning classifier system (LCS) machine learning algorithms that co-optimizes both rule shape and fuzziness using a four-parameter beta distribution. Our method integrates specialized genetic operators with generalization pressure mechanisms, such as subsumption and crispification operators, to favor crisp, interpretable rules when possible. Experiments on real-world classification tasks demonstrate competitive accuracy compared to state-of-the-art black-box models while maintaining superior interpretability. Our method can automatically determine appropriate rule representations for different feature space regions, evolving toward simpler crisp rules where possible while retaining fuzzy rules only where necessary for handling complex decision boundaries.

This paper summarizes the following IEEE TEVC article: Hiroki Shiraishi, Yohei Hayamizu, Tomonori Hashiyama, Keiki Takadama, Hisao Ishibuchi, and Masaya Nakata. 2025. Adapting Rule Representation With Four-Parameter Beta Distribution for Learning Classifier Systems. IEEE Transactions on Evolutionary Computation. https://doi.org/10.1109/TEVC.2025.3550915 [1]. Our implementation is available at https://github.com/YNU-NakataLab/Beta4-UCS.

Interpretable machine learning (ML) implies that structural relationships to exist between different parts of the ML model. We demonstrate how the tangled program graph (TPG) framework is able to demonstrate structural relationships for a suite of partially observable reinforcement learning tasks. The tasks are defined in terms of developing spell casting behaviours for the Invoker hero under the Dota 2 game engine. We show that TPG is able to demonstrate all 4 of the properties used to define interpretable machine learning. Moreover, a unique form of feature engineering / modularity takes place between programs that define state for (indexed) memory versus programs defining actions. The full article appears as Smith and Heywood (2024) "Interpreting Tangled Program Graphs under Partially Observable Dota 2 Invoker tasks" in IEEE Transactions on Artificial Intelligence, 5 (4): 1511–1524. https://doi.org/10.1109/TAI.2023.3279057

Demand for goods delivery services keeps growing, creating problems with last mile delivery. While autonomous delivery robots provide a solution to many of these problems, configuring their deployment to balance cost, performance, and safety is complex. Our industry partner Panasonic uses a multi-objective search approach to find configurations for their system, leveraging a simulator to assess the quality of the different configurations. However, due to the complexity of the simulator, this approach proved very computationally expensive. In this work, we propose an approach that uses a surrogate model to speed up fitness computation. Since building the surrogate model has a cost itself, the approach trains the model incrementally during the search: first, an imprecise model is used, while, as the search progresses, more precise models are used. The search stops when no improved solutions can be found. Experimental results show that this new approach, while it produces configurations of slightly lower quality, requires significantly less computing time. This is an extended abstract of "Alternating Between Surrogate Model Construction and Search for Configurations of an Autonomous Delivery System" by C.-H. Sun, T. Laurent, P. Arcaini, and F. Ishikawa, IEEE International Conference on Software Analysis, Evolution and Reengineering (SANER 2024).

We showcase work on "Evolutionary algorithms for solving single- and multiple-objective political redistricting problems: The case study of Poland" published in the Applied Soft Computing Journal 152 (2024) 111258. It proposes and evaluates new advanced evolutionary methods for solving political redistricting problems. The reported experiments involve diverse settings, among which the most extensive concerned a simultaneous optimization of four criteria: equality of populations in election districts, districts compactness, the dissimilarity of the districting plan with the one being in effect, and the number of mandates attainable by a selected party. Our algorithms demonstrate low computational complexity and the ability to well-approximate the Pareto front. The latter also proved meaningful for conducting a post-analysis, allowing us to understand how realizations of specific optimization criteria correlate.

This paper summarizes our recent work published in ACM Transactions on Evolutionary Learning and Optimization (2024), entitled "Explainable Benchmarking for Iterative Optimization Heuristics". We introduce IOHxplainer, a novel software library designed to systematically and explainably analyze the performance impact of various components and hyperparameters in modular or parametrized optimization heuristics. By leveraging explainable AI techniques such as SHAP values and machine learning models, IOHxplainer allows for an in-depth analysis of the contributions and interactions of algorithmic components across diverse benchmark scenarios.

Our approach significantly enhances transparency in algorithm benchmarking, facilitating informed algorithm selection and tuning. The original paper is available [9].

This paper summarizes our recent work published in IEEE Transactions on Evolutionary Computation (2025), entitled "LLaMEA: A Large Language Model Evolutionary Algorithm for Automatically Generating Metaheuristics". In this work we propose a novel evolutionary algorithm framework that leverages large language models (LLMs) like GPT-4 to automatically generate, evaluate, and refine metaheuristic optimization algorithms. Evaluations on the BBOB benchmark suite demonstrate that algorithms automatically discovered by LLaMEA can outperform established state-of-the-art methods, such as CMA-ES and DE, especially on lower-dimensional optimization problems. Our results illustrate the significant potential of using LLMs for automated algorithm design, setting a new direction for evolutionary computation research.

Here we briefly summarize the main findings of the above mentioned paper by Hao Wang et al., 2024. In this work, a novel set-based Newton method for Hausdorff approximations of the Pareto front is proposed for the use within multi-objective evolutionary algorithms (MOEAs). To this end, first a previously proposed set-based Newton step is generalized for the treatment of both equality and inequality constraints and for the use of general reference sets. Since the target reference set (i.e., the Pareto front) is not given, in a next step a particular strategy is proposed to obtain an approximation of this set via using the information of the used MOEA during its run. Finally, the strength of the resulting Newton method as post-processing step is demonstrated on several test functions and different base MOEAs.

Despite significant progress in the field of mathematical runtime analysis of multi-objective evolutionary algorithms (MOEAs), the performance of MOEAs on discrete many-objective problems is little understood. In particular, the few existing performance guarantees for classic MOEAs on classic benchmarks are all roughly quadratic in the size of the Pareto front.

In this work, we consider a large class of MOEAs including the (global) SEMO, SMS-EMOA, balanced NSGA-II, NSGA-III, and SPEA2. For these, we prove near-tight runtime guarantees for the four most common benchmark problems OneMinMax (OMM), CountingOnesCountingZeros (COCZ), LeadingOnesTrailingZeros (LOTZ), and OneJumpZeroJump (OJZJ), and this for arbitrary numbers of objectives. Our bounds depend only linearly on the size of the largest incomparable set, showing that MOEAs on these benchmarks cope much better with many objectives than what previous works suggested. Our bounds are tight apart from small polynomial factors in the number of objectives and length of bitstrings. This is the first time that such tight bounds are proven for many-objective uses of MOEAs.

This paper for the Hot-off-the-Press track at GECCO 2025 summarizes the work Simon Wietheger and Benjamin Doerr. Near-Tight Runtime Guarantees for Many-Objective Evolutionary Algorithms. In Parallel Problem Solving from Nature - PPSN XVIII. 153–168, 2024. [12].

In this paper we present the first rigorous theoretical analysis of the generalisation performance of a Geometric Semantic Genetic Programming (GSGP) system. More specifically, we consider a hill-climber using the GSGP Fixed Block Mutation (FBM) operator for the domain of Boolean functions. We prove that the algorithm cannot evolve Boolean conjunctions of arbitrary size that are correct on unseen inputs chosen uniformly at random from the complete truth table i.e., it generalises poorly. Two algorithms based on the Varying Block Mutation (VBM) operator are proposed and analysed to address the issue. We rigorously prove that under the uniform distribution the first one can efficiently evolve any Boolean function of constant size with respect to the number of available variables, while the second one can efficiently evolve general conjunctions or disjunctions of any size without requiring prior knowledge of the target function class. An experimental analysis confirms the theoretical insights for realistic problem sizes and indicates the superiority of the proposed operators also for small parity functions not explicitly covered by the theory.

Walking School Bus (WSB) promotes Active School Travelling (AST) while reducing congestion and pollution around schools caused by parental chauffeuring. We introduce a framework to generate WSB walking networks from public data and perform multi-objective routing optimisation to support efficient route planning. Our approach ensures optimal routes that balance multiple criteria and meet the needs of both parents and children.

The focus of manifold learning is to reduce the dimensionality of data. Typically, the geometric properties of the resulting manifold are only indirectly controlled, making them difficult to evaluate or manipulate during learning before the manifold is obtained. Dynamical tuning of manifold geometry solves the problem of complex manual topology assignment for data. This paper presents the method of extracting a geometry as a distance graph for data with minimum Dirichlet energy using an evolutionary algorithm, which demonstrates improved generalization over traditional manifold regularization. The effectiveness of the proposed approach is confirmed by validation on MNIST and Mammoth datasets.

We analyze the effect that numerical instabilities arising from the use of aggressive compilation optimization modes have on the performance of an evolutionary algorithm. Using two different C++ compilers with six optimization levels targeting the x86_64 architecture, it is shown that the algorithm is resilient even in the most aggressive mode.

The edge-cloud continuum's lack of unified standards often limits application development to the initially chosen platform. This challenges designers and developers to select the computation resources available in the edge/cloud continuum to optimize application performances while containing execution costs. In this context, this work proposes a methodology for assessing distributed application deployment configurations through simulation based on the Petri-net formalism. Furthermore, it investigates using the Differential Evolution (DE) algorithm to identify optimal configurations, considering multiple and potentially conflicting objectives.

In the wake of generative artificial intelligence and the exponential growth in the volume of data generated, the associated increase in data complexity in the sense of the quantity of different data types present in a single system poses a challenge to evolutionary algorithms. To allow for the development and testing of new algorithms adapted to this new data landscape, test problems are necessary as a way to both evaluate and compare algorithms performances. However, while recent advances extended known test problems such as the r-Leading-Ones marking the transition from binary to multi-valued variables, having different data-types coexisting in the search space is still an open question. We propose the h-Leading-Ones as an extension of the r-Leading-Ones to evaluate the ability of an algorithm to solve problems on a search space composed of multi-valued and real-valued data types. Its design with dependency between the different data-types and its continuity with the r-Leading-Ones provides a convenient new environment for benchmark and runtime analysis for mixed-category search spaces.

Cooperative Coevolutionary Algorithms have discovered coordinated behaviors in a variety of multiagent systems. Even though the team's performance is captured in team fitness, efficient learning requires shaped, local fitnesses for each agent. While traditional fitness shaping approaches capture each agent's direct contribution to team fitness, they are unable to capture agents' indirect contributions, such as supporting other teammates' actions. Recent work has incorporated a domain-specific heuristic to measure the influence each agent has on its teammates, and provide credit for those teammates' actions to the influencing agent. However, such a heuristic may be non-trivial to define for every domain, and may not capture all influential interactions between agents. We propose randomly choosing which teammates an agent receives credit for, and combining that with a mixed elites selection mechanism to retain high performing teams. This requires no domain expertise, and shows performance gains over traditional shaping techniques. Lastly, we propose bootstrapping as future work to gradually improve this random credit assignment through training to bias the coevolutionary search towards beneficial influence sets.

We investigate the statistical properties of bases derived from spanning trees in edge-based genetic algorithms for the Max-Cut problem. Edge-based algorithms represent solutions as combinations of basis elements, each formed by removing an edge from a spanning tree. We analyze how the distribution of flip sizes—defined as the number of edges whose cut status changes when a basis element is combined with a candidate solution via XOR (exclusive or) operator—affects algorithm performance. Experiments on graphs using Kruskal-like, depth-first search, and breadth-first search spanning trees show a moderate to strong positive correlation between higher frequencies of small flip sizes and improved solution quality. These results suggest intentionally promoting small flip sizes could enhance the performance of genetic algorithms for the Max-Cut problem.

Migrating monolithic applications to microservices is a challenging task. In particular, the monolith decomposition into small size, limited context, and independent microservices is the most addressed migration issue in the literature. To tackle this challenge, we introduce a novel approach to monolith decomposition by framing it as a multi-objective bin-packing problem. This is the first approach that leverages Non-dominated Sorting Genetic Algorithm III (NSGA-III) to address monolith decomposition integrating database decomposition with multi-objective optimization. Preliminary experimental results on a monolith application indicate the potential efficacy of the approach in obtaining high-quality monolith decompositions with independent databases.

This paper proposes a novel concept for automating innovization for route planning through the extraction and reuse of knowledge from route feature distributions. The resulting so-called innovized heuristic is applicable to an entire class of routing problems. Innovized heuristics offer a flexible stochastic structure that is still intuitively understandable in the context of vehicle routing. Concerning the bounds of problem classes, our case study on route planning in central Berlin versus Manhattan indicates that innovized heuristics are not transferable between cities with different layouts.

This paper presents an extended abstract for our competition on GNBG-II. For GECCO 2025 competitions, we introduce GNBG-II consisting of 24 box-constrained problem instances derived from the Global Numerical Benchmark Generator (GNBG), providing a diverse and challenging test suite for optimization algorithms. Although the core design of GNBG-II remains the same as in the 2024 competitions, the current version introduces additional complexities to further increase the difficulty of the benchmark problems. We invite authors to test and evaluate their algorithms on GNBG-II, the details are available at: https://dsmlossf.github.io/GNBG-Competition-2025/

When optimizing a highly complex real-world problem, the solution may not be sufficiently searched for, or it may take a long time to converge on the solution. On the other hand, companies often develop products with similar trends, such as improvements to existing products or product series. Therefore, when developing similar products using evolutionary multi-objective optimization, it is expected that solution search performance will improve by saving the design data of past products and including them in the initial solution. In this paper, we use NSGA-II to investigate the effect on the convergence speed to the Pareto front and the diversity of the solution distribution when a part of the non-dominated solution obtained in one problem is memorized and included in the initial solution when solving another similar problem. As a result, we show that the convergence speed improves when using solutions near the center of the Pareto front, which are commonly selected in product development, while solution search performance deteriorates for some benchmark problems, and that using solutions on the edge of the Pareto front is effective in improving the diversity of the solution distribution.

This paper investigates decentralized swarm intelligence for Heavy Articulated Vehicles (HAVs), which are traditionally automated through centralized Multi-Robot Systems. Unlike typical swarm robotics, where individuals are modeled as point masses with simple kinematics and circular collision footprints, HAVs present unique challenges. We focus on the specific issues related to jackknifing and mutual collision prevention among these elongated swarm members. Our proposed approaches aim to address and mitigate these challenges effectively.

In this paper, we propose a method for synthetically generating industrial data based on evolutionary approaches. The method involves applying evolutionary operators to the coordinates of a polygon describing an object's shape and then transferring the original image style to the resulting polygon geometry.

The proposed approach was validated for the laser welding problem. An augmented dataset expanded from 120 original weld images to 4500 synthetic examples, enabling the training of a convolutional neural network for weld segmentation.segmentation.

Soft computing refers to a computational paradigm aimed at providing approximate and heuristic solutions to hard problems, often adopting strategies inspired by nature or human reasoning: evolutionary computation and fuzzy systems are prime examples of this approach. In this article we present softpy, a Python library for soft computing designed to support the development of soft computing-based applications in both practical contexts as well as in educational use. Compared to other existing libraries and frameworks, softpy provides a common implementation of both evolutionary computing and fuzzy systems functionalities under an integrated API compatible with the Python data science ecosystem. After describing the design philosophy of the library, we provide a self-contained documentation of its contents and functionalities, and then provide a simple example aimed at illustrating its use in the development of an hybrid soft computing application. Finally, we describe potential directions for improvement and future extensions of the library.

Research in Cartesian Genetic Programming (CGP) is—in most works—of empirical nature. To further facilitate this, we present CRust_GP: A Rust framework for the construction of (generic) CGP varieties and their configuration. Furthermore, it includes various evolutionary operators and extensions that are commonly found in the CGP related literature. By using a component based architecture, we achieve high modularity and simplify the process of implementing extensions. This paper provides a general description of CRust_GP's features, integrated evolutionary operators, as well as its high level architectural design.

In this paper, we investigate the inherent structural bias of BBOB and CEC benchmark sets. First, we theoretically derive the advantage of central evaluation against random search on the Sum of Squares-like functions. We then provide an experimental analysis of the effectiveness of the central evaluation on functions from BBOB, CEC2014, and CEC2017. We utilize four variants of the Differential Evolution (DE) algorithm, in which by changing the boundary handling technique, we introduce different types of structural bias in the method and show the link between the performance of the biased DE variants and the inherent biases in the benchmark sets. We find that the high use of Sum of Squares-like functions and the BBOB-specific location of the optima give a substantial advantage to the center-biased DE variants, especially in high dimension on low function evaluation settings. On the selected CEC functions, this effect was much less pronounced.

Over the years, genetic programming (GP) has evolved, with many proposed variations, especially in how they represent a solution. Being essentially a program synthesis algorithm, it is capable of tackling multiple problem domains. Current benchmarking initiatives are fragmented, as the different representations are not compared with each other and their performance is not measured across the different domains. In this work, we propose a unified framework, dubbed TinyverseGP (inspired by tinyGP), which provides support to multiple representations and problem domains, including symbolic regression, logic synthesis and policy search.

Conference scheduling problems require the generation of schedules for conferences by considering multiple constraints to offer the best possible experience to participants. Previous studies have been published in the literature, however, the comparison and evaluation of the developed methods is challenging, as these methods have been designed to address rather specific requirements of the conferences being studied per se. In this work, we attempt to bridge this gap by making benchmark data publicly available to researchers. We also present a selection hyper-heuristic algorithm to solve the benchmark instances and provide computational results. We aim to raise awareness of the under-studied conference scheduling problem, and to encourage researchers to contribute to the benchmark dataset with new instances, constraints, and solving methods.

Modern solvers for combinatorial optimization problems are often the result of hybridizing several algorithmic techniques. Algorithmic frameworks such as MORK enable rapid prototyping and automatic design of such solvers. It is, however, difficult to explain the runtime behavior of complex solvers, whose algorithmic complexity may not be easy to analyze theoretically. In this work, we propose an empirical analysis of the runtime behavior of algorithms that provides an explanation of their complexity using big-Theta (Θ) notation. Our method relies on instrumenting algorithmic components and recording their runtimes, fitting the empirical data to various theoretical complexity models, and finally combining those individual models into a full model that matches the runtime data of the complete algorithm. We demonstrate its applicability, first, on a synthetic dataset, and then, on a state-of-the-art algorithm for a combinatorial optimization problem. In both cases, our method correctly predicts how the algorithmic components scale as instances become more challenging to solve.

Trying to design software systems in such a way that they consume a minimal amount of energy is simply good engineering practice. Scientific software is no exception; in this case, we will put our focus on evolutionary algorithms and the energy consumption patterns in memory and CPU for two different, low-level languages: The mainstream C++ and the emerging zig. By setting up a methodology that gives us a precise measure of the energy spent by key evolutionary algorithm functions, we can give the scientific software engineer some actionable insights on how to write energy-conscious, and thus energy-thrifty, evolutionary algorithms. Our experiments show that, even with very low energy consumption in both cases, C++ can achieve a significant reduction in energy consumption for some integer-based fitness functions, as well as very good performance on classical genetic operators. Besides, the experimental results have a low variability, as compared to zig, making it in the short and medium run the best of the two languages for evolutionary algorithms.

Othimi is an innovative educational software platform that provides a block-based visual programming environment for designing, implementing and running metaheuristics, with a particular focus on evolutionary algorithms applied to combinatorial optimization. Tailored for both teaching and practical exploration, Othimi reduces the barrier to entry for learners by abstracting complex algorithmic concepts into an intuitive drag-and-drop interface. The tool supports interactive customization and experimentation with various metaheuristic strategies, enabling users to visualize problem definition and algorithmic design, evaluate performance, and fine-tune parameters. Its encourages a deeper understanding of metaheuristic principles by facilitating hands-on learning experiences. Othimi stands out as a unique resource in Computer Science education, providing a dynamic platform that bridges theoretical instruction and applied algorithmic development.

This paper proposes "Evolve On Click" (EvOC) - an open-source intuitive web-based platform to simplify the implementation, execution, and visualization of Evolutionary Algorithms (EAs) including genetic programming, by providing a user-friendly interface. This facilitates easier accessibility of evolutionary algorithm software packages such as DEAP, to users with minimal programming experience. EvOC guides users through the EA design process, allowing them to experiment with different algorithms, parameters, and configurations without the need for programming expertise. The platform also incorporates features to show code created based on the configuration so that users can also learn from it, thus enhancing collaboration and enabling users to easily share their results with others. The architecture used by EvOC also supports ease of access for parallel and distributed EAs with real-time log streaming / monitoring and visualization of the evolution runs. By incorporating the latest DevOps techniques during the development process, EvOC does not require extensive maintenance and allows for the platform to be run as a service, supporting multiple users on a single instance. This paper details the design, implementation, and evaluation of EvOC towards increasing accessibility and ease of comfort with EAs for novice learners - thus broadening the reach of the community.

Many optimization benchmarks have been proposed for single and multi-objective problems to assess the performance of optimization algorithms, including evolutionary algorithms. They are manually generated or developed based on real-world scenarios. However, manually generated benchmarks often fail to capture essential properties of real-world problems. On the other hand, real-world-based benchmarks require an extensive run time or high cost of creating benchmarks and are sometimes inaccessible due to confidential restrictions. To overcome these limitations, this study proposes a large language model-driven evolutionary optimization benchmark generator (LLM-EBG) that automatically generates benchmarks with desired characteristics. LLM-EBG integrates an evolutionary algorithm with a large language model (LLM). Candidate benchmarks are generated through crossover and mutation using an LLM and refined through an evolutionary process. As an initial attempt, we generated unconstrained single-objective benchmarks designed to emphasize the difference between genetic algorithms (GA) and differential evolution (DE). Experimental results demonstrated that the proposed method can generate benchmarks where the performance gap between GA and DE is significant; in particular, GA outperforms DE, and vice versa. These results highlight the potential of the proposed method to create tailored and informative benchmarks for optimization algorithm evaluation.

The paper presents "evorobotpy3", a flexible and easy-to-use Python-based simulation environment for implementing and testing various algorithms, addressing diverse benchmark problems, and supporting different neural network controllers. Although existing simulators can model real robots accurately, they are often limited in generalizability and tailored to specific domains and applications. In contrast, evorobotpy3 is designed to be extensible and adaptable, not only by allowing customization for different domains but also by inherently incorporating the operational principles of evolutionary algorithms by design. To demonstrate these capabilities, we evaluated the OpenAI-ES algorithm on a series of benchmark tasks, including Pybullet locomotion tasks and classic control problems such as pole balancing. This study underscores the potential of evorobotpy3 as a powerful and extensible tool for robotics and artificial intelligence research.

This paper introduces IGJSP, a Benchmark Generator for Job Shop Scheduling Problems (JSP), which generates customized instances to evaluate optimization algorithms. JSP requires assigning tasks to jobs and machines while minimizing makespan, energy consumption, and tardiness, key aspects for industrial process optimization and energy-efficient scheduling. IGJSP fills a gap by providing flexible, reproducible benchmarks that mirror real-world complexities, unlike existing libraries such as JSPLIB that do not support modern multi-objective scenarios essential for advanced optimization techniques.

IGJSP supports large-scale instance generation incorporating energy efficiency, job flexibility, and dynamic constraints. The tool offers multiple configuration options and outputs, including JSON, DZN, and Taillard formats, ensuring compatibility with both complete solvers and modern heuristic or metaheuristic algorithms. Its modular design allows precise customization of parameters such as the number of jobs, machine configurations (with speed scaling), processing times, and statistical distributions. By enabling rigorous algorithm comparisons and fostering reproducibility and meta-learning, IGJSP provides a trusted, scalable framework for testing diverse heuristics and metaheuristics. This contribution promotes standardized benchmarking practices and supports the development of adaptive, efficient algorithms, making it an essential resource for research and algorithm evaluation in scheduling problems. Overall, IGJSP significantly advances cutting-edge scheduling research and practice, providing robust solutions.

Random number generation is widely used in many different algorithms, yet its inner workings and performance are poorly understood among many of its users. In this paper, we aim to explore one of its lesser-known aspects: energy consumption. Most studies on the subject tend to focus on the quality of the generators or on measuring their execution times. However, energy consumption is a critical concern today, particularly for mobile devices.

In this work, we have measured the energy consumption of standard C++ random number generators. The results reveal differences in energy usage of over a thousand-fold, which could be significant for applications that require the generation of large quantities of random numbers, such as learning algorithms and metaheuristics.

There are many areas of scientific endeavour where large, complex datasets are needed for benchmarking. Evolutionary computing provides a means towards creating such sets. As a case study, we consider Conway's Surreal numbers. They have largely been treated as a theoretical construct, with little effort towards empirical study, at least in part because of the difficulty of working with all but the smallest numbers. To advance this status, we need efficient algorithms, and in order to develop such we need benchmark data sets of surreal numbers. In this paper, we present a method for generating ensembles of random surreal numbers to benchmark algorithms. The approach uses an evolutionary algorithm to create the benchmark datasets where we can analyse and control features of the resulting test sets. Ultimately, the process is designed to generate networks with defined properties, and we expect this to be useful for other types of network data.

When comparing different metaheuristics, the behaviour of the search process is a central feature towards distinguishing them beyond their mere metaphors. However, with large-scale studies, i.e. featuring hundreds or more configurations on large sets of benchmark functions, which are important to assess true capabilities, the sheer number of runs, high-dimensional data, and complex presentations make the traditionally employed visual evaluation of behaviours impossible. To remedy this, techniques that can summarise data without loosing important information are vital. In this paper, we investigate the effectiveness of five established techniques from the field of unsupervised learning in an example study featuring configurations of random search, genetic algorithms, and particle swarm optimisation on a set of optimisation benchmark functions. We find that the data reduction techniques do not perform equally well and that they can not be used to their full effect with default parameters. However, we demonstrate that these techniques can provide valuable insights into algorithmic behaviour.

We introduce autoverse, a symbolically parameterizable Neural Cellular Automata (NCA)-based game engine for single-player grid-worlds. Users specify a set of spatial rewrite rules, which are sufficient for implementing a broad swath of the types of game environments (e.g. mazes, dungeons, sokoban puzzles) that currently serve as popular testbeds for Reinforcement Learning (RL) agents. These are compiled to a convolutions (i.e. an NCA), allowing for environments to be parallelized on the GPU, thereby drastically accelerating RL training. Meanwhile, rules and levels are encoded as binary strings, and applying mutations to these strings results in new, admissible environments, making autoverse a natural fit for evolutionary PCG.

We use autoverse to explore a novel method for automatically generating sets of complex game worlds, wherein environments are evolved so as to maximize the number of iterations required by greedy tree search to discover a new best solution. We find that spending more time in this evolutionary loop results in training sets that produce more general agents in terms of their performance on novel, held-out tasks. We use the compressibility of environment rollouts as a proxy measure of complexity and characterize evolved environments in an initial step toward generating more interpretable and aligned autoverse worlds.¹

This work presents a hybrid optimization approach combining the global search capabilities of the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) with Variable Neighborhood Descent (VND). The proposed methodology addresses critical SAR operations objectives, such as minimizing mission completion time, prioritizing high-impact tasks, and balancing UAV energy consumption. NSGA-II provides a robust framework for exploring the solution space and generating diverse Pareto-optimal solutions, while VND systematically refines them for better convergence and quality. Simulation results indicate statistically significant improvements, achieving average reductions of 4.80% in travel distance and 8.91% in mission completion time compared to standalone NSGA-II. Although the current framework does not support dynamic task reassignment in real-time, it demonstrates potential for practical applications in static SAR scenarios.

This paper studies the effects of extending an evolvable modular robot system by 'bones' of evolvable length. Based on simulations, we investigate whether evolution exploits this possibility, and we compare different ways to attain desired morphological features alongside preferred behavioral traits. To validate the outcomes, we select a robot with a high fitness and interesting morphology and construct its physical twin. Comparing the simulated and real-world behaviors of the twins, we gain insight into the reality gap.

Soft robots have gain increasing attention due to their flexible morphologies suited for complex tasks in dynamic environments. However, the co-design of structure and control remains challenging due to the large search space and high demand of computational costs. To tackle this challenge, we proposed an N-gram-based controller inheritance framework that integrates genetic algorithms for structural evolution with Proximal Policy Optimization (PPO) for training controllers. The method captures sequential behavioral patterns from multiple ancestor policies and reuses them across generations to reduce redundant learning progress. Experimental results in the EvoGym benchmark show faster coveragence and improved final fitness compared to a non-inheritance baseline. Our approach provides a scalable framework for exploring policy inheritance in the evolutionary co-design of soft robots.

The Container Relocation Problem (CRP) is an NP-complete combinatorial optimization problem, indicating that no exact algorithms can solve it within a reasonable time. For this reason, heuristic methods are most commonly used to address this problem. Relocation Rules (RRs) are a simple and fast heuristic applicable in dynamic environments, making them widely used in practice. Designing RRs is a challenging task, which is why this process has recently been automated using Genetic Programming (GP). To develop RRs, GP requires a training set. However, the literature lacks research on which training model and instance types should be used for RR development, even though this choice can significantly impact solution quality. Thus, we proposed and compared several different training models in this study. The results indicate that it is possible to improve results by selecting the right training models, highlighting the need for further research.

Designing bent Boolean functions for cryptographic applications is a challenging combinatorial task due to the super-exponential growth of the search space. We propose Evolutionary Boolean Reaction Systems (EvoBRS), an optimization method based on Reaction Systems (RS)—a bio-inspired model abstracting biochemical reactions. EvoBRS finds functions with competitive nonlinearity while providing a compact and interpretable representation. Unlike traditional methods such as Genetic Algorithms (GA), which rely on full truth tables, EvoBRS leverages a more expressive yet concise encoding.

This paper proposes a destination-oriented route construction method (DORC) for ant colony optimization (ACO) to effectively solve minmax multiple traveling salesmen problems (MTSP) with multiple depots. Unlike existing studies, DORC first determines the destination for each salesman before building his route. Then, it constructs the routes for all salesmen by integrating the information of the current visiting city and the destination. In this way, the selection of cities for all salesmen is directional toward the destination. Therefore, DORC expectedly helps ACO build promising routes for all salesmen. Thereafter, this paper embeds DORC into the five classical ACO algorithms, namely ant system (AS), elite AS (EAS), max-min AS (MMAS), rank-based AS (RAS), and ant colony system (ACS) to solve MTSP. Experiments conducted on MTSP instances with different numbers of cities and different numbers of salesmen demonstrate that DORC helps the five ACO algorithms achieve much better performance. Particularly, the experimental results reveal that the helpfulness of DORC is more significant for the five ACOs in solving large-scale MTSP with a large number of cities and a large number of salesmen.

Recent advances in quantum computing have shown great potential for solving combinatorial optimization problems. A notable example is the quadratic knapsack problem, a constrained binary optimization problem. However, current quantum-inspired algorithms require Quadratic Unconstrained Binary Optimization (QUBO) formulations. Transforming constrained optimization into QUBO impacts the algorithms' speed and efficiency. In this study, we evaluate five existing transformation methods and propose four novel approaches. We assess them by using Simulated Annealing (SA), and find that three of our approaches outperform existing methods in terms of execution time as well as quality and quantity of feasible solutions found. Also, we tested these transformations on a quantum annealer, which was unable to solve even small instances, due to limitations in connectivity and error rates. In general, our results highlight the advantages of the new approaches, which reduce the number of variables in the QUBO representation.

Deep Optimisation is a recently developed Estimation of Distribution Algorithm that has shown notable efficiency in solving the Multi-Dimensional Knapsack Problem. However, since this optimiser relies on an auto-encoder that is sequentially trained, we posit it is susceptible to catastrophic forgetting, a phenomenon where previously learned knowledge is lost during successive trainings. This issue can diminish the optimiser's performance, motivating the present work. To address this challenge, we explore the application of Elastic Weight Consolidation (EWC), a deep learning technique that mitigates forgetting by associating weight variations during future training with their importance in predicting current tasks. EWC has previously demonstrated significant reductions in forgetting across various tasks and architectures. Our results show that applying EWC to Deep Optimisation significantly enhances performance on Multi-Dimensional Knapsack Problems. Furthermore, we analyse how these improvements are linked to the resilience of information retained within the auto-encoder, highlighting the critical role of preserving learned knowledge in sequential training scenarios.

Priority rules are widely utilised in combinatorial optimisation because they effectively balance solution quality and computational cost. This makes them particularly suitable for addressing problems with extreme time constraints, such as real-time or dynamic scenarios. In contrast, other methods such as metaheuristics or exact algorithms are less frequently applied in these contexts due to their higher computational complexity. However, designing effective rules is a challenging task. To address this, genetic programming has been widely used for the automated generation of rules. Despite their advantages, individual rules can sometimes yield suboptimal results. However, numerous studies demonstrated that by using a set of rules instead of individual rule significantly improves their effectiveness. This paper examines various strategies of how a set of rules generated by genetic programming can be utilised to solve optimisation problems and introduces a novel algorithm, named the greedy randomised adaptive solution builder, for solving the travelling salesman problem. The experimental results demonstrate that the proposed method is capable of obtaining reasonably good solutions under highly time-constrained scenarios.

This paper introduces L-DEGR, a hybrid metaheuristic designed to solve the NP-hard Multi-Skill Resource-Constrained Project Scheduling Problem (MS-RCPSP). L-DEGR combines the L-SHADE method with the Greedy Schedule Builder (GSB) proposed in the Differential Evolution (DE) Greedy (DEGR) algorithm, incorporating several enhancements to improve its effectiveness. Despite DE generally being used for continuous optimization, we showcase that it can be effectively employed to solve combinatorial MS-RCPSP. L-DEGR was compared to the state-of-the-art method on the iMOPSE d36 instance set, as well as to L-SHADE using two different greedy approaches. Both L-DEGR and L-SHADE methods were calibrated using the Taguchi design-of-experiment method, thus ensuring robust parameter configurations and a fair comparison. Additionally, this study introduces new, significantly larger industrial-size problem instances for MS-RCPSP, which expands the scope of evaluation and demonstrates the scalability and robustness of the proposed method. Furthermore, a CP-SAT approach was used to compute reference solutions for all instances, providing a reliable lower bound for comparison. Experimental results demonstrate that L-DEGR achieves statistically significant results in comparison to state-of-the-art methods, setting new best-known makespans for the MS-RCPSP iMOPSE d36 and large-scale instances.

Among all combinatorial optimization challenges, the class of routing represents a well-known set of problems whose optimized solutions can significantly improve overall solution quality. Within this set, the Orienteering Problem presents a complex challenge: finding a set of Hamiltonian paths from a selected subset of objective points within a given time frame to maximize a global score. In this paper, the Multi-constrained Team Orienteering Problem is addressed by incorporating time windows and constraints on the maximum number of categories. The inclusion of an additional objective to balance route sizes is also explored. The problem is solved by adapting the NSGA-II algorithm, incorporating an integer-based solution representation and a set of transformation operators to achieve high-quality, densely populated Pareto fronts with reduced computation times compared to complete solvers.

Hypervolume subset selection (HSS) is an important problem in evolutionary multiobjective optimization (EMO). It may be used to guide EMO algorithms, to bound Pareto archives, or to select a reduced set of the most representative solutions of a multiobjective problem for further analysis by the decision maker. Lazy greedy incremental and decremental hypervolume subset selection algorithms are currently the fastest approximate methods for more than 4 objectives and moderate sizes of the candidate sets. In this paper, we show that the efficiency of these lazy algorithms could be further improved by adaptive update of previously calculated hypervolume contributions instead of always recalculating the contributions from scratch. We show also that the Improved Quick Hypervolume algorithm is well-suited for such a context because its recursion tree does not depend on dominated points which often appear when hypervolume contributions are updated.

Ant Colony Optimization (ACO) has been proven to be very effective in solving Traveling Salesman Problems (TSP). However, its effectiveness encounters limitations when solving large-scale TSP involving a considerably large number of cities. To alleviate this issue, clustering algorithms have been popularly used to help ACO effectively solve large-scale TSP, leading to Clustering-Assisted ACO (CA-ACO). Though there are a few studies in this direction, no research has been done to explore in depth the influence of clustering algorithms on ACO in solving large-scale TSP. To fill this gap, this paper investigates the effectiveness of three classical clustering algorithms (k-means, mini-batch k-means, and fuzzy c-means) on five classical ACOs (ant system (AS), elite AS (EAS), rank-based AS (RAS), max-min AS (MMAS), and ant colony system (ACS)) in solving large-scale TSP. To further boost the optimization performance, this paper designs a new sub-route merging scheme and a new local search method to effectively combine sub-routes and refine the final global route. Experiments conducted on six ArtTSP instances have proved that K-means is the most effective among the three clustering algorithms to cooperate with the five ACOs and ACS is the most effective among the five variants to cooperate with the three clustering algorithms to solve large-scale TSP.

In this paper, we propose a Tabu search algorithm based on symmetry local search (TS-SLS) that can be regarded as a search component for multi-objective evolutionary algorithms (MOEAs) to solve multi-objective traveling salesman problems (MOTSPs). In TS-SLS, the symmetry local search is designed by the symmetry feature of solution space in MOTSPs. We discuss and analyze the relation between the solution space and several common search operators and in turn obtain an interesting conclusion. In addition, considering the importance of diversity preservation in MOEAs, TS-SLS adopts the Tabu search (TS) as the main search mechanism to preserve diversity in MOTSPs. For experiments, we take 15 MOTSP benchmark instances and three classical and representative MOEAs as reference algorithms to assess the performance of TS-SLS. Experimental results show that the MOEAs embedded with TS-SLS can achieve competitive performances in terms of convergence and diversity.

Feature selection methods are important for machine learning (ML), as they can make learned models more accurate, easier to understand, and reduce their size and resource consumption. Interestingly, these methods may also induce multimodal fitness landscapes that are non-trivial to find optima in. In this work, we consider multimodal fitness landscapes induced by feature selection for ML by means of random forests. Among the genetic algorithms developed to handle multimodality, we study the crowding approach, specifically generalized crowding. Empirically, we consider how varying the scaling factor of generalized crowding influences the number of global and local optima found when performing feature selection for random forests for different datasets. While the real-world feature selection problems studied are modest in size, we hope that this research will enable improved understanding of and performance for larger feature selection problems in the future.

In this paper, we introduce and solve the Balanced Task Planning Problem, which originates from real-life industrial domains. The aim of this problem is to assign tasks to machines and planning periods so that machine loads are balanced around a target value while prioritizing more critical tasks. We provide a formal problem description and use Constraint Programming and Integer Programming solvers to find optimal solutions. For large-scale instances, we propose local search variants based on Tabu Search. To evaluate the methods, we generate a large number of random problem instances and perform an experimental evaluation of the different approaches. The results show that most of the small instances can be solved using the exact approach, and, for some, optimal solutions can be obtained. Using Tabu Search, high-quality solutions could be found for the large majority of large-scale instances.

The electric vehicle routing problem (EVRP) is a complex optimisation problem concerned with constructing efficient routes for electric vehicles, while considering constraints such as battery capacity and charging station availability. Due to the inherent difficulty of the problem, heuristics are the most common method used for solving them. Routing policies (RPs) are simple constructive heuristics that solve the problem by incrementally constructing the solution to it. This means that whenever a decision needs to be made, RPs determine it. Although this makes RPs well-suited for solving dynamic and large-scale problems, it is difficult to design such heuristics manually. For this reason, genetic programming is usually used, as it can generate better RPs than those designed manually. However, until now, most of the RPs were designed using the full recharging strategy for batteries. However, a lot of research demonstrated that this is suboptimal, and that better results can be obtained by using different partial recharging strategies. Therefore, in this study we use GP to generate RPs that incorporate several partial recharging strategies, including both fixed and adaptive recharging rates. The experimental study demonstrates that RPs that use partial recharging strategies outperform the full recharging strategy, leading to more efficient solutions.

Using surrogate-assisted optimization is an efficient way to deal with computationally expensive black-box problems. This method guides the search towards promising solutions and therefore reduces the time needed to find good solutions. In this paper, we focus on surrogates based on Walsh functions that are effective to solve pseudo-Boolean problems. An example is given with the bus stops spacing problem on single and multiple bus lines. One of the main issues with surrogate-assisted optimization is the growth of the number of terms of the model when the dimension gets high. To address this problem, we use a sparse model using only a small amount of relevant terms that is simpler to optimize. To choose the relevant terms, we use in this paper a spectral analysis that allows us to identify main terms and quantify their importance. An asynchronous surrogate-assisted master-workers optimization algorithm is also proposed to tackle this problem.

Swarming systems, such as for example multi-drone networks, excel at cooperative tasks like monitoring, surveillance, or disaster assistance in critical environments, where autonomous agents make decentralized decisions in order to fulfill team-level objectives in a robust and efficient manner. Unfortunately, team-level coordinated strategies in the wild are vulnerable to data poisoning attacks, resulting in either inaccurate coordination or adversarial behavior among the agents. To address this challenge, we contribute a framework that investigates the effects of such data poisoning attacks, using explainable AI methods. We model the interaction among agents using evolutionary intelligence, where an optimal coalition strategically emerges to perform coordinated tasks. Then, through a rigorous evaluation, the swarm model is systematically poisoned using data manipulation attacks. We showcase the applicability of explainable AI methods to quantify the effects of poisoning on the team strategy and extract footprint characterizations that enable diagnosing. Our findings indicate that when the model is poisoned above 10%, non-optimal strategies resulting in inefficient cooperation can be identified.

As machine learning algorithms are increasingly employed for critical decision-making, ensuring algorithmic fairness has become imperative. Fairness-aware Automated Machine Learning has emerged as a flexible and effective method for enhancing both model accuracy and fairness. However, most existing studies focus on hyperparameter optimization for a single model. In this study, we frame the problem as a multi-objective Combined Algorithm Selection and Hyperparameter Optimization (CASH) problem, aiming to jointly optimize both accuracy and fairness across a diverse set of machine learning algorithms and their corresponding hyperparameters. To address this challenge, we apply Multi-Objective Grammatical Evolution (MOGE). The results demonstrate that MOGE not only effectively identifies models that achieve higher fairness and accuracy, while also exploring the trade-offs between accuracy and fairness efficiently.

This paper explores evolutionary algorithms for launching physical adversarial attacks against end-to-end autoencoder communication systems. While these systems enhance communication efficiency and security, they remain vulnerable to adversarial interference, where attackers manipulate transmitted signals to deceive the autoencoder. For white-box attacks, we introduce PAGA, an approach utilizing evolutionary algorithms and elite population initialization to generate attack signals that maximize reconstruction errors and misclassification rates. For black-box attacks, where attackers lack knowledge of the receiver, we propose PAMFGA, a multifactorial variant of PAGA designed for enhanced effectiveness. Experimental results confirm that our attack methods significantly degrade communication quality, outperforming existing techniques. This study highlights the necessity of integrating robust security mechanisms into autoencoder-based communication systems.

Neural architecture search (NAS) and neuroevolution have emerged as key methods for designing artificial neural networks (ANNs). While several nature-inspired algorithms, such as Continuous Ant-Based Neural Topology Search (CANTS), have successfully automated the design of recurrent neural networks (RNNs), they suffer from certain limitations, including fixed search constraints and limited exploration strategies. This paper introduces Genetic Programming Collaborative Ant-Based Neural Topology Search (CG-CANTS-N), a novel graph-based NAS framework that employs multiple colonies of simulated ants which move through a continuous search space based on previously placed pheromones. The ant paths through the search space are used to construct graphs which are used as neural architectures. Both the individual ant agents and the ant colonies evolve over time using evolutionary strategies. CG-CANTS-N extends on CANTS by allowing more flexible graph structures, and by utilizing genetic programming functions (e.g., addition, multiplication, trigonometric functions) with trainable weights on graph edges as opposed to traditional neural network neurons. Key innovations include adaptive colony evaporation control, dynamic ant movement strategies, and cycle removal via depth-first search. We demonstrate that CG-CANTS-N is capable of designing graph based genetic programs for time series forecasting tasks which outperform existing state of the art methods.

Local Interpretable Model-agnostic Explanations (LIME) is a widely used technique in machine learning for generating instance-level explanations by fitting simple surrogate models to approximate the predictions of black-box models. However, a key limitation of LIME is that it operates on a very small local region around an instance, which may yield trivial explanations. This weakness can be evaluated qualitatively via a novel fidelity metric we introduce, K-Neighbours Fidelity (K-NF), which measures how well an explanation is faithful to the black-box model on a supralocal (i.e., larger than local) region. Additionally, the commonly used linear surrogates in LIME often fail to capture non-linear relationships present in the underlying model. To address these issues, we propose SLIME (SupraLocal Interpretable Model-agnostic Explanations), a novel method that uses evolutionary symbolic regression (ESR) to build concise equation-based surrogates that function as explanations faithful to the supralocal region around an instance. By replacing LIME's linear surrogate with equation-based models generated via ESR, we demonstrate that SLIME has greatly improved fidelity over LIME across a wide range of experiments on real-world datasets from UCI and PMLB.

Diabetic retinopathy (DR) is one of the most severe complications of diabetes, often leading to complete vision loss if untreated. The study presents a novel framework for the early and accurate prediction of DR based on fundus images. The proposed method leverages features extracted from the Gray Level Co-occurrence Matrix (GLCM) and employs genetic algorithms (GA) for two purposes: optimizing the parameters of a LightGBM classifier and selecting the most relevant GLCM features. Experiments were conducted on the publicly available APTOS dataset, and various crossover strategies were evaluated. The Blend Crossover (BLX-α-β) yielded the best results, achieving a classification accuracy of 0.9263, an F1-score of 0.928, recall of 0.9355, and precision of 0.9206. Notably, the feature set was reduced by nearly 75%, significantly decreasing model complexity while maintaining performance. This approach demonstrates the potential for effective DR prediction and lays the groundwork for its application to other medical images.

Differential Evolution (DE) and Particle Swarm Optimization (PSO) are well-established metaheuristics known for their significant parameters. This paper presents DE and PSO enhanced by Q-learning, which adaptively controls parameters such as differential weight and crossover probability for DE, and cognitive coefficient, social coefficient, and inertia weight for PSO. These methods were applied to optimize dose distribution in radiotherapy, aiming to maximize tumor coverage. Additionally, Q-learning refines the number of radiation shots. The introduced methods, Q-Learning assisted DE (QLDE) and Q-Learning assisted PSO (QLPSO), are evaluated against classical DE and PSO. Experimental results indicate that QLDE and QLPSO outperforms classical implementations, with QLDE achieving the highest rank. These results underscore the advantages of integrating reinforcement learning with DE and PSO in radiotherapy dose planning, highlighting its efficacy and adaptability for personalized cancer treatment.

We consider the problem of representation learning for evolutionary clustering. Evolutionary clustering algorithms are plagued by the difficulty of defining representations that are non-redundant, effective under crossover and avoid the introduction of strong assumptions regarding relevant cluster properties. At the core of our paper is a simple question: could recent advances in deep learning be leveraged to identify new representations for this unsupervised learning setting? We describe a Siamese Autoencoder as a first attempt to investigate this question on small toy problems and proceed to analyze the assumptions, generalization performance and limitations of the approach.

Evolutionary Algorithms have been successfully applied in Automated Machine Learning (AutoML) to evolve effective machine learning (ML) pipelines. Here, we use 12 OpenML classification tasks and the AutoML tool TPOT2 to assess the impact of lexicase and tournament selection on the generalizability of pipelines. We use one of five stratified sampling splits to generate training and validation sets; pipelines are trained on the training set, and predictions are made on the validation set. Lexicase and tournament selection use these predictions to identify parents. At the end of a run, TPOT2 returns the pipeline that achieved the best validation accuracy while maintaining the lowest complexity. The generalizability of this pipeline is assessed using the test set provided for an OpenML task. We found that lexicase produced pipelines with higher validation accuracy than tournament selection in all tasks for at least one split. In contrast, tournament selection produced pipelines with greater generalizability for 10 of the 12 tasks on at least one split. For most cases where tournament selection outperformed lexicase on test accuracy, we detected differences in validation accuracy and pipeline complexity.

High-dimensional and imbalanced data often pose significant challenges, including the risk of biased learning models that disproportionately favor the majority class and the adverse effects of the curse of dimensionality. To address these two challenges simultaneously, this paper proposes a multiform multi-objective feature selection method tailored for high-dimensional imbalanced classification tasks. The proposed method reformulates the target problem by prioritizing minority class performance, rather than focusing solely on overall classification accuracy. Through performing an evolutionary search on the alternative formulation, valuable features identified through the auxiliary task can be transferred back to the target task, steering the feature subset search towards both enhanced overall classification performance and minority class performance. The proposed method is a general framework and could be integrated into three mainstream multi-objective optimization frameworks to tackle imbalanced classification tasks. Experimental results on 12 real-world datasets show that the three instantiations of the proposed method enhance both overall and minority class performance when compared to their respective baselines.

Neural networks have repeatedly demonstrated the ability to accurately model complex nonlinear relationships. However, the black-box nature of such models has led to concerns about bias and trustworthiness especially in settings like healthcare where it impacts multiple aspects of patient care including prognosis and resource-allocation. Existing model-agnostic methods to enhance neural network interpretability only offer an external perspective on the working of neural networks. To solve this issue, we designed an Evolutionary Multiple Gaussian Model that replaces the activation function of a perceptron with an aggregate of multiple Gaussian functions. The parameters of this model were evaluated using the gravitational search algorithm with the objective of minimizing a function of the mean absolute percentage error (MAPE) and mean squared error between the predicted and actual values. We performed multiple experiments on the Medical Information Mart for Intensive Care-IV dataset to predict the patient length of stay in Intensive Care Units. Results indicate that the proposed algorithm outperforms it's popular counterparts in terms of MAPE while offering better interpretability.

In recent years, transformer models have achieved remarkable success across various fields. However, reducing the computational complexity while minimizing performance degradation has become a critical challenge. To address this challenge, we propose a pruning method for transformers, using a genetic algorithm, aimed at forecasting long-term time-series data. We used binary encoding to remove unnecessary information from the multi-head attention layers in the transformer encoder. It also leverages Fisher information-based fitness approximation to reduce the evaluating time for each individual. Additionally, we modified the knapsack problem formulation to penalize individuals exceeding the predefined threshold, ensuring a balance between maintaining a compression rate and selecting the best-performing individuals. Using eight time-series datasets, the sparse transformer consistently achieved superior performance compared to the vanilla transformer, with significantly fewer computational complexity. These results demonstrate that the proposed method effectively eliminates redundant attention heads.

Large Language Models (LLMs) have demonstrated remarkable abilities in responding to natural language instructions, but their performance depends on prompts, with high-quality prompts requiring human expertise and effort. Current prompt optimization techniques include continuous prompt-based and discrete prompt-based methods. The former requires access to LLMs' parameters which is time-consuming and the latter might lead to suboptimal results due to confined search space. To address the above limitations, we propose PSOPrompt, which retains exploratin capabilities of continuous prompts without altering LLMs' parameters. Noting the continuous nature of embeddings and the success of PSO for continuous optimization problems, it is used as the optimization method, with each embedding treated as an individual. To integrate continuous prompts with discrete prompts, embedding inversion is employed and a new encoding strategy is conceived. In the evolution process, it is discovered that incorporating expert knowledge into the initialization contributes to better outcomes. Experimental results demonstrate that PSOPrompt matches or outperforms existing approaches.

Discrete prompt search (DPS) aims to automatically find high-performing prompts that yield top accuracy in interactions with a pretrained language model. In the context of few-shot learning, evaluations of candidate prompts can only be done via a limited number of labeled examples. The search is often formulated as an optimization problem where prediction accuracy, F1 score, or cross-entropy loss is used as the objective function. While resulting prompts achieve top performance, they are mostly unreadable and uninterpretable, i.e., unlike natural languages. In this paper, we formulate DPS as a true multi-objective optimization (MOO) problem considering simultaneously both prompt performance and readability as separate objectives. We show that there exist certain degrees of conflict between the objectives, making the search for human-readable and highly-accurate prompts a challenging problem. We then propose the Multi-objective Evolutionary Algorithm for Predictive Probability guided Prompting (MoEAP3) to address the problem. Our MoEAP3 returns not a single final prompt as in conventional methods but a whole front of multiple candidate prompts, each representing an efficient trade-off between the objectives. Decision makers can straightforwardly investigate this front and intuitively select the prompt that yields the desired trade-off. Source code can be found at: https://github.com/ELO-Lab/MoEAP3.

UAV-assisted Mobile Edge Computing (MEC) improves IoT wireless systems but struggles with increasing computational demands, resource limitations, and stringent latency requirements. This work optimizes computation offloading (OLMEC) in UAV-assisted MEC using evolutionary algorithms. UAVs provide offloading services to user equipment (UE), balancing local and offloaded task execution. The goal is to minimize delays while adhering to latency and energy constraints. Two solutions are proposed: OMEA, a fine-tuned evolutionary algorithm, and OMEDR, which integrates evolutionary algorithms with deep reinforcement learning. Experimental results demonstrate the superiority of the proposed methods over existing approaches, highlighting their effectiveness in addressing the OLMEC problem.

Reinforcement Learning (RL) offers a fundamental framework for discovering optimal action strategies through interactions within unknown environments. Recent advancement have shown that the performance and applicability of RL can significantly be enhanced by exploiting a population of agents in various ways. Zeroth-Order Optimization (ZOO) leverages an agent population to estimate the gradient of the objective function, enabling robust policy refinement without estimating auxiliary functions such as value functions or advantage functions. As another application, genetic algorithms (GA) boosts the exploration of policy landscapes by mutational generation of policy diversity in an agent population and its refinement by selection. A natural question is whether we can have the best of two worlds that the agent population can have. In this work, we propose Ancestral Reinforcement Learning (ARL), which synergistically combines the robust gradient estimation of ZOO with the exploratory power of GA. The key idea in ARL is that each agent within a population infers gradient by exploiting the history of its ancestors, i.e., the ancestor population in the past, while maintaining the diversity of policies in the current population as in GA.

Generative text-to-image models have become increasingly ubiquitous thanks to their applications in digital art. However, since they are built on deep neural networks, they are typically vulnerable to adversarial samples, which are subtle changes that cause undesirable generations. To study such phenomena, many works try to automatically craft these samples to shift the models' output to be as irrelevant as possible while changing the original input text as little as possible. This can be formulated as a multi-objective optimization problem, where the stealthiness of the adversarial texts is treated as another objective to optimize. However, we argue that diversifying stealthiness in adversarial text-to-image generation might be a better choice since it is more flexible and effective to study the robustness of the model. We apply MAP-Elites, a Quality-Diversity algorithm, to find adversarial texts varying in the degree of stealthiness while preserving the best-found solutions in local niches. Experimental results show that MAP-Elites outperforms the genetic algorithm (GA) and the widely-used multi-objective evolutionary algorithm NSGA-II, approximately twice on diversity metrics and achieves competitive results on max fitness score and hypervolume. Moreover, the collection of returned solutions exhibits insight into the influence of each attack strategy on the adversarial attack performance.

Scientific workflows are a popular tool for running experiments and simulations. Moreover, Cloud infrastructures are widely used to execute workflows since they can handle elastic demand of multiple resources. However, this requires an effective autoscaling strategy to guarantee good performance and low cost. Reinforcement Learning (RL) has been used in the past to obtain efficient autoscalers. Nevertheless, RL approaches often exhibit poor initial performance, a problem than can hurt overall performance. We present a novel two-phase autoscaling strategy that combines Evolutionary Computation (EC) and RL. The proposal ensembles and provides a pre-optimized initial policy, obtained offline via EC, to an existing RL-based online autoscaler. The strategy aims to improve the overall performance during the learning process reducing makespan and execution cost.

Medical image segmentation for brain tumor analysis requires accurate and efficient models due to complex multimodal MRI data and tumor variability. This study presents PSO-UNet, which integrates Particle Swarm Optimization (PSO) with U-Net for dynamic hyperparameter tuning of filters, kernel size, and learning rate. PSO-UNet achieves state-of-the-art segmentation with DSCs of 0.9578 and 0.9523 and IoU scores of 0.9194 and 0.9097 on BraTS 2021 and Figshare datasets. The model uses only 7.8M parameters and executes in 906 seconds, outperforming standard U-Net frameworks. PSO-UNet generalizes well across modalities and tumor types, offering a lightweight and clinically viable solution. This framework offers a novel integration of automated PSO-driven hyperparameter tuning into U-Net, enhancing segmentation performance while reducing computational overhead. Future work will explore hybrid optimizations and further scalability.

In machine learning, evolutionary algorithms have traditionally depended on fixed rules and predefined building blocks. The Guided Evolution (GE) framework transforms this approach by incorporating Large Language Models (LLMs) to directly modify code and intelligently guide both mutations and crossovers. A key element of GE is the "Evolution of Thought" (EoT) technique, which establishes positive feedback loops, allowing LLMs to refine their decisions iteratively based on successful results. Building on this concept, we introduced the LLM-guided evolution to modify the architecture of a You Only Look Once (YOLO) model and enhance its performance on the KITTI dataset. Our findings show that LLM-Guided Evolution produced variants with significant performance improvements, such as an increase in Mean Average Precision from 92.5% to 94.7%. we also evaluated various LLM-GEs with different LLMs, including Mixtral-8x7B, Llama-3.1-70B, and Llama-3.3-70B, to assess their impacts on the evolutionary process. Our analysis shows that GE with Llama-3.1 and Llama-3.3 surpassed Mixtral-8x7B in performance, underscoring the importance of LLMs selection in refining evolutionary algorithms. These results highlight the flexibility and effectiveness of GE in real-world computer vision challenges, offering a novel paradigm for autonomous model optimization that combines LLM-driven reasoning with evolutionary strategies.

Deep neural networks are vulnerable to adversarial attacks, where perturbations added to input images lead to incorrect predictions. Black-box adversarial attacks, which do not require access to the internal model, are more practical in real-world scenarios. While evolutionary algorithms have been employed for black-box attacks, their effectiveness is hindered by high-dimensional decision spaces. Therefore, we propose a two-stage explanation-based method using Particle Swarm Optimization (PSO) for black-box adversarial attacks. The first stage employs a multi-objective optimization approach to generate explanations by directly selecting feature subsets extracted through the Segment Anything Model (SAM). Subsequently, the second stage leverages PSO to generate perturbations based on the derived explanations. Experiments on ImageNet validate the method's effectiveness, demonstrating superior performance in solving the black-box adversarial attack problem.

This paper tackles the challenge of simultaneously selecting and tuning mutation operators in multi-objective evolutionary optimization. The proposed Local Self-Adaptive Mutation extends the Adaptive Non-dominated Tournament Genetic Algorithm. Unlike global approaches, it selects operators based on effectiveness in specific regions of the objective space. A key innovation is the adaptive mutation probability, replacing predefined values and allowing dynamic adjustment across the Pareto Front. Applied to two real-world problems—Multi-Skill Resource Constrained Project Scheduling and Multi-Stage Resource Allocation. The enhanced method matched or outperformed manually tuned approaches.

A major assumption often made during the resolution of NP-Hard Multi-Objective optimization Problems is that problem instances are different from each other. Then, the same process is repeated integrally to solve these instances without benefiting from prior resolutions of similar problem instances. Consequently, resolution systems lose a lot of time to solve problems that were already partially or integrally treated beforehand. In this paper, we assume that previous Pareto Front solutions can guide new problem instance resolutions to accelerate the convergence to the optimal solutions. According to this assumption, our objective is to propose a framework that first learns a feature model on the previous solutions and second integrates this model in the resolution process. To this end, we introduce a new heuristic, called COTLEA, for COpula-based Transfer Learning Evolutionary Algorithm. COTLEA is a simple and fast transfer learning framework that incorporates a Copula model to learn the feature representation of a source problem and uses an evolutionary algorithm to make the transfer of knowledge. The empirical study of our proposal shows significant performance in terms of convergence speed compared to typical evolutionary approaches.

Multiobjective optimization problems require algorithms capable of efficiently approximating the Pareto optimal front while ensuring good convergence and diversity. In this paper, we introduce and analyze two approaches designed to refine the search process in the later stages of evolutionary multiobjective optimization algorithms. Our proposal takes an approximation of the Pareto optimal front for a multiobjective optimization problem. Then, it defines different subregions, reference points, and weight vectors, to better converge to the true Pareto optimal front. We propose two approaches: (1) defining subregions based on objective space partitioning and (2) dynamically adapting weight vectors distributions based on the front's geometry. These strategies allow for a more precise approximation of the Pareto optimal front while maintaining a well-distributed set of solutions.

Experimental results on the WFG benchmark suite demonstrate that our proposal improve the convergence, in terms of hypervolume, and diversity, in terms of spread, of the well-known evolutionary algorithm NSGA-III. This work highlights the potential of integrating the proposed mechanisms into evolutionary multiobjective optimization algorithms for biobjective optimizations problems. It is the start for future extensions to many-objective problems.

Surrogate-assisted constrained multi-objective evolutionary algorithms are popular for solving expensive constrained multi-objective optimization problems. They build computationally cheap surrogate models to replace time-consuming function evaluations. In this way, algorithms can obtain optimal solutions within a limited number of function evaluations. However, most surrogate models are built for approximating each expensive objective function and constraint. These models may accumulate approximation errors into a nonnegligible level, and their frequent updates bring tremendous computational overhead. In this paper, a large language model (LLM)-assisted constrained multi-objective evolutionary algorithm (LECMO) is proposed. LECMO adopts the two-stage evolutionary search strategy. In the first stage, an existing surrogate-assisted evolutionary algorithm ignoring constraints is applied to drive solutions across infeasible regions. In the second stage, an LLM-assisted constrained multi-objective evolutionary algorithm is proposed to locate the constrained Pareto front. Experimental results on well-known test suites demonstrate the superiority of LECMO over compared algorithms.

Using an archive to store nondominated solutions found during the search of a multi-objective evolutionary algorithm (MOEA) is a useful practice. However, as nondominated solutions of a multi-objective optimisation problem can be enormous or infinitely many, it is desirable to provide the decision-maker with only a small, representative portion of all the nondominated solutions in the archive, thus entailing a truncation operation. Then, an important issue is when to truncate the archive. This can be done once a new solution generated, a batch of new solutions generated, or even keeping all nondominated solutions generated and truncate it later. Intuitively, the last approach may lead to a better result since we have all the information in hand before performing the truncation. In this paper, we study this issue and investigate the effect of the timing of truncating the archive by using the criteria commonly used in MOEAs' population maintenance procedure. We show that, interestingly, truncating the archive once a new solution generated tends to be the best, whereas considering an unbounded archive is often the worst. Our results highlight the importance of developing effective subset selection techniques (rather than employing the population maintenance methods in MOEAs) when using a large archive¹.

In this work, we address multi-objective combinatorial optimization problems, which require managing the discrete nature of the search space while simultaneously optimizing the conflicting objective functions. Local search is widely recognized as a cornerstone in the development of advanced algorithms for discrete search spaces, while evolutionary paradigms such as decomposition, dominance-based methods, and indicator-based approaches are often employed to tackle the multi-objective nature of these problems. We consider a simple combination of iterated local search with the well-established MOEA/D approach — where single-objective subproblems are generated via objective aggregation. This approach is compared to a simple evolutionary algorithm and its superiority demonstrated on a broad range of challenging binary MNK-landscapes used as benchmarks.

The convergence and diversity of a population significantly influence the performance of evolutionary multi-objective optimization (EMO) algorithms. This paper introduces a novel quantitative metric for multi-objective optimization problems, termed spreadability, which serves as a guide for algorithm selection and performance evaluation of EMO algorithms. Spreadability is defined as the proportion of the decision space where a given solution remains mutually nondominated, calculated as the mathematical expectation of this proportion across all solutions. To support empirical analysis, we design several test problems with adjustable spreadability and conduct comprehensive experiments to evaluate the diversity-preserving capabilities of three classical EMO algorithms. The results indicate that MOEA/D-M2M with a diversity enhancement mechanism demonstrates superior performance. Furthermore, we propose survival and mortality rates for solutions based on spread-ability to intuitively demonstrate the impact of the enhancement mechanism on population diversity.

Multi-objective optimization algorithms aim to identify a set of non-dominated solutions that capture the complex and often conflicting trade-offs between objectives. In black-box settings, where the input-output relationship is usually analytically intractable, these algorithms face two major challenges: limited evaluation budgets, especially when objective evaluations are costly, and computational difficulties in proposing new candidates. While all non-dominated solutions hold equal mathematical value, the Decision-Maker is typically interested in only the most preferred trade-offs. This adds an additional challenge for preference-driven optimization: the cost of human interaction. To address these challenges, this paper proposes leveraging surrogate-assisted evolutionary multi-objective optimization methods, combined with advanced discretization techniques and strategic filtering of preferred solutions to mitigate the overall computational burden. After evaluating against similar methods in the literature, the experimental results suggest the method to be competitive in enhancing both the efficiency and precision of the decision-making process.

Addressing unwanted biases has become critical as Artificial Intelligence systems are increasingly integrated into various aspects of society. Bias in decision-making can lead to unfair outcomes, perpetuating social inequalities and discrimination. Causal graphs enable the identification of causal mechanisms that may contribute to biased outcomes. Evolutionary computation techniques are well known for exploring large, complex solution spaces and evolving approximate optimal solutions over successive generations. We propose a novel approach that combines causal structures with grammatical evolution to create directed acyclic graphs for modelling and evolving solutions using fairness and accuracy as fitness criteria. Our approach evolves causal graphs that balance model fairness and performance in single-objective and multi-objective settings. Results show that the multi-objective optimization improved fairness by 32 percent while reducing accuracy by only 2.85 percent compared to the single-objective case. This demonstrates that integrating causal mechanisms with evolutionary computation can effectively develop Artificial Intelligence systems that are both accurate and fair.

This paper introduces the optimization of time-variant placement of charging stations on a dynamic road network, with changing traffic conditions. We aggregated Uber Movement data from San Francisco into an hourly representation of a typical day, resulting in 24 snapshots of the network's traffic. The placement is optimized independently for each time interval by Evolutionary Algorithm, leading to distinct placements. that adapt to changing traffic conditions of each hour. Various network variables—length, speed, and travel time—are tested as heuristics, both as alternatives to optimization and for their effectiveness when combined with optimization. With enough charging stations, heuristic sampling yields near-optimal solutions, and combined with optimization, it slightly improves performance, with travel time outperforming the others.

State-of-the-art multi-objective optimization often assumes a known utility function, learns it interactively, or computes the full Pareto front—each requiring costly expert input. Real-world problems, however, involve implicit preferences that are hard to formalize. To reduce expert involvement, we propose an offline, interpretable utility learning method that uses expert knowledge, historical examples, and coarse information about the utility space to reduce sample requirements. We model uncertainty via a full Bayesian posterior and propagate it throughout the optimization process. Our method outperforms standard Gaussian processes and BOPE across four domains, showing strong performance even with biased samples, as encountered in the real-world, and limited expert input.

We present a novel Arithmetic Optimization Algorithm for solving a deadline-constrained many-objective workflow scheduling problem. Our approach incorporates an adaptive evolutionary state that dynamically balances exploration and exploitation within the search space. Additionally, we introduce an adaptive method for repairing infeasible solutions, further enhancing algorithm convergence and solution quality. An extensive experimental evaluation on workflows of real-world applications confirms the effectiveness of our approach.

The new generation of programmable networks should allow efficient bandwidth control and quality of service (QoS) management of different delay- and loss-sensitive services. To this end, we propose specially tailored evolutionary algorithms for solving routing problems in next-generation networks such as SDN, IoT, and 5/6G. In particular, we optimize network routing for three critical parameters: throughput, loss, and delay, which forms a multi-criteria optimization problem. We propose two evolutionary algorithms: NSGA-II and ISPEA2 to solve the problem and perform simulation tests for selected real and artificial network topologies of various sizes. The results obtained show that NSGA-II performs significantly better than ISPEA2.

This kind of algorithm composed of multiple operators, when solving different constrained multi-objective optimization problems (CMOPs), always has operators with good effects guiding the population to seek a better Pareto Front (PF). However, in the evolutionary process of such algorithms, there exist operators that have no effect but still generate offspring, thereby slowing down the convergence speed of the algorithm. To accelerate the convergence speed of the algorithm, a constrained multi-objective co-Evolutionary algorithm based on operator score and reward (SRCA) is presented in this paper, this SRCA algorithm has proposed an operator evaluation and operator reward mechanism which attempt to select operators that are beneficial to the convergence and diversity of the population for reproduction. The experimental results demonstrate that SRCA algorithm can effectively expedite the convergence speed and enhance the diversity of the population.

Existing decomposition-based constrained multi-objective evolutionary algorithms (CMOEAs) use fixed decomposition methods to partition the search space, which may limit their ability in solving some certain constrained multi-objective optimization problems (CMOPs). To address this issue, this paper introduces the concept of hyper-feasible solutions, which are extracted from feasible solutions and promising infeasible solutions. Based on these solutions, we propose a novel algorithm called HSWU, which adaptively partitions the search space and guides the search direction to enhance the efficiency of solution searching. Experimental results on three benchmark test suites demonstrate that HSWU outperforms five state-of-the-art CMOEAs in terms of performance.

Many-objective optimization problems (MaOPs) present unique challenges, particularly in achieving both convergence and diversity across high-dimensional Pareto fronts. These challenges become even more pronounced when the Pareto fronts are irregular or disconnected. Traditional methods that rely on uniformly distributed reference points often struggle to perform well under such conditions. This paper introduces a new algorithm called Model Adaptive Reference Points NSGA-III (MARP-NSGA-III) to address these issues. The algorithm uses Gaussian Processes (GPs) to generate reference points based on the dynamic distribution of solutions. By incorporating NSGA-III, MARP-NSGA-III models the evolving Pareto front and adaptively allocates reference points, ensuring they align more closely with the front's structure. This study provides a detailed framework explaining the core components of the method, including how the GP model is constructed, how areas of interest are estimated, and how reference points are generated. MARP-NSGA-III represents a significant step forward in solving 11 MaOPs, offering a flexible and adaptive approach. Our experiments show that, for benchmark problems, our proposed algorithm (MARP-NSGAIII) performs better than other many-objective competing algorithms. Gaussian Process-Driven Adaptive Reference Point Generation for Many-Objective Optimization.

Many real-world problems involve optimizing multiple conflicting objectives simultaneously, often by a series of decisions. Multi-objective reinforcement learning addresses these challenges by training agents to learn policies that balance multiple reward signals from the environment.

In recent years, the community has increasingly paid attention to these problems. However, the necessity for more effective solutions persists. In this context, we propose a methodology for approximating optimal policies using evolutionary algorithms.

Our approach enhances the search process by leveraging uncertainty quantification in the hypervolume computation of candidate solutions. We adapt the classical evolutionary process, changing the evaluation of agents to prioritize those contributing more to the hypervolume and using uncertainty quantification as a guiding metric.

Further, we analyzed four evolutionary algorithms under different uncertainty measures and tested them in diverse multi-objective reinforcement learning environments with up to four objectives. The work revealed that the expected improvement was the most effective uncertainty quantification for guiding the search across all algorithms.

Sunshades integrated into building facade design critically influence the building's thermal conditions, natural lighting, energy usage, and occupant comfort. However, heuristic designs often neglect the multi-faceted trade-offs among these objectives. This study compares two multi-objective evolutionary algorithms, NSGA-II and MO-CMA-ES, in optimizing five performance metrics: thermal comfort, Useful Daylight Illuminance (UDI), energy consumption, outside view obstruction, and cost. We integrate annual energy and daylight simulations, incorporating real-world weather data from Cape Town, South Africa, and Nairobi, Kenya. Results indicate that both MO-EAs generate Pareto-optimal sunshades exceeding the performance of five traditional designs for all metrics. In cooler climates, the best solutions featured upward-angled fins to admit beneficial solar gain, while warmer climates favored configurations blocking high-angle sunlight. These findings underscore the importance of climate-specific optimization for identifying cost-effective, occupant-friendly building designs to balance daylight management and energy efficiency.

The Travelling Thief Problem (TTP) is a multi-objective, combinatorial, NP-hard optimisation problem with constraints and interwoven objectives resembling real-world problems. This paper proposes a Cluster-Based Region Selection Genetic Algorithm (CRSGA) utilising clusterisation of individuals coupled with a 2-layer selection operator: (1) tournament density-based selection that favours regions with sparsely distributed individuals, for which (2) individuals from those clusters are selected into pairs for reproduction. CRSGA focuses on balancing the exploration and exploitation of clusters, improving the quality of the results. The performance of the CRSGA is investigated on 24 benchmark instances with varying complexity. CRSGA outperforms 5 state-of-the-art methods.

This paper explores the multi-objective optimization of the generalized bin packing problem, which involves allocating both compulsory and non-compulsory items into a set of bins. The items have attributes such as weight, width, height, and due date, while the bins have characteristics including capacity and cost. The primary objective is to minimize cost, typically by reducing the number of bins used. However, real-world scenarios often involve multiple, competing objectives, such as meeting item due dates and achieving load balancing. To address these complexities, the paper proposes a multi-objective evolutionary model to solve the generalized bin packing problem. This approach optimizes multiple objectives, such as minimizing cost and reducing item lateness, allowing decisionmakers to balance trade-offs between solutions represented as a Pareto front. The model was tested on one- and two-dimensional problem instances, demonstrating its ability to minimize the objectives while offering a range of conflicting solutions in certain cases. The results also identified some limitations of the algorithm, including premature convergence and insufficient solution diversity. The paper discusses potential reasons for these issues and suggests directions for future research to improve the algorithm's performance, ensuring better handling of multiple objectives and enhancing solution variety.

Multi-objective reinforcement learning (MORL) addresses the challenge of simultaneously optimizing multiple, often conflicting, rewards, moving beyond the single-reward focus of conventional reinforcement learning (RL). This approach is essential for applications where agents must balance trade-offs between diverse goals, such as speed, energy efficiency, or stability, as a series of sequential decisions.

This paper investigates the applicability and limitations of multi-objective evolutionary algorithms (MOEAs) in solving complex MORL problems. We assess whether these algorithms can effectively address the unique challenges posed by MORL and how MORL instances can serve as benchmarks to evaluate and improve MOEA performance. In particular, we propose a framework to characterize the features influencing MORL instance complexity, select representative MORL problems from the literature, and benchmark a suite of MOEAs alongside single-objective EAs using scalarized MORL formulations. Additionally, we evaluate the utility of existing multi-objective quality indicators in MORL scenarios, such as hypervolume conducting a comparison of the algorithms supported by statistical analysis. Our findings provide insights into the interplay between MORL problem characteristics and algorithmic effectiveness, highlighting opportunities for advancing both MORL research and the design of evolutionary algorithms.

This paper addresses the Multi-objective Traveling Salesman Problem with Profits and Passengers (MoTSPPP), an extension of the Traveling Salesman Problem with Profits, to model ridesharing systems in multi-objective contexts. This problem, which considers three objective functions (minimizing travel cost, minimizing travel time, and maximizing the bonuses collected), has not been studied before. We implement a mathematical formulation to compute Pareto-optimal solutions, two non-evolutionary heuristics, and two evolutionary algorithms (NSGA-II and MOEA/D). Non-evolutionary heuristics solve the salesman route, bonus collection, and passenger assignments sequentially, whereas NSGA-II and MOEA/D combine these three decision levels via genetic operators. Experiments on 84 instances with up to 200 vertices assess the difficulty of optimally solving the problem and the performance of the algorithms.

Counterfactual explanations effectively interpret model decisions by identifying input modifications that lead to different outputs. However, generating realistic and actionable counterfactuals is challenging due to the lack of methodologies that effectively capture complex feature relationships and user-imposed constraints. This study introduces GraCo, a novel counterfactual generation (CG) method driven by Grammatical Evolution. GraCo automatically incorporates feature-domain knowledge and user preferences to generate plausible and actionable counterfactuals. We evaluate its effectiveness through empirical validation against state-of-the-art methods across multiple datasets. We propose a goodness metric for CG that accounts for class probability shifts and the differences between the counterfactual and the original input. GraCo achieves an average goodness score of 0.6231 across four datasets, outperforming all the compared approaches.

Dynamic constrained multiobjective optimization problems (DC-MOPs) are multiobjective optimization problems in which both the objectives and constraints can change over time. Prediction-based dynamic constrained multiobjective evolutionary algorithms (DCMOEAs) have demonstrated superior performance by predicting initial population that is hopefully near the Pareto-optimal set (PS) in each new environment. However, the simultaneous changes in both the objectives and constraints make it difficult for these DCMOEAs to predict an initial population actually near the PS. Through observation, it has been found that the PS of DCMOPs typically lies along the path converging to the unconstrained PS (UPS). With this in mind, this paper introduces a novel DCMOEA based on Convergence Path Interpolation (CPI-DCMOEA). Specifically, when the environment changes, CPI-DCMOEA employs an autoencoder to predict the estimated UPS in the new environment. Then, CPI-DCMOEA uses Optimal Transport (OT) to approximate the convergence path toward the estimated UPS, which is defined as the trajectory from the random population to this estimated UPS. Finally, CPI-DCMOEA generates new solutions in batches by interpolating along this convergence path, with the interpolation parameter adaptively adjusted, ultimately producing a high-quality population in promising regions. Experimental results on DCF test suite show that the proposed CPI-DCMOEA has a significant advantage.

In this paper, we investigate a Weight-Guided Random Bit Climbing algorithm (wgRBC) for tackling multi and many-objective binary epistactic optimization problems. The algorithm integrates scalarizing functions with a random bit climber and leverages predefined weights to explore diverse search directions while maintaining a well-distributed reference population. By performing weight-guided hill climbing, wgRBC combines global exploration in the direction of the weights with local search through hill climbing. This fusion of global and local search enables the algorithm to explore widely distributed yet uniformly spaced solutions in objective space. The hill climbing process is analyzed, including the roles of weights in reaching local optimum. To evaluate the effectiveness of wgRBC, extensive experiments were conducted on MNK-landscapes with varying levels of epistasis and objectives, comparing wgRBC against established methods such as dRBC, NSGA-III, and MOEA/D. The results show the superiority of wgRBC in achieving higher hypervolume (HV) across almost all objectives, particularly for problems with moderate to high epistasis (K > 1). Although wgRBC is simpler than decomposition-based algorithms, it consistently outperforms them in most scenarios, highlighting its potential for scalable optimization in challenging binary landscapes.

Drones are increasingly adopted in logistics due to their flexibility and efficiency, presenting novel solutions for complex service systems. This study develops a bi-objective optimization model for medical sampling service systems, where technicians and drones independently collect samples from patient locations. The model addresses critical challenges by simultaneously minimizing system completion time and patient test kit waiting duration, while incorporating realistic constraints, such as technicians' dynamic velocity variations reflecting traffic conditions and drone energy consumption dependent on load. A hybrid algorithm combining Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Tabu Search is proposed, ensuring elite solution preservation and genetic diversity. Experimental validation demonstrates better performance compared to NSGA-II, Tabu Search, and Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) across hypervolume and non-dominated solution metrics, highlighting the approach's effectiveness in optimizing medical sampling logistics with disease outbreaks serving as a compelling use case.

In this poster, we showcase a new algorithm for approximating the Pareto set of two-objective (unconstrained) optimization problems based on the idea of continuation. The algorithm tries to move "along" the Pareto set from one single-objective optimum to the other and back via a single-objective reformulation of the two-objective problem and the well-known CMA-ES as single-objective solver. The introduced algorithm BOG-CMA-ES (standing for bi-objective gradient based CMA-ES) is visually analyzed on simple convex-quadratic objective functions and extensively benchmarked on the bbob-biobj test suite of the COCO platform, including comparisons with current state-of-the-art algorithms.

The real-world constrained multi-objective optimization problems (CMOPs) pose significant challenges for evolutionary multi-objective optimization (EMO) algorithms due to complex constraints. This paper explores the impact of reformulation strategies on EMO algorithms, focusing on equality constraint substitution and cumulative variable introduction. Experiments on 21 real-world CMOPs and their reformulated versions using NSGA-II, CCMO, and PPS-MOEA/D show that reformulation enhances feasibility rates and solution quality, particularly for low-feasibility and high-dimensional problems. Reformulating problems simplifies the search space, allowing algorithms like NSGA-II and CCMO to achieve significantly higher feasibility rates. These results underscore the effectiveness of problem reformulation in alleviating the difficulty of solving real-world CMOPs and provide valuable insights for improving EMO algorithm performance on complex problems.

Effective visualisation techniques for Pareto front (PF) approximations are crucial in understanding and developing new methodologies for many-objective optimisation (MaOP) analysis. However, the state-of-the-art visualisation methods in the literature fail to reveal the regional diversity of PF properties in a high-dimensional objective space. A new method named Cardinality Distribution (CD) is proposed in this paper, which reveals PF approximations by analysing the cardinality distribution of PF solutions in the objective space. The PF solutions are grouped in a sequence of rings (in three-dimensional space, 3D) or hyper-rings (in higher-dimensional space, mD) in the objective space, where cardinalities are calculated and compared to what they would be if the PF solutions thoroughly and evenly covered the space. CD may detect fully or partially covered or degenerated PF approximations more effectively than state-of-the-art methods. MaF benchmark problems are used to demonstrate the effectiveness of the proposed method.

Hot rolling is an important production process connecting continuous casting and cold rolling in the iron and steel industry. Considering both the actual production process and rolling management regulations, a self-adaptive multi-objective differential evolution algorithm based on the least recent use algorithm Least Recently Used-based Self-adaptive Multi-objective Differential Evolution Algorithm(LRU-SaMODE) has been proposed to solve the problem. The experimental results show that LRU-SaMODE has good performance compared to traditional differential evolution algorithms in most multi-objective benchmark functions and the multi-objective model for hot rolling production rescheduling proposed in this paper, which is verified using actual production data from iron and steel enterprises. It also has significant improvements in convergence and diversity, especially in the hot rolling production rescheduling problem with actual production as the background, which can achieve satisfactory scheduling results, and provide strong decision support for decision-makers.

Multi-objective optimization (MOO) aims to optimize multiple conflicting objectives simultaneously. Gradient-free methods are widely used in MOO problems. However, in some scenarios, such as multitask learning, gradient-free algorithms are not suitable due to the high dimensionality of the solution space. Thus, many gradient-based multi-objective optimization methods have been proposed to find the Pareto front effeciently. However, these methods suffer from the difficulty of escaping local optima. In this paper, we propose a multiple gradient descent algorithm based on decomposition (MGDA/D), which can easily escape from the local optima and find a set of good and diverse Pareto solutions. MGDA/D first decomposes a multi-objective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously by gradient descent. When the solution of a subproblem falls into local optima, MGDA/D uses information from its neighboring subproblems to update the solution to escape. Experimental results confirm that MGDA/D outperforms the state-of-the-art algorithms on both benchmark problems and multi-task learning applications.

This paper proposes a customized algorithm named MOEA/D-AEPM for direction finding array (DFA) design. The aim of DFA design is to search a set of optimal spacing between array elements that minimizes the direction finding error (DFE), the correlation peak ratio (CPR), and the active S-parameter, resulting in an expensive multiobjective optimization problem (EMOP). Different from traditional EMOPs with expensive objectives, an active element pattern (AEP) from electromagnetic simulation is added with Gaussian noise to simulate the received signals. To avoid the influence of noise level on DFE and CPR, an AEP surrogate model (AEPM) is built to reduce cost. The experimental results demonstrate that MOEA/D-AEPM achieved reasonably good results within a limited cost, together with effective AEPM prediction, which can also provide a deep insight into radiation knowledge for antenna experts.

Constrained multimodal multiobjective problems (CMMOPs) are challenging due to multiple objectives, modalities, and constraints. State-of-the-art algorithms often use the constrained dominance principle (CDP) and multimodal mechanisms to balance feasibility and diversity. However, relying solely on CDP may overemphasize feasible solutions, neglect infeasible ones, and affect diversity and global search performance. To address this, we propose a simulated annealing-based evolutionary algorithm, called CMMOSA. It integrates the constrained dominance principle based on simulated annealing (CDP-SA) with an archival mechanism. In the high-temperature stage, the algorithm accepts larger constraint-violating solutions, preventing premature convergence to local optima while maintaining feasible solutions in the archive. As the temperature decreases, the algorithm converges towards feasible solutions, exploring multiple constrained Pareto optimal solutions using global information from the archive. Experimental results show that CM-MOSA enhances global search capability in CMMOPs, overcomes local search limitations, and significantly improves solution quality and optimization efficiency.

For constrained multi-objective optimization problems (CMOPs), this paper introduces a multi-environmental selection strategy guided by reinforcement learning. The proposed method dynamically assesses the feasibility, convergence, and diversity of the population with respect to both decision and objective space distributions. It incorporates three interaction-force-driven selection mechanisms and adaptively identifies optimal strategies through reinforcement learning. Experimental outcomes indicate that this approach outperforms existing algorithms in managing complex constraints, handling discontinuous feasible regions, and addressing circuit testing challenges, thereby confirming its efficacy and robustness.

Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is a highly effective optimization technique. A primary challenge when applying CMA-ES in high dimensionality is sampling from a multivariate normal distribution with an arbitrary covariance matrix, which involves its decomposition. The cubic complexity of this process is the main obstacle to applying CMA-ES in high-dimensional spaces.

We introduce a version of CMA-ES that uses no covariance matrix at all. In the proposed matrix-free CMA-ES, an archive stores the vectors of differences between individuals and the midpoint, normalized by the step size. New individuals are generated as the weighted combinations of the vectors from the archive. The probability distribution of individuals generated by the proposed method is identical to that of the standard CMA-ES.

Experimental results show that reducing the archive size to store only a fixed number of the most recent populations is sufficient, without compromising optimization efficiency. The matrix-free and matrix-based CMA-ES achieve comparable results on the quadratic function when the step-size adaptation is turned off. When coupled with the step-size adaptation method, the matrix-free CMA-ES yields comparable results to those of plain CMA-ES, according to the results obtained for the CEC'2017 benchmark suite.

The field of numerical optimization has recently seen a surge in the development of "novel" metaheuristic algorithms, inspired by metaphors derived from natural or human-made processes, which have been widely criticized for obscuring meaningful innovations and failing to distinguish themselves from existing approaches. Aiming to address these concerns, we investigate the applicability of statistical tests for comparing algorithms based on their search behavior. We utilize the cross-match statistical test to compare multivariate distributions and assess the solutions produced by 114 algorithms from the MEALPY library. These findings are incorporated into an empirical analysis aiming to identify algorithms with similar search behaviors.

This paper presents Variable Interaction Graph Particle Swarm Optimization (VIGPSO), an adaptation to Particle Swarm Optimization (PSO) that dynamically learns and exploits variable interactions during the optimization process. PSO is widely used for real-valued optimization problems but faces challenges in high-dimensional search spaces. While Variable Interaction Graphs (VIGs) have proven effective for optimization algorithms operating with known problem structure, their application to black-box optimization remains limited. VIGPSO learns how variables influence each other by analyzing how particles move through the search space, and uses these learned relationships to guide future particle movements. VIGPSO was evaluated against standard PSO on eight benchmark functions (three separable, two partially separable, and three non-separable) across 10, 30, 50 and 1000 dimensions. VIGPSO achieved statistically significant improvements (p < 0.05) over the standard PSO algorithm in 28 out of 32 test configurations, with particularly strong performance extending to the 1000-dimensional case. The algorithm showed increasing effectiveness with dimensionality, though at the cost of higher variance in some test cases. These results suggest that dynamic VIG learning can bridge the gap between black-box and gray-box optimization effectively in PSO, particularly for high-dimensional problems.

When tackling expensive constrained optimization problems (ECOPs), existing surrogate-assisted evolutionary algorithms (SAEAs) often overlook the differences in evaluation time between constraints and the objective. However, real-world optimization problems exhibit significant differences in evaluation time, termed heterogeneous expensive constrained optimization problems (HE-COPs). To explore the impact of this heterogeneity, we propose an adaptive two-stage SAEA based on differential evolution (ATS-SADE) to tackle scenarios where inequality constraints are relatively inexpensive to evaluate. In the proposed algorithm, by leveraging ample constraint evaluations, an adaptive surrogate-assisted repair strategy is developed to guide the population toward the feasible region in the first stage. Moreover, an adaptive two-stage switch strategy is introduced to transition to the second stage under opportune conditions, thereby adapting to different problems. Experimental results on benchmark problems from CEC 2010 and CEC 2017 show that ATS-SADE outperforms four state-of-the-art algorithms.

Automated algorithm performance prediction in numerical blackbox optimization often relies on problem characterizations, such as exploratory landscape analysis features. These features are typically used as inputs to machine learning models and are represented in a tabular format. However, such approaches often overlook algorithm configurations, a key factor influencing performance. The relationships between algorithm operators, parameters, problem characteristics, and performance outcomes form a complex structure best represented as a graph.

This work explores the use of heterogeneous graph data structures and graph neural networks to predict the performance of optimization algorithms by capturing the complex dependencies between problems, algorithm configurations, and performance outcomes. We focus on two modular frameworks, modCMA-ES and modDE, which decompose two widely used derivative-free optimization algorithms: the covariance matrix adaptation evolution strategy (CMA-ES) and differential evolution (DE). We evaluate 324 modCMA-ES and 576 modDE variants on 24 BBOB problems across six runtime budgets and two problem dimensions.

Achieving up to 36.6% improvement in MSE over traditional tabular-based methods, this work highlights the potential of geometric learning in black-box optimization.

To improve Covariance matrix adaptation evolution strategy (CMA-ES), which needs tuning of hyperparameters for optimizing multimodal and noisy problems, learning rate adaptation CMA-ES (LRA-CMA-ES) was proposed. This method adapts the learning rates based on the signal-to-noise ratio (SNR) of the update directions. On several high-dimensional optimization problems, part of the design variable affects the evaluation value and other variables are redundant. This property is called low effective dimensionality (LED). Although LRA-CMA-ES shows robust performance on multimodal and noisy problems, its performance is deteriorated by LED. To improve the performance on functions with LED, this paper introduces the countermeasures for LED to LRA-CMA-ES. The proposed method, LRA-CMA-ES-LED, estimates the element-wise SNR on the direction along the eigenvector of the covariance matrix to compute the effectiveness of each direction. We reduce the influence of redundant directions on the learning rate adaptation mechanism based on the estimated effectiveness. In the numerical experiments, we used benchmark functions in tens of dimensions containing 10 effective directions, which shows the performance improvement on multimodal and noisy problems with LED.

Noisy black-box continuous optimization using evolution strategies (ES) involves a trade-off between computational cost and estimation precision. While several approaches have been proposed to address this issue, most focus on optimizing the expected objective value, leaving Value-at-Risk (VaR) optimization largely unexplored. To address the trade-off problem in black-box VaR optimization, we propose an individual adaptive reevaluation mechanism that adjusts the number of reevaluations of the noisy objective function for each solution to estimate the VaR. This mechanism dynamically adapts the number of reevaluations for each solution by monitoring ranking deviations using bootstrapping. The proposed method is integrated into CMA-ES, named IR-CMA-ES, and evaluated against two baselines: CMA-ES with Monte Carlo VaR estimation using fixed reevaluation, and UH-CMA-ES modified for VaR optimization. Experiments under various noise settings demonstrate the competitive performance of IR-CMA-ES.

In this paper, we propose some improvements to the CMA-ES-PDM algorithm for solving mixed-integer black-box optimization problems. First, the discrete distribution model for the integer variables is fitted to a normal distribution. This fitted distribution is then further smoothed using an initial normal distribution that is quite similar to the uniform distribution over the search domain of integer variables. Second, when the upper bound of the probability within the model is reached for certain integer variables, the model is used exclusively for sampling the integer components of the candidate solutions. Additionally, the marginal probability of the model is selected randomly from a predefined set. The numerical experiments on the MI-BBO benchmark problems demonstrate that the proposed improvements enable CMA-ES-PDM to achieve better performance on some benchmark functions.

Current Quality Diversity (QD) algorithms rely on a loop of repeatedly generating and evaluating solutions to obtain a set of diverse and high-quality solutions. To apply these algorithms to domains with expensive evaluations, prior work has leveraged Bayesian Optimization with surrogate models, improving the sample efficiency at the cost of reduced computation-time efficiency. In this paper, we propose a novel method combining Monte Carlo simulation with Online Sparse Variational Gaussian Processes to speed up Bayesian Optimization for Quality Diversity. We evaluate the proposed method, called Monte-Carlo Bayesian Optimization of Elites (MCBO-Elites), on standard optimization benchmarks, demonstrating improvements in both sample-efficiency compared to model-free QD approaches, and computation-time efficiency compared to model-based QD approaches. Furthermore, we propose new metrics to quantify the computation-time efficiency and predict how expensive evaluations need to be for our approach to be preferred.

Cooperative Co-evolution, by decomposing the problem space, is a key approach for large-scale global optimization. While it outperforms non-decomposition algorithms when subspaces are disjoint, overlapping variables complicate decomposition and degrade performance. To address this, we propose a novel two-phase cooperative co-evolution framework for complex overlapping problems, incorporating an effective method for decomposing overlapping problems based on their mathematical properties. We also introduce a customizable benchmark to extend existing ones for experimentation. Extensive experiments show that our framework significantly outperforms existing algorithms, revealing the characteristics of overlapping problems and the strengths of cooperative co-evolution and non-decomposition algorithms. The work is open-source at: https://github.com/GMC-DRL/HCC.

In several real-world applications, each element of the solution incurs a cost, such as manufacturing or computational costs. Considering the limitation of the total cost, the desired solution contains some parts tuned in the high-cost space and other parts selected from the low-cost set. We term these optimization problems as the search space selection problem, which has a constraint on the cost computed by which subspace the corresponding part of the solution belongs. This paper considers the case where each dimension consists of the low-cost integers and the high-cost complementary set in the continuous space. Then, we propose an optimization method for the search space selection problem by extending a mixed-integer optimization method, (1+1)-CMA-ES with margin, which incorporates the margin correction to prevent premature convergence in the discrete space. We first address the stagnation that occurs when directly applying existing constraint handling in mixed-integer optimization. The proposed method also considers the additional variables for search space selection and applies the margin correction to both the dimensions for search space selection and the selected dimensions as low-cost integer space. Numerical simulations show that the proposed method could find better solutions than comparative methods on the search space selection problem.

This paper presents a genetic algorithm (GA) with novel crossover and mutation operators to solve the three-dimensional bin set selection problem (3D-BSSP). The goal is to find the optimal bin set from standard-sized bins to minimize packaging and shipping costs for an e-commerce company. We utilize minimal feasible bin sets (MFBS) to ensure, that each order can be packed. Evaluations with various item dimension distributions show that the GA achieves near-optimal solutions faster than a mixed-integer programming model.

In brain-computer interface (BCI) technologies, neuronal communication occurs via electrical impulses, manifesting itself as undulating patterns in electroencephalography (EEG) recordings. This work investigates the cerebral activity associated with the opening and closing of the eyes, with the aim of identifying the EEG channels that are most crucial to analyzing this particular activity. Six unique characteristics were derived from the EEG data of 64 channels. The genetic algorithm has been applied to determine the optimal set of channels that maintain a high classification accuracy in the detection of eye states. After optimizing the channels, a carefully selected subset was utilized for the final assessment using six classifiers. The comparative study revealed that multilayer perception (MLP) reached a maximum accuracy of 93.12%, with channels refined by the suggested method. This technique facilitates maintaining an ideal number of channels, thus minimizing costs associated with preprocessing large data sets for BCI studies.

In Production Scheduling (PS), the Flexible Job Shop Problem with Worker Flexibility (FJSSP-W) demands to determine a (near) optimal sequence of jobs while assigning their corresponding operations to admissible machine-worker combinations. The paper proposes a Genetic Algorithm (GA) variant designed for the FJSSP-W. It maintains a population of feasible candidate solutions throughout the search process and derives its parameter configuration from problem-specific attributes, e.g., the flexibility of the production environment, and the variety of the processing times. Further, the GA adapts its mutation and recombination parameters and employs a restarting scheme with population growth to avoid premature convergence. Experimental results are compared to state-of-the-art FJSSP-W solvers. The results demonstrate the GA's scaling potential in terms of problem complexity. The GA keeps its performance, while other approaches decline when exposed to problems of higher complexity. The GA appears to be beneficial for problems with a high amount of assignment options per operation and low variety in processing times. The results confirm the suitability of problem-specific parameter settings and the restarting scheme for a wide range of PS problems, and FJSSP-W, particularly.

Large Language Models (LLMs) have gained recognition as valuable assets across virtually all industries, yet they rely heavily on manually crafted input prompts. In real-world applications, the dependence on specialized staff, skilled prompt engineering, and domain-specific knowledge often leads to suboptimal performance and increased costs. This paper investigates the use of Genetic Algorithms (GAs) to autonomously generate, evolve, and judge LLM prompts. Specifically, we customized a standard GA implementation to handle textual individuals, which are manipulated by LLM-guided genetic operators that iteratively create and enhance candidate prompts. Additionally, LLMs are employed to assess the correctness of outputs, forming the basis of our GA's fitness function. Our findings suggest that GA-driven prompt engineering can consistently produce solutions that are superior in both accuracy and efficiency compared to those acquired by prompt engineers who possess technical skills but lack domain-specific knowledge and a full understanding of vendor-specific prompting idiosyncrasies. This conclusion is supported by experimental results obtained from four public datasets and three modern LLMs developed by OpenAI, Meta, and Mistral AI. Ultimately, this study highlights the viability and potential of fully automated optimization tools in minimizing human effort in writing high-performance prompts.

The Colored Traveling Salesman Problem (CTSP) is a generalization of the Multiple Traveling Salesman Problem (MTSP), wherein multiple salesmen are allowed to visit cities with specific restrictions. The CTSP introduces numerous constraints, making it complex and computationally challenging for conventional optimization techniques. This work advances the field by introducing four Genetic Algorithms (GAs) designed to solve CTSP efficiently: a basic GA, GA with greedy initialization (GAG), GA enhanced by a 2-opt local search, and GAG also enhanced by 2-opt. These algorithms employ tournament selection, city crossover, and city mutation techniques. The performance of these approaches is evaluated on 20 small- and medium-scale CTSP instances and compared with existing GAs for CTSP. The results show that integrating the 2-opt algorithm significantly enhances the balance between exploration and exploitation in GAs, improving solution accuracy. Among them, GA with 2-opt is particularly effective, optimizing both the solution quality and computational efficiency.

The Flexible Job Shop Scheduling Problem (FJSSP) is a complex combinatorial optimization problem with applications in manufacturing and cloud computing. Designing effective dispatching rules manually is time-consuming and requires expertise. Genetic Programming (GP) can evolve rules automatically but lacks mechanisms to prioritize important features. This paper proposes GPGA, a hybrid approach combining GP with a Genetic Algorithm (GA) to optimize feature weights and enhance rule quality. Leaf nodes are augmented with weight parameters, which GA evolves to minimize a scheduling objective. Weight refinement is applied to high quality rules every ten GP generations. Experiments on ten benchmark instances show that GPGA significantly reduces total weighted tardiness, outperforms a gradient-based GP method (GPGD) in two cases, lowers computational time in five instances, matches GPGD in test-time efficiency, and converges faster in training. These results highlight the benefits of integrating GA into GP for automated scheduling.

Genetic algorithm is a well-established optimization approach especially for black-box optimization systems. However, traditional genetic algorithms have been known to suffer from premature convergence to suboptimal regions and inability to escape local optima. This is particularly applicable for systems with many local optima. Genetic operators designed to tackle this issue by increasing population diversity are not always optimal for a wide variety of applications. We propose an adaptive multi-restart heuristic approach that encourages exploration of the search space as needed to improve accuracy and robustness of existing genetic algorithms. The decision to continue exploration for global optima or to converge to an already found optimal region is guided by statistical evidence via clustering of the existing best solutions from parallel islands. Empirical results demonstrate that our proposed adaptive exploration strategy boosts the performance of traditional genetic algorithms by enabling to escape local optima with higher accuracy and improved robustness.

Deep learning-based face verification systems are typically vulnerable to adversarial attacks, i.e., unnoticeable perturbations of input images making neural network models misrecognize images of the same person. Generating adversarial attacks to evaluate the robustness of these systems is crucial for their reliable deployment. However, most effective attack methods focus on classification tasks and operate in the white-box setting, where attackers can access the gradient information and the internal architecture of victim models. Such unrealistic scenarios overestimate the adversarial risk. We investigate the potential of crafting adversarial perturbations in the black-box setting, where attackers can observe only input images and output responses of victim models. We employ the genetic algorithm (GA) to search for adversarial patches that can camouflage well into facial images. The search involves two conflicting objectives: attack performance and reconstruction quality. We consider four GA variants: a GA optimizing the combined fitness function of the two objectives, a GA that favors well-blended adversarial patches, a GA that focuses on attack performance, and a multi-objective GA that optimizes both objectives separately and simultaneously. Our methods demonstrate strong performance in attacking face verification systems under the realistic black-box setting and generate more natural-looking patches compared to baseline approaches.

Initialization profoundly affects evolutionary algorithm (EA) efficacy by dictating search trajectories and convergence. This study introduces a hybrid initialization strategy combining empty-space search algorithm (ESA) and opposition-based learning (OBL). OBL initially generates a diverse population, subsequently augmented by ESA, which identifies under-explored regions. This synergy enhances population diversity, accelerates convergence, and improves EA performance on complex, high-dimensional optimization problems. Benchmark results demonstrate the proposed method's superiority in solution quality and convergence speed compared to conventional initialization techniques.

Deep Optimization (DO) is a recently proposed metaheuristic that uses deep neural networks for optimization. It shows promise solving various Combinatorial Optimization (CO) problems; however, it only operates on binary data, requiring problems to be transformed using Quadratic Unconstrained Binary Optimization (QUBO). The study explores the use of DO for the Single-Stage Job Scheduling Problems (SSJSP), a constrained CO problem. As SSJSP does not naturally fit QUBO, these problems require a workaround to use the number partitioning problem as part of the transformation process and introduce binary and Lagrangian penalty methods to integrate the constraints as part of DO. Performance testing across various parameter settings using generated datasets with controlled slack demonstrates that the method works well and DO with penalty integration performs satisfactorily on all datasets. Both penalty integration methods are found to be effective in guiding DO toward feasible and optimized solutions, however their relative effectiveness varies depending on the specific scenario.

This paper explores how a state-of-the-art hybrid metaheuristic for Curriculum-based Course Timetabling, composed of several algorithmic building blocks, can be deconstructed and reconfigured to produce a better algorithm. In particular, an Iterated Local Search strategy is proposed that allows reordering, chaining and looping together the building blocks, and to configure both the global and local search components. This then gives irace, an automatic configurator, the flexibility to explore configurations instantiating different hybrid metaheuristic configurations that outperform the original method. Since using such a configurator can be seen as a black-box process, we provide a comprehensive analysis that determines which parameters are decisive in obtaining the best configurations, finds relevant associations, and analyses the distribution of crucial parameters. In particular, we find that the best configurations discard the simulated annealing component of the original algorithm, as well as some neighborhood operators. The range of necessary algorithmic mechanisms to achieve the new state-of-the-art performance can therefore be reduced.

We investigate two representation alternatives for the controllers of teams of cyber agents. We combine these controller representations with different evolutionary algorithms, one of which introduces a novel LLM-supported mutation operator. Using a cyber security scenario, we evaluate agent learning when one side is trained to compete against a side that does not evolve and when two sides coevolve with each other. This allows us to quantify the relative merits and tradeoffs of representation and algorithm combinations in terms of team performance. The scenario also allows us to compare the performance impact and dynamics of coevolution versus evolution under different combinations. Across the algorithms and representations, we observe that coevolution reduces the performance highs and lows of both sides while it induces fluctuations on both sides. In contrast, when only one-side is optimized, performance peaks are higher and is more sustained than when both sides are optimized with coevolution.

Evolutionary algorithms to solve multi-modal and multi-objective optimization problems do not follow any specific order of convergence to different optimal solutions. However, there exist certain problems, in which a hierarchical discovery of multiple critical solutions is must to constitute the desired set of solutions. A recently introduced innovation path (IP) problem is one such problem. In solving such problems, point-based algorithms, which find one targeted solution in a single application, becomes relevant. In this paper, we address this important aspect of convergence behavior of an evolutionary multi-objective optimization (EMO) algorithm visa-vis a point-based algorithm. The challenges of both approaches are discussed with examples. Results on a number of problems show that despite the apparent advantage of a point-based approach for finding hierarchical solutions one by one, the proposed population-based EMO approach enables a flexible and global search for finding multiple IP solutions in a single run.

Artificial Intelligence has recently made rapid advancements, blurring the boundaries of intelligence between humans and machines. Its characteristic of generating different answers to the same question often evokes the thought process of humans. This study explores how AI-generated code, with minimal human intervention, can improve performance. There are over 100 algorithms capable of solving an NP-hard problem, the traveling salesperson problem, and it is difficult for one person to know all of them. Therefore, it is nearly impossible for a human to manually combine the advantages of various algorithms into a hybrid code. However, by leveraging AI, even someone who has no knowledge of the algorithms can generate a hybrid code that combines the strengths of different algorithms. In this experiment, AI-generated codes based on multiple algorithms are applied to genetic algorithms. The performance of hybrid codes, after undergoing crossover and mutation, was evaluated. The results showed that the performance of the AI-generated hybrid code surpassed that of the best-performing single algorithm code. This study demonstrates that AI can go beyond the mere application of existing algorithms by autonomously generating code and combining different algorithms to implement hybrid optimization techniques.

Effective recombination operators utilizing interdependence of genes ensure that specific arrangements or combinations of genes are preserved, allowing offspring to inherit beneficial traits from both parents without disrupting important gene interactions. However, such operators are easiest to implement for fixed-length genetic representations such as vectors of genes. In this work, we show that for some problems with variable-length representations, it is possible to design an algorithm that employs the GOM (Gene-pool Optimal Mixing) operator without the need to learn dependencies between specific genes. Instead, our approach - Compatible Substitutions Optimization (CoSO) - leverages expert-driven models of compatible substitutions that take advantage of the characteristics of the representation. Our experiments indicate that the proposed method performs better than standard evolutionary algorithms on a problem of evolving tall 3D structures, while also providing significant potential for further enhancements.

This paper proposes a novel framework for automatically setting penalty weights in the Quadratic Unconstrained Binary Optimization (QUBO) to handle problems with multiple constraints. Quantum computing and quantum-inspired methods have gained prominence, with QUBO models widely used for their unified representation of optimization problems. However, QUBO performance is highly sensitive to penalty weight settings, especially in multiple constraints scenarios, where setting different penalty weights to different constraints may further affect performance. Existing methods for setting common penalty weights for all constraints in QUBO can be generally categorized into manual methods based on expert experience, exact methods based on the objective function values, and sequential methods based on searching within an upper bound. This study introduces a novel framework for multiple constraints optimization that utilizes exact and sequential binary search methods to determine common penalty weight while integrating constraint sensitivity analysis to adjust each penalty weight dynamically. This approach enhances the efficiency and quality of QUBO solutions. Experimental results on the Travelling Salesman Problem show that the proposed framework achieves superior solution quality and feasibility on both the D-Wave quantum annealer and classical simulated annealing solvers, outperforming traditional methods and demonstrating strong adaptability.

Route personalization is essential for designing tourist trips, but incorporating all influencing factors into mathematical models is challenging. An alternative is to obtain a diverse set of high-quality routes in advance and rank them a posteriori based on user profiles, simplifying the models and enabling straightforward solutions. This paper examines the combined use of the Modeling to Generate Alternatives (MGA) technique and route similarity measures in a Tourist Trip Design Problem (TTDP) for the generation of diverse routes. Two MGA approaches were compared to a basic evolutionary algorithm (EA) that does not prioritize diversity. Results show that while the basic EA yields solutions with higher average tourist interest, the MGA methods yield more diverse solutions with acceptable tourist interest levels. Statistically significant differences in solution diversity were found between the MGA variants, but differences were not significant in terms of the tourist interest or when different route similarity measures were considered.

In recent years, hybrid algorithms have demonstrated significant potential for addressing constrained multi-objective optimization problems by combining global exploration with local exploitation. A central challenge in such approaches lies in designing effective local search mechanisms that maintain diversity while ensuring convergence to high-quality solution sets. This work integrates a local search strategy into the NSGA-II framework, guided by the Riesz Energy Indicator, to enhance the search process. We introduce a novel candidate selection scheme for local search based on the individual contribution of each population member; a property inherited by the Riesz Energy Indicator. Different approaches were evaluated to exploit this property. The numerical results show that the proposed hybrid algorithm improves both convergence and diversity, highlighting the advantages of incorporating local search strategies informed by the Riesz Energy indicator.

Evolutionary algorithms have achieved significant success in solving many-objective optimization problems (MaOPs). However, their performance often declines when dealing with MaOPs that have irregular Pareto fronts (PFs). To address this issue, we propose the many-objective evolutionary algorithm that combines adaptive reference vectors and generalized Pareto dominance (GPD), named CARVGPD, where a novel environmental selection strategy is introduced. It can increase selection pressure by using GPD to ensure convergence, while reference vectors are used to maintain diversity. The adaptive reference vector strategy adjusts the reference vectors according to different PF shapes. Experiments were conducted on 18 irregular problems with various PF shapes. Experiments show that, compared with five advanced algorithms, the proposed CARVGPD method is highly competitive in solving MaOPs with irregular PFs.

The field of automatic programming has made significant advances in recent years, particularly through the development of semantic-aware algorithms in Genetic Programming (GP) and the emergence of Large Language Models (LLMs) designed for code. This raises a natural question: can these two approaches be combined to achieve synergistic effects? In this paper, we explore whether the semantic information embedded in vector representations of source code, generated by dedicated LLMs, can enhance GP performance. Specifically, we integrate code representation models expected to capture both syntactic and semantic attributes of GP-generated programs into their embeddings, and propose informed selection operators that leverage these embedded attributes. Experimental results on a diverse set of benchmark problems demonstrate that embedding-based selection methods significantly improve convergence speed in GP. This integration of code embeddings into the selection process offers a promising direction for enhancing the efficiency of GP evolutionary search.

In many applications, the relative order of the outputs is more crucial than their absolute numerical values. Geometric semantic genetic programming (GSGP) typically operates on function outputs directly but lacks an inherent behaviour to represent the order structure of a function, making it less suitable for problems where decisions are driven by comparison of outputs. In this study, we explore a novel perspective of semantics in the context of GSGP rooted in the order structure of real-valued functions referred to as order semantics. We show that existing geometric semantic operators for real-valued functions retain their geometric properties under order semantics when an alternative notion of semantic distance is considered instead of Euclidean distance. Consequently, the fitness landscape seen by these operators is unimodal with respect to this choice of distance in order semantic space. We validate our method through experiments comparing standard GSGP and a newly proposed GSGP based on order semantics on randomly generated functions. Our results demonstrate that the proposed GSGP improves ranking accuracy at the cost of numerical precision.

Code review is an essential practice for software quality assurance. However, code review can be cumbersome as patches often undergo multiple rounds to fix bugs, enforce coding standards, and improve structure before merging or abandonment. Predicting the number of review rounds can help developers prioritize tasks and streamline the process. Existing machine learning models for review round prediction suffer from key limitations. Their black-box nature makes them difficult to interpret, reducing trust and adoption. Additionally, they rely on data re-balancing techniques that introduce artificial points, causing concept shifts and reducing reliability. To address these issues, we propose MORRP, a novel Multi-Objective Review Rounds Prediction approach. MORRP is based on Multi-Objective Genetic Programming (MOGP) to predict review rounds. Our method evolves interpretable models while optimizing precision, recall, and specificity without relying on data re-balancing. We evaluate our approach on three large open-source projects: Eclipse, OpenDaylight, and OpenStack. Results show that MORRP achieves competitive performance, with a micro F1 score between 0.65 and 0.75, outperforming complex ML models like Random Forest and LightGBM.

Genetic programming is an optimization algorithm inspired by evolution which automatically evolves the structure of interpretable computer programs. The fitness evaluation in genetic programming suffers from high computational requirements, limiting the performance on difficult problems. Consequently, there is no efficient genetic programming framework that is usable for a wide range of tasks. To this end, we developed Kozax, a genetic programming framework that evolves symbolic expressions. We implemented Kozax using JAX, a framework for high-performance and scalable machine learning, which allows the fitness evaluation to scale efficiently to large populations or datasets on GPU. We demonstrate successful applications of Kozax to discover equations of natural laws, recover equations of hidden dynamic variables, evolve a control policy and optimize an objective function. Overall, Kozax provides a general, fast, and scalable library to optimize white-box solutions in the realm of scientific computing.

Feature Selection (FS) is a key characteristic of any Machine Learning method. Genetic Programming (GP) performs it inherently, using evolution pressure to exclude redundant or irrelevant features. However, this ability is lost in Geometric Semantic Genetic Programming (GSGP), where Geometric Semantic Operator (GSO) keep adding genetic material to the individuals, inevitably adding noisy features. This work focuses on comparing the FS abilities of GSGP and Semantic Learning algorithm based on Inflate and deflate Mutations (SLIM), a promising new variant that employs Deflate Geometric Semantic Mutation (DGSM), a genetic operator that is able to remove genetic material while still inducing an unimodal fitness landscape. The experimental results show how SLIM has superior FS abilities compared to GSGP.

Selecting models from a well-fit, evolved population that generalizes beyond training data is difficult. We introduce a pragmatic method using Hessian rank to align model complexity with dataset intrinsic dimensionality (ID) for post-processing selection in symbolic regression. Our method efficiently estimates model complexity by averaging Hessian rank across strategic points, aligns this with dataset ID estimated using conventional ID estimators, and identifies an ideal complexity window that balances expressiveness with accuracy. Using StackGP with the Penn Machine Learning Benchmark, we demonstrate that models within this targeted complexity window generalize better than those outside it, without the bias common in methods reliant on user-defined parameters.

In this work, we develop a novel method for estimating model curvature to be used in model selection and evaluation in symbolic regression by symbolically evaluating the model's Hessian matrix at the maximum, minimum, and median points with respect to the response surface. We demonstrate that this estimator is unique from previous methods for computing model complexity and demonstrate that it is relatively computationally efficient. We further validate the method by showcasing that the estimator ranks equations in line with expectations while also exploring the impact of using the max, min, and median points as the references for assessing a model's curvature. Finally, we explore how the metric impacts evolutionary search when used during selection.

Genetic programming (GP) and large language models (LLMs) have both achieved notable success in program synthesis. However, the methods for specifying the desired program behavior (i.e., user intent) differ: GP relies on input-output examples, whereas LLMs use text descriptions. In this work, we compare the capabilities of a GP system, PushGP, and an LLM model, GPT-4o, in synthesizing programs where the user intent is specified through input-output examples. Using tasks from the PSB2 program synthesis benchmark, we found that PushGP solved more tasks than GPT-4o. While some tasks were successfully solved by both synthesizers, others were uniquely solved by only one of them, highlighting their complementary strengths. In addition to the prompt with just input-output examples (data-only), we tested GPT-4o with another prompt containing only a textual description of the task (text-only). Both prompt variants successfully solved the same 7 tasks (with different success rates), with the data-only prompt solving an additional task. Ultimately, each synthesizer is successful in distinct ways, highlighting differences in their underlying methodologies.

Evolutionary computation (EC) is a kind of artificial intelligence (AI) for optimization. However, traditional EC algorithms require the careful design of parameters and/or operators from experts. Designing an operator with generalization ability is a tough task, and the manually design process is often limited by the structures of existing operators, which lacks diversity. In order to explore operators with diverse structures and good generalization ability so as to provide inspiration for the manually design of operators, this paper proposes a generative EC approach for the automatic design of operators by using genetic programming (GP). We apply the generative approach to a typical EC variant named gene targeting differential evolution (GTDE), so as to propose a new automatic GTDE (AGTDE) algorithm. The AGTDE utilizes the advantage of GP in optimizing structural features to automatically generate and refine the targeting vector generation operator within GTDE. This way, the operator of AGTDE is generated automatically rather than manually designed, which is more robust and optimal. The experimental results demonstrate that AGTDE is capable of identifying appropriate and even better operator for solving optimization problems, when compared with GTDE with manually design operator. Moreover, the results show that the operator obtained for one problem can be applied to other problems and obtain promising results, which reflect the robustness and generalization ability of the operator generated by GP. Therefore, this generative approach may provide some novel avenues of thought for the automatically design of EC algorithm operators.

In high-dimensional real-world datasets, a critical challenge for feature engineering (FE) in machine learning (ML) is that it must balance predictive accuracy with feature interpretability. This paper introduces a novel nested genetic programming (GP) approach that includes evolutionary feature construction integrated with mutual information (MI)-based feature selection. Our approach adopts a custom GP fitness function based on minimal-redundancy-maximal-relevance (mRMR) criterion, guiding the evolutionary process to construct features that maximize mutual information with target variables while minimizing redundancy among the constructed features. The proposed approach addresses the critical challenge mentioned above by improving predictive performance while yielding interpretable features that are backed by information theory principles. Extensive experiments across diverse datasets demonstrate that our approach, even when utilizing a substantially reduced feature count, consistently outperforms both baseline methods using all original features and other contemporary FE techniques when compared at the same feature dimensionality. The effectiveness of our approach is validated across multiple ML models in regression tasks, showing improved accuracy and better generalization across diverse datasets and varying feature dimensionality.

Genetic programming (GP) is an evolutionary approach to the automated synthesis of computer programs. A critical challenge in GP is balancing population diversity and efficiency to prevent premature convergence while avoiding excessive program growth, commonly referred to as bloat. This work introduces a new syntactic-based crossover mechanism, Heterosis-based Crossover (HBC), which prioritizes structural differences over semantic criteria. Specifically, HBC enforces mating constraints by employing a structural diversity metric that restricts mating between individuals deemed too similar, effectively preventing "inbreeding." Through a series of symbolic regression tasks, we investigate how HBC influences population diversity, introns (structurally non-effective code), and bloat. Our findings reveal that HBC reduces premature convergence, preserves diversity, and mitigates bloat, enabling more effective exploration of the solution space. This study demonstrates that syntactic-based techniques offer a robust alternative to semantic-aware methods, emphasizing the importance of structural diversity in optimizing the trade-offs among exploration, exploitation, and computational resources in GP.

Genetic Programming (GP) faces two major challenges: the inability to use knowledge from past problems, as each run is independent, and the difficulty in identifying building blocks in the early stages of evolution. These limitations result in high computational costs and slower convergence. Transfer learning can provide a solution by leveraging past experiences to enhance performance in GP. A mutual-information-based transfer learning method is proposed in this paper to identify and transfer beneficial knowledge fragments. The method is evaluated on ten polynomial and trigonometric symbolic regression problems from previous literature and compared with standard GP and SubTree50 as state-of-the-art methods. Results of the above experiment demonstrate improved or comparable performance of the proposed method in terms of accuracy, statistical significance, and generalization. The contribution of this paper includes: a mutual-information-based technique for identifying and transferring knowledge fragments. Results highlight the potential of mutual information to address key challenges in GP effectively.

Innovations in evolutionary computation often emerge from combining distinct optimization paradigms. This paper presents a novel hybrid approach: the synergistic integration of Genetic Programming (GP) and Differential Evolution (DE), referred to as GP*. In this framework, GP serves a dual role. It computes objective function values for DE while simultaneously generating candidate solutions in the form of symbolic expressions. We demonstrate this concept in the task of chaos stabilization using the Hénon map. The GP* algorithm enables efficient exploration of the solution space by taking advantage of the complementary strengths of GP and DE. Experimental results show that in some cases, GP* outperforms conventional two-phase strategies in which GP and DE operate independently, achieving better solution quality and faster convergence. Beyond chaotic system control, the GP* framework is applicable to broader classes of problems involving tightly coupled structural and parametric optimization. This work introduces a new perspective on algorithmic hybridization, where structural evolution directly defines the fitness landscape for parameter search. The results presented here contribute to the field of genetic programming and evolutionary optimization and open avenues for further exploration in interpretable modeling, controller synthesis, and dynamic system design.

This paper proposes a genetic programming approach for the analysis of contagion spreading on a graph. In the analyzed problem, graph vertices can get infected from their neighbours along the edges of the graph. The genetic programming technique is used in this paper to build interpretable expressions describing the spreading of the contagion based on simulation results. Bi-objective optimization is performed with the goal of maximizing both the precision and recall of predictions produced by the optimized expressions. In this paper, a Logical Search procedure is proposed that efficiently searches though multiple combinations of expressions found in each generation of the algorithm. Presented experimental results show, that the use of the Logical Search procedure greatly increases the chances of discovering the actual contagion spreading mechanism.

Program Trace Optimization (PTO) is a framework that provides automatic representation design for arbitrary problem structures by separating problem specification from search algorithm application. Problems in PTO are specified through two components: a generator that creates candidate solutions and a fitness function that evaluates them. A key strength of PTO is its ability to work with unrestricted programs as generators. We explore PTO's application to sophisticated generators based on language models, using the Abstraction and Reasoning Corpus (ARC) as our case study. Our results demonstrate how PTO can effectively search the space of programs generated by language models trained on domain-specific languages, with context-aware operators that automatically preserve the model's statistical patterns during evolutionary search. This work shows how PTO can seamlessly incorporate advanced generative methods without requiring modification of the underlying search algorithms.

Feature construction has been proven to be an effective method for improving classification performance. Genetic Programming (GP) has demonstrated its immense potential in automatic feature construction due to its flexible representation. Multi-tree GP can enhance the search ability and efficiency of GP, and has been used for feature construction. However, existing multi-tree methods often require a predetermined number of trees in each individual, which limits the flexibility and adaptability of the algorithm. In this paper, a novel Adaptive Multi-tree GP (AMTGP) based feature construction method is proposed, which can automatically adjust the number of trees in each individual based on the current state and fitness feedback. Experiments on 10 datasets show that our proposed AMTGP can achieve better classification performance than the single-feature construction method (SFC). Compared to the traditional Multi-tree GP (MTGP) methods, AMTGP not only reduces the workload of parameter tuning but also enhances the algorithm's adaptability to different datasets, resulting in better classification performance. Compared to four state-of-the-art benchmark techniques, in most cases, our proposed method can achieve better classification performance.

System identification is the task of automatically learning the model of a dynamical system, which can be represented as a system of ordinary differential equations (ODEs), using data points from time-series trajectories. This challenge has been addressed through various methods, including sparse regression, specialized neural networks, and symbolic regression. Applying standard symbolic regression, however, requires transforming trajectory data to frame the problem as learning a set of regular equations. This study presents a first thorough comparison of the two most common data transformation approaches for system identification, evaluating their performance on a recently published benchmark suite of ODE systems. Our findings reveal that both approaches are highly sensitive to even moderate amounts of added noise, to different degrees. More surprisingly, we also show that data transformations can generate misleading search spaces, even under noise-free conditions.

Fitness landscapes in test-based program synthesis are known to be extremely rugged, with even minimal modifications of programs often leading to fundamental changes in their behavior and, consequently, fitness values. Relying on fitness as the only guidance in iterative search algorithms like genetic programming is thus unnecessarily limiting, especially when combined with purely syntactic search operators that are agnostic about their impact on program behavior. In this study, we propose a semantics-aware search operator that steers the search towards candidate programs that are valuable not only actually (high fitness) but also only potentially, i.e. are likely to be turned into high-quality solutions even if their current fitness is low. The key component of the method is a graph neural network that learns to model the interactions between program instructions and processed data, and produces a saliency map over graph nodes that represents possible search decisions. When applied to a suite of symbolic regression benchmarks, the proposed method outperforms conventional tree-based genetic programming and the ablated variant of the method.

Genetic programming (GP) algorithms are widely used for solving symbolic regression (SR) problems. However, traditional GP struggles to effectively leverage knowledge gained from previous tasks when tackling new ones, leading to inefficient search processes. At the same time, the Transformer architecture has demonstrated superior performance through extensive experimental validation. To address this issue, we propose a novel approach called Transformer-GP. The core idea behind this method is to train a Transformer-Tree model to learn the distribution characteristics of node and edge components in symbolic trees. The model's predicted outputs are subsequently utilized as prior knowledge to guide genetic operations, including initialization and mutation, within the GP population. We conducted experiments on 12 benchmark problems, and the results demonstrate the effectiveness of the proposed method.

This work considers a realistic variant of the Electric Vehicle Charging Scheduling Problem (EVCSP), formulated to maximize the number of satisfied charging requests under grid capacity and charger-specific constraints. A bi-level optimization framework is introduced, where the upper level handles request-to-charger assignment using several Hybrid Genetic Algorithms (HGAs) enhanced by reinforcement learning techniques—Q-learning, Double Q-learning, SARSA, and Expected SARSA—to dynamically guide mutation decisions. The lower level applies an integer programming model to ensure feasible energy allocation under operational constraints. Extensive experiments on diverse benchmark instances demonstrate that RL-guided HGAs achieve substantial performance gains over existing methods, with the Q-learning-based variant consistently delivering the best results, particularly in large-scale and complex scenarios. These results highlight the effectiveness of integrating evolutionary search, adaptive learning, and mathematical programming for resource-constrained scheduling problems.

Optimizing blackbox functions requires a structured approach to ensure an effective and efficient search for the optimal solution, supported by a deep understanding of the problem domain, algorithmic behavior and programming abilities. Large Language Models (LLMs) offer a powerful tool to enhance this understanding by excel at solving diverse tasks such as text summarization, code generation, and question answering. This paper presents a novel method using a structured LLM-based multi-agent collaboration approach, to perform numerical blackbox optimization for complex or highly non-linear functions. The tasks of algorithm selection, constraint analysis, code generation, execution, hyperparameter tuning, and solution evaluation are handled by separate agents within the framework. Experiments on standard optimization benchmarks demonstrate the feasibility of mapping the entire optimization process from problem definition to evaluation, achieving competitive results.

The Algorithm Configuration Problem aims to find suitable parameter values for metaheuristics. irace is a well-known tuner successfully applied in the literature to obtain proper parameter values for several algorithms. Understanding the search process of irace (and tuners) can be complex due to several factors, including its hyperparameters and the inherent stochasticity of both the tuner and the target algorithm. In this work, we analyze irace's search process through Search Trajectory Networks (STNs), focusing on the role of elite configurations, network structure, and the impact of the soft-restart component. Using ACOTSP (11 parameters) as the target algorithm, our results show that elite configurations represent only 4% of all visited configurations. Additionally, the soft-restart component enhances exploration, leading to more diverse and structurally distinct trajectories.

In this poster, we introduce a rank-based surrogate-assisted variant of CMA-ES. Unlike previous methods that employ rank information as constraints to train an SVM classifier, our approach employs a linear-quadratic regression on the ranks. We investigate the method's invariance empirically. While this first algorithm outperforms CMA-ES with a few exceptions, it falls short to entirely meet the lq-CMA-ES performance levels. To address this, we propose an enhanced variant that handles together two alternative surrogates, one based on the ranks and one based on the original function values. Although this variant sacrifices strict invariance, it gains in robustness and achieves performance comparable to, or even exceeding, lq-CMA-ES on transformed problems. This last algorithm shows how simply incorporating new transformations of rank values could improve any surrogate-based CMA-ES variant.

Automated algorithm selection aims to help users to select the best algorithm for new optimization problems without any expertise. As a machine learning task, algorithm selection maps the problem features to the best algorithm. Exploratory landscape analysis is a feature extraction method for algorithm selection based on random samples, which has been widely applied in algorithm selection methods. However, their instability and redundancy greatly affect the accuracy of algorithm selection. To enhance these features, we apply a feature construction method based on multi-tree genetic programming for algorithm selection, which creates more discriminating features by combining or transforming multiple features and further counteracts the negative correlation noise from random samples. The selection process in genetic programming can reduce the redundancy of features by selecting more relevant features. Experimental results show that this method achieves the best performance compared with genetic programming based feature construction methods and algorithm selection methods on the four datasets.

Various methods for formulating practical combinatorial optimization problems as an Ising model have been developed, expanding real-world applications of Ising machines. Nevertheless, the usability of Ising machines remains limited since the formulation process involves complicated tasks, such as fine-tuning parameters or selecting options, which can be challenging for non-expert users. Moreover, the existing formulation technique is often insufficient to design an Ising model that facilitates efficient solution search by Ising machines. This paper proposes a novel approach in which the Boltzmann machine, an energy-based machine learning model, autonomously optimizes the Ising model based on solutions obtained from an Ising machine. The proposed combinatorial optimization flow iteratively alternates between solution search by the Ising machine and model refinement by the Boltzmann machine, gradually improving solution quality without manual adjustments of parameters or options. Experimental results demonstrate that the proposed method consistently outperforms the standalone Ising machine in several benchmark problems, achieving superior solution quality under a comparable computational budget.

Algorithm selection is commonly used to predict the best solver from a portfolio per per-instance. In many real scenarios, instances arrive in a stream: new instances become available over time, while the number of class labels can also grow as new data distributions arrive downstream. As a result, the classification model needs to be periodically updated to reflect additional solvers without catastrophic forgetting of past data. In machine-learning (ML), this is referred to as Class Incremental Learning (CIL). While commonly addressed in ML settings, its relevance to algorithm-selection in optimisation has not been previously studied. Using a bin-packing dataset, we benchmark 8 continual learning methods with respect to their ability to withstand catastrophic forgetting. We find that rehearsal-based methods significantly outperform other CIL methods. While there is evidence of forgetting, the loss is small at around 7%. Hence, these methods appear to be a viable approach to continual learning in streaming optimisation scenarios.

An outcome accumulation-type evolutionary rule discovery method (GNMiner) has been proposed, which has a directed graph structure and is characterized by the accumulation of outcomes acquired in the evolutionary process. Because GNMiner is less efficient at discovery with respect to large feature sets, a feature-selection mechanism is required. In this paper, we propose a framework that integrates evolutionary rule discovery using GNMiner and evolutionary feature selection to refine the search space. The framework is characterized by problem-solving through an evolutionary process in which the two components are interdependent. The experimental results show that the proposed method increases the number of important rules discovered and enhances the fitness value of GNMiner individuals compared with conventional GN-Miner. For feature selection, the results also show that evolutionary computation based on the acquired outcomes of GNMiner is effective.

By employing large language models (LLMs) we build a general genetic algorithm, i.e., a genetic algorithm (GA) that can solve various domains without any changes to its algorithmic components. Our approach requires only a problem description in natural language and a black-box fitness function and can then handle any type of data via natural-language-based evolutionary operators that call an LLM to compute their application. The relevant prompts for the operators can be human-designed or self-optimized with similar performance results. Compared to the only other generalist GA approach, i.e., asking an LLM to write a new specific GA, our natural-language-based genetic algorithm (NaLaGA) offers not only a better class of safety (since no LLM-generated code is executed by NaLaGA) but also greatly improved results in the two example domains "Schwefel" and "grid world maze".

To deal with challenging expensive many-objective optimization problems, this study proposes a novel ranking-prediction based evolutionary algorithm. Instead of approximating the objectives directly, our algorithm introduces M symmetrical ranking cases in the generalized Pareto dominance to construct a single comprehensive Kriging model. Moreover, we design a novel method referred to as the expected ranking advantage (ERA) for model management to cooperate with ranking-prediction, which is capable of providing sufficient information and avoiding the accumulation of errors compared to traditional surrogate models. In addition, our proposed algorithm achieves a significant improvement in the time complexity of model construction. The outstanding performance and efficiency of the ERA-based algorithm are demonstrated in two benchmark test suites with the comparison of four state-of-the-art algorithms.

Soft robots have proven to outperform traditional robots in applications related to propagation in geometrically constrained environments. Designing these robots and their controllers is an intricate task, since their building materials exhibit non-linear properties. Human designs may be biased; hence, alternative designing processes should be considered. We present a cooperative neuro co-evolution approach to designing the morphologies of soft actuators and their controllers for applications in drug delivery apparatus. Morphologies and controllers are encoded as compositional pattern-producing networks evolved by Neuroevolution of Augmented Topologies (NEAT) and in cooperative coevolution methodology, taking into account different collaboration methods. Four collaboration methods are studied: n best individuals, n worst individuals, n best and worst individuals, and n random individuals. As a performance baseline, the results from the implementation of Age-Fitness Pareto Optimisation (AFPO) are considered. The metrics used are the maximum displacement in upward bending and the robustness of the devices in terms of applying to the same evolved morphology a diverse set of controllers. Results suggest that the cooperative neuro coevolution approach can produce more suitable morphologies for the intended devices than AFPO.

Molecular Property Prediction (MPP) plays a critical role in accelerating drug discovery by efficiently predicting the molecular characteristics. Despite advancements in multi-modal MPP methods, different modalities capture molecular features from different perspectives and different MPP tasks require specific modal features. Therefore, selecting the optimal combination of molecular modalities remains an open challenge. To achieve high accuracy while minimizing the number of modal features and model parameters, this paper proposes a modality-adaptive MPP method based on an improved multi-objective optimization algorithm. The molecular modalities we leverage include the pre-trained ChemBERTa model based on SMILES, six different molecular fingerprints, molecular graphs and 3D conformations. The improved multi-objective optimization algorithm integrates Topological Data Analysis (TDA), the teacher learning mechanism and graph centrality measures, achieving more diverse exploration and faster convergence. TDA refines the initial population for the uniform distribution, teacher learning mechanism directs offspring toward the Pareto front, and graph centrality measures combined with crowding distance enhance exploration of sparse regions. The experiments are conducted on three classification tasks and two regression tasks. Compared with the state-of-the-art methods, our method achieved the promising performance, demonstrating the effectiveness and adaptability of our method in improving molecular property prediction.

Recently, Convolutional Neural Networks (CNNs) have performed well in pattern recognition tasks such as image segmentation. However, designing a CNN for a particular dataset requires experience in choosing from feature extraction and aggregation operators. Neural Architecture Search (NAS) is automating the design of neural networks for a specific task. By leveraging its syntax tree representation, genetic programming (GP) can be adapted as a search strategy in the NAS (ENAS) problem. Solutions evaluation implies the models' weight optimization, making ENAS computationally expensive. Nonetheless, surrogate models can reduce the costly evaluations by predicting fitness solutions. Generating a surrogate model from variable-size tree-based GP solutions usually requires a tree-to-structured data conversion to use standard baseline regression models. This paper compares several surrogate models used to assist GP-based algorithms. Also, phenotype-level features are proposed to be included in converting syntax-tree solutions to sequence-vectors. The surrogate models are applied to optimize U-Net-type networks, showing promising results in reducing the number of costly evaluations and the execution time without affecting the segmentation performance.

Deep neuroevolution is a highly scalable alternative to reinforcement learning due to its unique ability to encode network updates in a small number of bytes. Recent insights from traditional deep learning indicate high-dimensional models possess intrinsic, low-rank structure. In this work, we introduce low-rank, factorized neuroevolution-an indirect encoding through which we can search a small space of low-rank factors that enforce underlying structure across a network's weights. We compare our approach with non-factorized networks of similar and smaller size to understand how much performance can be attributed to the smaller search space. We evaluate our method on a language modeling task using transformers. Our study shows that low-rank, factorized neuroevolution outperforms or is competitive with non-factorized neuroevolution, performing notably well on language modeling. More broadly, these results show how we can use insights from backpropgation-based methods to enhance neuroevolution.

We consider the problem of efficiently searching for high-performing neural architectures whilst simultaneously favouring networks of reduced complexity. It is theorised that a complementary set of proxies can be employed for multi-objective optimisation to balance model performance with the size of the network. We demonstrate that a low-cost proxy for the test accuracy of a candidate architecture can be derived from a series of inferences alone. The proxy is paired with a complexity metric based on the number of parameters in the model and the two properties are used in a multi-objective setting. A Pareto Archived Evolutionary Strategy is used to optimise the two objectives simultaneously and deliver a diverse collection of solutions as output. This method is shown to successfully discover low-complexity architectures with minor loss of accuracy as compared to the global optima and does so with statistical reliability. This work offers a proof-of-concept Neural Architecture Search algorithm that removes training from the process entirely. The proposed approach is examined in terms of search behaviour and the complexity reduction that can be achieved by comparing discovered solutions to the top-performing architectures in the search space.

SGD dominates deep learning despite the demonstrated advantages of evolutionary algorithms (EAs) for non-convex optimization. In this paper we introduce MO-DL-HEA, a multi-objective hybrid EA that outperforms SGD in real-world tasks while addressing the generalization gap through simultaneous training and validation optimization, demonstrating superior alternatives to SGD for deep learning. Our experiments across multiple architectures and datasets consistently show MO-DL-HEA achieving better generalization with comparable or lower training loss than SGD. The algorithm's two-tier selection mechanism—using validation loss for parent selection and generalization gap for survivor selection—effectively balances exploration of novel solutions with refinement of near-optimal ones, driving the population toward models that generalize well to unseen data.

Neural Architecture Search (NAS) automates neural network design, reducing dependence on human expertise. Whilst NAS methods are computationally intensive and dataset-specific, utilising auxiliary predictors to estimate architecture properties has proved advantageous, reducing the number of models requiring training and search time. This strategy is employed to generate architectures meeting multiple computational constraints. Transferable NAS generalised the search from dataset-dependent to task-dependent. In this domain, DiffusionNAG represents the state of the art. This diffusion-based method generates architectures optimised for accuracy on unseen datasets without requiring adaptation. However, by focusing solely on accuracy, DiffusionNAG neglects crucial objectives such as complexity, computational efficiency and latency—essential factors for deployment in resource-constrained environments. This paper introduces POMONAG (Pareto-Optimal Many-Objective Neural Architecture Generator), extending DiffusionNAG through a many-objective diffusion process. POMONAG simultaneously considers accuracy, parameter count, multiply-accumulate operations and latency. It integrates Performance Predictor models to estimate secondary metrics and guide diffusion gradients. Optimisation is enhanced by expanding the training Meta-Dataset, applying Pareto Front Filtering and refining embeddings for conditional generation. These improvements enable POMONAG to generate Pareto-optimal architectures that surpass the state of the art in both performance and efficiency. Results were validated on two search spaces—NASBench201 and MobileNetV3—and evaluated across 15 image classification datasets.

A key challenge in reinforcement learning (RL) is managing the exploration-exploitation trade-off without sacrificing sample efficiency. Policy gradient (PG) methods excel in exploitation through fine-grained, gradient-based optimization but often struggle with exploration due to their focus on local search. In contrast, evolutionary computation (EC) methods excel in global exploration. To address these limitations, this paper proposes Evolutionary Policy Optimization (EPO), a hybrid algorithm that integrates neuroevolution with policy gradient methods for policy optimization. EPO leverages the exploration capabilities of EC and the exploitation strengths of PG, offering an efficient solution to the exploration-exploitation dilemma in RL. Experiments with the Atari Pong and Breakout benchmarks show that EPO improves both policy quality and sample efficiency compared to standard PG and EC methods.

This study investigates comparative methods for two-step collective behavior evolution (evolving group behaviors from pre-evolved behaviors), to encourage the evolution of behavioral diversity in swarm-robotic applications. Specifically, we investigate behavioral diversity evolution given pre-evolved behaviors in collective behaviors that are effective across increasingly complex and difficult collective herding task environments. Results indicate that specific complements of pre-evolved (lower task-performance) collective herding behaviors was suitable for achieving high task performance across all environments and task difficulty levels. Results support the efficacy of the two-step approach for evolving behaviorally heterogeneous groups in collective behavior tasks that benefit from groups comprising various complementary behaviors.

Neural Architecture Search (NAS) has proven to be a highly effective technique for automating neural network design, overcoming challenges posed by complex datasets, class imbalance, and the high time consumption associated with manual architecture selection. Although NAS shows promise, it frequently suffers from high computational costs and the risk of data loss due to insufficient training. This paper presents a novel NAS method that incorporates class visualization to mitigate computational costs and a bilevel optimization framework to address class imbalance. The hierarchical structure comprises an upper level formulated as a multi-objective optimization problem to maximize performance, measured by the Matthews correlation coefficient, while minimizing model complexity. The lower level focuses on neural network training using a reduced dataset obtained by class visualization. The proposed approach combines NSGA-II (for the upper-level problem) with stochastic gradient descent (for the lower-level problem). This method significantly reduces NAS runtime on MNIST and CIFAR-10 subsets while maintaining accuracy and robustness.

State-of-the-art Deep Neural Networks (DNNs) often incorporate multi-branch connections, enabling multi-scale feature extraction and enhancing the capture of diverse features. This design improves network capacity and generalisation to unseen data. However, training such DNNs can be computationally expensive. The challenge is further exacerbated by the complexity of identifying optimal network architectures. To address this, we leverage Evolutionary Algorithms (EAs) to automatically discover high-performing architectures, a process commonly known as neuroevolution. We introduce a novel approach based on Linear Genetic Programming (LGP) to encode multi-branch (MB) connections within DNNs, referred to as NeuroLGP-MB. To efficiently design the DNNs, we use surrogate-assisted EAs. While their application in simple artificial neural networks has been influential, we scale their use from dozens or hundreds of sample points to thousands, aligning with the demands of complex DNNs by incorporating a semantic-based approach in our surrogate-assisted EA. Furthermore, we introduce a more advanced surrogate model that outperforms baseline, computationally expensive, and simpler surrogate models.

Evolving increasingly complex skills requires remembering and efficiently re-using past ones. This can be enabled by appropriately designing the genotype to phenotype (GP) map of an evolving system: skills can be encapsulated into modules that can be hierarchically combined during development. Here we study cellular encodings (CE), an early family of GP maps that can create such modular phenotypes by employing a genomic representation specifically designed to support hierarchy and modularity: grammar trees. Like functions in a computer program which can be called multiple times during execution, grammar trees can be executed at various points during development. Here, we apply CE in a curriculum learning setup and show that it can quickly progress across tasks of increasing difficulty by re-using its past solutions. In contrast, an algorithm that searches directly in the phenotypic space (NEAT) does not benefit from a curriculum while another GP map (HyperNEAT) fails when the curriculum is present. We show that enforcing hierarchy in the CE, through the use of a nested set of grammar trees, is necessary to observe these benefits. We believe that future work should scale such approaches, either by scaling CEs directly or integrating these ideas into more powerful approaches.

Accurate segmentation of medical images is a crucial part of pathology research and clinical practice. Currently, deep neural network (DNN)-based models are commonly used for medicad image segmentation. However, most DNN-based models are manually designed by experts which is a time-consuming and labor-intensive process as well as poorly generalized for different applications. Therefore, we propose EM-NAS, a novel evolutionary multi-scale NAS method with a cell-based design for medical image segmentation. Specifically, the structures of encoder and decoder cells are represented by directed acyclic graphs (DAGs). Moreover, some non-subsampling multi-scale decomposition operations are introduced into the candidate operation set to capture multi-scale, multi-directional and multi-frequency features of medical images. Subsequently, we specify the cell of the network through a well-designed discrete coding strategy, and a GA is used to search for the optimal network architecture. The experimental results demonstrate the effectiveness of the proposed model on two public datasets.

We compare the ability of a simulated annealing program and an evolutionary algorithm to find molecules with large molecular average hyperpolarizabilities. This property is an important component of nonlinear optical materials. Both optimization programs represent molecules as SMILES strings, a method that is widely used by chemists to describe molecular structure using short ASCII strings. Our results suggest that both approaches are comparable and can be used to solve a variety of more realistic problems of interest to chemists and material scientists.

This paper presents a new Deep Q-Network (DQN) method to improve the efficiency of solving the Dial-a-Ride Problem (DARP). We focus on the solution quality of DARPs, aiming to enhance the Total Travel Cost. Our approach begins by generating initial solutions through an insertion heuristic, which are then represented within a Markov Decision Process (MDP). Based on the DQN's ability to learn from experience, the system refines its decisions over time. A local search is integrated through the DQN process improving upon the baseline solutions. The results of our experiments demonstrate that the DQN leads to more efficient vehicle routes by improving the overall system performance for DARPs.

This study addresses a variant of the Electric Vehicle Charging Scheduling Problem (EVCSP), which aims to maximize the number of satisfied charging requests while adhering to grid capacity and charger availability constraints. A hybrid approach is proposed that decomposes the problem into two stages: EV-to-charger assignment and energy allocation. For the assignment stage, two methods are evaluated: a heuristic method and a variable neighborhood search (VNS) algorithm. Both methods are integrated with an exact mathematical model at the second stage to optimize energy delivery for each assignment configuration. Experimental results show that the VNS algorithm consistently provides the best solution quality, outperforming both the heuristic method and existing solutions from the literature.

We address the problem of game level repair, which consists of taking a designed but non-functional game level and making it functional. This might consist of ensuring the completeness of the level, reachability of objects, or other performance characteristics. The repair problem may also be constrained in that it can only make a small number of changes to the level. We investigate search-based solutions to the level repair problem, particularly using evolutionary and quality-diversity algorithms, with good results. This level repair method is applied to levels generated using a machine learning-based procedural content generation (PCGML) method that generates stylistically appropriate but frequently broken levels. This combination of PCGML for generation and search-based methods for repair shows great promise as a hybrid procedural content generation (PCG) method.

Social networks may contain privacy-sensitive information about individuals. The objective of the network anonymization problem is to alter a given social network dataset such that the number of anonymous nodes in the social graph is maximized. Here, a node is anonymous if it does not have a unique surrounding network structure. At the same time, the aim is to ensure data utility, i.e., preserve topological network properties and retain good performance on downstream network analysis tasks. We propose two versions of a genetic algorithm tailored to this problem: one generic GA and a uniqueness-aware GA (UGA). The latter aims to target edges more effectively during mutation by avoiding edges connected to already anonymous nodes. After hyperparameter tuning, we compare the proposed GAs against two existing baseline algorithms on several real-world network datasets. Results show that the proposed genetic algorithms manage to anonymize on average 14 times more nodes than the best baseline algorithm. Additionally, data utility experiments demonstrate how the UGA requires fewer edge deletions, and how our GAs and the baselines retain performance on downstream tasks equally well. Overall, our results suggest that genetic algorithms are a promising approach for finding solutions to the network anonymization problem.

Despite their capabilities to generate human-like text and aid in various tasks, Large Language Models (LLMs) are susceptible to misuse. To mitigate this risk, many LLMs undergo safety alignment or refusal training to allow them to refuse unsafe or unethical requests. Despite these measures, LLMs remain exposed to jailbreak attacks—i.e., adversarial techniques that manipulate the models to generate unsafe outputs. Jailbreaking typically involves crafting specific prompts or adversarial inputs that bypass the models' safety mechanisms. This paper examines the robustness of safety-aligned LLMs against adaptive jailbreak attacks, focusing on a genetic algorithm-based approach.

Coverage Path Planning (CPP) is a fundamental problem in robotics with diverse applications, including area surveillance or search and rescue. The weighted continuous CPP problem extends the classical CPP by focusing on maximizing the coverage of a value function using continuous and free-form paths. This extension introduces unique challenges, particularly the computational effort required for equidistant path evaluation and the difficulty of achieving locally optimal paths. To address these challenges, this work proposes a bilevel optimization approach. In this framework, the upper-level decision-maker (DM) solves the continuous CPP problem, while the lower-level DM periodically optimizes sub-elements of the solutions. By leveraging this hierarchical structure, the proposed approach aims to achieve improved computational efficiency and enhanced adaptation to local scenario variations.

Multi-Objective Data Analysis is a technique used for the exploration of conflicting variable relationships in biological data. The use of biological variables as objectives necessitates the assumption that measurement noise could be present in the objective space. This study explores the effect of noise on Multi-Objective Data Analysis and particularly on non-dominated sorting and the extraction of an estimate of the gradient of the fitness landscape between the objective and decision spaces. We study the effect of noise on dominance relation and the ability of the inter- and intrafront clustering methods to maintain clusters with the addition of noise. In this paper, we propose the delta-domination as a new definition for domination, which allows one to consider larger sets of solutions in the fronts of the non-dominated sorting algorithm. This method allows for a better estimation of the contours of the fitness landscape gradient. To investigate its impact, we construct circularly distributed synthetic data and add noise of various magnitudes and explore the effect using metrics such as dominance relationship loss, changes in ranks, and F1 scores. Our experiments show that the proposed methodology can be used on noisy data and can be easily applied to the Multi-Objective Data Analysis.

In semiconductor manufacturing, the scan routing fabric (SRF) technology enables efficient hardware testing by concurrently running multiple test patterns. However, its total test time depends on the scheduling algorithm used. Current approaches rely on greedy algorithms which provide good but sub-optimal results. In this paper, we define the SRF test scheduling as an optimization problem, discuss its challenges, and propose a solution based on a combination of existing optimization algorithms.

We explore linear optimization as a way to reduce the search space and present the substantial positive impact it has on the tested algorithms. The evolutionary algorithm presented in this paper is an enhancement to the (pc)CMA-ES algorithm and uses multiple instances to focus on promising areas of the search space, limiting the effect of high dimensionality and noise. We show that this approach outperforms both existing methods as well as alternate evolutionary algorithms and that it improves existing approaches on a real-world dataset, reaching a global optimum. As this method was developed to improve the production of a major manufacturer, the dataset is not public. However, we did bracket it with both easier and more difficult artificial datasets in order to meaningfully compare our algorithms.

Boolean functions with good cryptographic properties like high nonlinearity and algebraic degree play an important role in the security of stream and block ciphers. Such functions may be designed, for instance, by algebraic constructions or metaheuristics. This paper investigates the use of Evolutionary Algorithms (EAs) to design homogeneous bent Boolean functions, i.e., functions that are maximally nonlinear and whose algebraic normal form contains only monomials of the same degree. In our work, we evaluate three genotype encodings and four fitness functions. Our results show that, while EAs manage to find quadratic homogeneous bent functions (with the best method being a GA leveraging a restricted encoding), none of the approaches result in cubic homogeneous bent functions.

Menu planning in food services is a complex process that involves multiple objectives and a large solution space. Its core purpose is to offer an appealing yet diverse selection of dishes every week, whilst maintaining operational efficiency. Here, the underlying problem of ingredient selection is formulated as a multi-objective knapsack problem, considering historical ingredient scores with regard to customer satisfaction and ingredient frequency. We also evaluate an extension of the model that starts to consider the impact of repeat decisions in this problem and attempts to control diversity of ingredient sets over time. The model is implemented on data supplied by an industry partner, and used to derive approximation fronts for both formulations.

Many techniques in formal verification and software testing rely on repOk routines to verify the consistency and validity of software components with complex data representations. A repOk function encodes the state properties necessary for an instance to be a valid object of the class under analysis, enabling early error detection and simplifying debugging. However, writing a correct and complete repOk can be challenging. This paper introduces Express, the first search-based algorithm designed to automatically generate a correct repOk for a given class. Express leverages simulated annealing, using the source code and test suite of the class under analysis to iteratively construct a repOk. We demonstrate how Express works on the LinkedList class of the Java standard library, and show that it produces a correct and complete repOK.

Efficient course scheduling in higher education institutions is a complex problem that directly impacts student retention and terminal efficiency. This research explores an optimization model that integrates Genetic Algorithms (GA) and Monte Carlo Simulation to enhance academic planning. The proposed approach assigns courses dynamically, considering constraints such as faculty availability, student demand, and institutional policies. Markov Chains and the Metropolis-Hastings Algorithm are employed to model enrollment patterns and predict scheduling outcomes. By simulating multiple scenarios, the model identifies optimal schedules that maximize course availability while minimizing conflicts. The results demonstrate that our methodology improves student progression rates and reduces scheduling inefficiencies of the current assignment. Additionally, our approach provides a flexible framework that can be adapted to different institutional contexts. The findings contribute to the development of intelligent scheduling systems that support data-driven decision-making in higher education administration.

Offshore wind farms have emerged as a crucial component of renewable energy generation, offering higher energy production rates due to stronger and more consistent wind conditions. However, these advantages come with significant installation and maintenance costs, necessitating comprehensive optimization analyses of wind farms projects to ensure economic feasibility and maximize energy output. One of the most significant challenges in this context is the effective placement of wind turbines within an offshore wind farm, considering the historic wind intensity and direction of candidate areas, along with the impact of wake effects. This study presents a framework that integrates a genetic algorithm to optimize wind farm layouts with a simulation tool for evaluating configurations of wind farm projects. In this paper, we describe the optimization module implemented with genetic algorithms. The proposed approach demonstrates high modularity and achieves competitive results compared to established benchmarks, highlighting the effectiveness of our framework for optimization analysis in wind farm projects.

More efficient programs can be obtained by applying compiler optimization flags, i.e., sequences of code transformations. However, these generic sequences often underperform, as their effectiveness depends on both the software and hardware characteristics. This highlights the need for tailored transformation sequences. This paper introduces a new problem composed of two combinatorial optimization tasks aimed at finding optimal and minimal-length source code transformation sequences. Shorter sequences enable faster compilation using only the most effective transformations for a given program and hardware. We propose a two-step methodology to solve the problem: first, find sequences that minimize program runtime; second, reduce their length without degrading performance. Our approach produces sequences up to 51.27% shorter and over 26% faster compared to the -O3 flag.

The three-dimensional bin packing problem represents a central challenge in logistics. It enables the efficient modeling of transportation and storage capacity usage, which optimization can lead to lower costs and enable more sustainable transportation practices. Alongside minimizing the storage capacity of loads, practical applications should also take into account factors such as stability. This work introduces a novel method that addresses the problem as a multi-objective optimization challenge, considering multiple factors for minimizing the required height and maximizing stability simultaneously. This approach combines evolutionary algorithms with the extreme point heuristic to achieve an adaptive solution. Additionally, a geometric model based on interval trees is presented, which serves as the foundation for solving the problem. The effectiveness and flexibility of the proposed method are evaluated through experiments on publicly available benchmarks. Experimental results show that the proposed method significantly enhances packing efficiency and stability, making it highly applicable to real-world logistics.

This paper introduces a novel enhancement for Monte Carlo Tree Search (MCTS) which consists of using a Genetic Algorithm (GA) to evolve macro-actions for a particular domain. A macro-action is a sequence of actions treated as a single action; using this approach MCTS searches over a set of macro-actions rather than the domain's default actions. If macro-actions are appropriate for a domain their use increases search tree depth and avoids unproductive actions. This is particularly useful in video game domains where it is often prohibitively expensive to build a sufficiently deep search tree for effective play due to expensive simulations, a small amount of computation time per action, and action spaces where each individual action usually has a very small effect on the state. Macro-action approaches have previously been shown to address look-ahead issues and improve MCTS performance in video game domains. However, previous implementations have relied on hand-designing very simple macro-actions. Our evolutionary approach automates this design process and significantly improves MCTS performance in the game Flappy Bird and several Atari 2600 games.

This paper addresses the dynamic economic emission dispatch (DEED) problem by integrating EVs as a flexible demand-side resource for peak shaving and valley filling considering the widespread adoption of Gridable Vehicles (GVs). The DEED problem introduces additional complexities of balancing energy supply and demand over time compared to traditional Emission Dispatch (EED). In order to enhance adaptability and exploration, the proposed Local Search Memory Algorithm based on Decomposition (LSMOMAD) combines dynamic crossover and mutation strategies to improve global search efficiency and prevent premature convergence. Additionally, an adaptive local improvement strategy accelerates convergence and avoids local optima. The simulation results demonstrate the effectiveness of the proposed algorithms when applied to the IEEE-30 and IEEE-39 bus systems and compared with the results from current state-of-the-art approaches.

The design optimization of analog integrated circuits (ICs) typically requires time-consuming simulation processes spanning several weeks to identify an optimal configuration that accounts for numerous performance-influencing variables under complex operating conditions. Currently, machine learning and evolutionary algorithms are being utilized to automatically design analog circuits, offering promising prospects. However, the high cost of performance evaluation remains a major obstacle to the automation of the design process. This paper proposes a surrogate-assisted multi-objective evolutionary algorithm based on decomposition (S-MOEA/D) for optimizing analog integrated circuit parameters. S-MOEA/D adopts the light gradient boosting machine (LGBM) to train a surrogate model, replacing real-world simulation validation. S-MOEA/D leverages historical solutions to periodically update surrogate model, improving prediction accuracy. Moreover, a dynamic weight vector adjustment strategy is designed to accelerate population convergence. Finally S-MOEA/D is evaluated on two analog circuit problems, and results demonstrate that S-MOEA/D significantly outperforms or is competitive with state-of-the-art peer algorithms. The proposed S-MOEA/D provides a promising optimization tool for analog integrated circuit design problems.

The optimization of cold-rolling production plans is critical in practical steel production management, as it not only improves production efficiency but also ensures the uninterrupted operation of downstream production lines. However, this problem is highly complex due to the existence of multiple parallel cold-rolling production lines and the intricate many-to-many production relationships between these lines and their downstream counterparts. To further complicate matters, objectives are often conflicting, with manufacturers striving to increase production volume while simultaneously reducing cost. To address this challenge, we propose a multi-objective approach that minimizes both setup and outsourcing cost, which in turn contributes to both higher production volume and overall cost reduction. This approach combines a mixed 0-1 integer optimization model with a greedy-based multi-objective evolutionary algorithm (GMOEA) incorporating problem-specific evolutionary strategies. Experimental results, based on real-world data of different scales, demonstrate that these strategies significantly enhance the performance of the algorithm. GMOEA also outperforms other state-of-the-art multi-objective evolutionary algorithms that are widely used in real-world applications, confirming the effectiveness of the proposed approach, and demonstrating its potential for practical application in the steel industry.

This study considered the problem of reconstructing an overall graph from multiple partially disclosed subgraphs such as supply chains and social networks. Modifying a part of a subgraph can make grasping the structure of the overall graph a challenge, thereby reducing the possibility of identifying essential nodes. However, there is a trade-off between the accuracy of modified subgraphs and the difficulty of grasping the overall structure. We formulated this as a multi-objective optimization problem and investigated its characteristics and the performance of the search operators using evolutionary multi-objective optimization and synthetic problems.

We propose a machine learning-based approach for the rapid and accurate prediction of drifter trajectories in marine accidents. Five machine learning models were constructed to predict the latitude and longitude changes of an object after one hour, using hourly position measured by drifters and corresponding wind and current data. These models showed an average performance improvement of 16.7% compared to a representative Lagrangian trajectory model, OpenDrift. In addition, prediction accuracy in new environments with different drift characteristics was improved through incremental learning. We then combined the five machine learning models using a voting-based ensemble. Furthermore, we developed an ensemble model that integrates a genetic algorithm to optimize voting weights with the weighted majority algorithm, further improving prediction performance. Experimental results demonstrated that the proposed method achieved an average performance improvement of 46.2% over OpenDrift. This research show significant potential to enhance the efficiency of maritime safety and rescue operations, offering a more adaptive and accurate solution for predicting drifter trajectories in various marine environments.

Cloud scheduling is a complex optimization problem balancing fast task execution for cloud users and efficient resource utilization for cloud operators. The requirements by both parties are usually limited by Service Level Agreements and Quality of Service constraints that define the level of provided service. Although many scheduling algorithms exist, the ability of nature-inspired metaheuristics to solve complex multiobjective optimization problems motivates their investigation in the context of cloud scheduling. This work evaluates the ability of modern Differential Evolution algorithm versions to schedule cloud jobs. The computational experiments are performed with a recent cloud scheduling dataset and demonstrate a large variance in the results obtained by different algorithms. Finally, is pointed out that cloud scheduling is a real-world constrained multiobjective optimization problem with a good potential to serve as a benchmark for nature-inspired metaheuristics.

Developing effective search paths to cover the movements of survivors or lost objects drifting in the ocean is critical for maritime rescue operations, which can save many lives. The goal of this study is to generate more efficient and realistic search paths while reducing execution time. A prior study used a memetic algorithm (MA) to develop search paths that consider particle drift movements, showing improved particle coverage compared to simple paths. However, the time required posed limitations for practical real-time applications. To overcome these limitations, we propose an improved approach that integrates surrogate models into the MA framework. We modify the objective function by incorporating probabilistic coverage, which reflects the uncertainty of locating drifting particles in real-world scenarios. Two encoding methods were applied and experiments were conducted on a 6×9 grid to evaluate the effects of model and encoding combinations. Among the combinations tested, the continued fraction regression model combined with one of the encoding methods achieved the best performance. Experimental results indicate that the proposed surrogate-assisted MA reduces execution time by 70% while maintaining a comparable performance. These findings suggest that the proposed approach has significant potential for real-time rescue operations.

The metabolic fluxes in cells are regulated by metabolites that bind to enzymes and modulate their activities. Metabolites can stabilize their own concentrations by exerting a negative feedback on their production pathways. Although metabolic networks have been studied extensively, many regulation arrows remain unknown. To model the costs and benefits of direct enzyme regulation, we apply multi-objective optimization with one loss function describing how regulation stabilizes the metabolic state against random perturbations and another loss function scoring the extra enzyme amounts required by regulation arrows. Using the number of arrows as a third objective for ease of interpretation, we study how activating and inhibiting arrows should be arranged in the system. Using an evolutionary multi-objective approach, simulating an evolution under biological trade-offs, we explore optimal arrow configurations. Our framework can also be used with other biological objectives, including optimal adaptation or information transmission in metabolic networks, to study their trade-offs with objectives such as energy or enzyme investment in cells.

Germany's Energy Transition aims to significantly reduce CO₂ emissions by 2045. This requires a substantial increase in the integration of renewable energies across the electricity, mobility and heating sectors. The decarbonization of the latter is primarily driven by municipal heat planning: Cities must outline strategies for incorporating more renewable energy sources. The city state of Hamburg (Germany's second largest city with approx. 2 million inhabitants) plans to expand its heating network, connecting new urban areas and decarbonizing supply through waste heat and large heat pumps. The Hamburg heat plan identifies areas that are well and not so well suited for district heating. For areas without access to district heating, alternative heating options must be explored. Our research analyzes conditions under which local heating networks are (more) viable vis-à-vis building-based solutions. We employ an adapted biased random-key genetic algorithm (BRKGA) utilizing geo-information from Hamburg and cost data for heating supply and networks. This paper shows the application of BRKGA to a new domain and contributes to the ongoing discourse on urban sustainable heating solutions.

Mathematical models can help to describe complex biological systems. In the case of sepsis, which is a dysregulated immune response to infection, mathematics can help shed a light on the immune dynamics and highlight the mechanisms that lead to septic results. However, the complexity underpinning biological systems and the difficulty of interpretation of experimental outputs, often make modellers reliant on standard prototype equation systems. We propose to overcome these limitations with a genetic programming informed approach to modelling. We aim to highlight the potential of this approach whilst demonstrating that genetic programming cannot simply replace modellers. Instead, traditional modelling and genetic programming can be combined, to capture the complexity of these systems and work synergistically towards an understanding of the underlying biological processes.

This study applies Evolutionary Algorithms (EAs) to optimize the profitability of a hybrid refueling network for conventional and electric vehicles. Three strategies are explored: reconfiguring existing stations, siting new ones, and combining both methods. A multiagent simulation models stakeholder interactions in a Spanish city, incorporating behavioral dynamics between users and operators. The approach features problem-specific objective functions, a compact encoding scheme, and a heuristic to reduce computational cost. Results show that small, strategically located mixed-use stations maximize profitability and support EV adoption.

The ETSAP-TIAM Model is a process-based optimisation model of the global energy system, integrated with a climate and economy model that explicitly represents detailed energy technology processes including generation, transmission, and end-use across sectors. It provides a tool to inform policy by examining the effects of policy changes on outcomes. However, the model is complex, large, and unwieldy. In this paper, we develop a suite of Genetic Programming Symbolic Regression (SR) surrogate models. The benefits are both interpretability and instant response of the new model to parameter changes. Considering both regression performance and model complexity, we compare a SR system with strong baselines, exploring different points on the performance—interpretability curve. Finally, we read and interpret several of our models.

Establishing profitable trading strategies in financial markets is a challenging task. While traditional methods like technical analysis have long served as foundational tools for traders to recognize and act upon market patterns, the evolving landscape has called for more advanced techniques. We explore the use of Vectorial Genetic Programming (VGP) for this task, introducing two new variants of VGP, one that allows operations with complex numbers and another that implements a strongly-typed version of VGP. We evaluate the different variants on three financial instruments, with datasets spanning more than seven years. Despite the inherent difficulty of this task, it was possible to evolve profitable trading strategies. A comparative analysis of the three VGP variants and standard GP revealed that standard GP is always among the worst whereas strongly-typed VGP is always among the best.

A novel evolutionary computation technique known as genetic network programming-based rule mining, which accumulates outcomes obtained throughout the evolutionary process, has been developed to discover sets of itemset (ItemSB) with statistically distinctive backgrounds. This method builds upon traditional association rules by expanding the consequent part to include statistical expressions, such as correlation coefficients. In this study, we propose a method to extend the statistical representation part of ItemSB from correlation between two variables to an approximate logistic function. The rule set obtained using the proposed method can be used to add probability prediction to class classification by introducing a functional treatment to rule-based class classification. By varying the values of the variables treated in the logistic function, the transition of the predicted probability can be obtained; the flexible rule representation of ItemSB enables the identification of the items that are responsible for the change in predicted probability, thereby improving the explanatory nature of the prediction. The validation results of the proposed method on a medical dataset show that the proposed method enables predictions that consider explanatory and individual characteristics.

Gas-solid fluidized beds are used in industry for fluid-solid processing, e.g., coating and mixing of particles. Fluidized beds are operated by driving a fluid flow through a collector of particles, leading to a chaotic motion of these particles. A control of the spatio-temporal variation of the fluid velocity at the inlet of the fluidized bed can achieve a prescribed pattern (the objective), thus controlling the fluidization. Our study proposes a repair algorithm to account for the suitable constraints for using hardware-in-the-loop. We evaluate the work for a single objective optimization, i.e., to maximize the fluidized bed expansion. Due to the hardware-in-the-loop feature, we focus on initialization methods to achieve a faster convergence towards the objective. We show that using evolutionary algorithms to control the inlet velocity profile in a fluidized bed using a suitable initialization approach, a control for a specific objective can be achieved.

Maritime accidents can cause significant damage to both human life and the environment. To respond quickly and effectively, accurate wind prediction is crucial. This study focuses on optimizing the weights of an ensemble voting model for wind data prediction using genetic algorithms (GAs). The GA-based approach significantly improved wind prediction accuracy by optimizing the weights of various models. Data from seven observation stations near South Korea was used, and the GA-based model outperformed the ECMWF High-Resolution model, achieving a 24.6% improvement in RMSE. This highlights the potential of GA in wind prediction models and its significant application in maritime accident response systems.

Automating part of enemy balancing may save precious resources for developers, allowing them to focus on more creative tasks, while also enabling developers to create enemies that cater to specific kinds of players. In this paper, we adapt the "Evolutionary Boss Improvement" (EBI) method to the DOOM game, modifying the Cyberdemon enemy. This increases the method's generality by testing its effectiveness in another game genre. By implementing the EBI pipeline with appropriate adaptations to the encoding, decoding, crossover and mutation algorithms, we were able to improve the fitness of our enemies, which was evaluated by having a set percentage of remaining health after testing with bots. We asked anonymous volunteers to play the game against either the original Cyberdemon or our modified version (evolved using EBI) and to fill a survey about their experience, allowing us to assess their opinions about the boss fight. The version each player fought was randomly selected when starting the game, making it a double-blind experiment. The results indicate we created an individual with a similar feel to the original, maintaining player satisfaction, whilst also requiring less manpower from the developer.

Omics data can contain predictive information of the onset of diseases and chronic conditions. Applying machine learning (ML) techniques to omics data is a promising venue of research, but domain data sets are typically high-dimensional and low-sample-size, presenting significant challenges to classic ML approaches. Another obstacle is the black-box nature of many ML algorithms, which prevents them from being deployed in medical practice. Symbolic regression (SR) is a possible solution to obtain human-interpretable models; but even equations cannot be easily understood, if they include hundreds or thousands of features. While feature selection can help reducing the number of features to be considered, most algorithms make unrealistic assumptions or bias the selection using a single classifier. In this work, we apply the Recursive Ensemble Feature Selection (REFS) algorithm, designed to avoid over-relying on a single ML model, with a modern SR algorithm, to obtain interpretable models predictive for different diseases, starting from real-world omics data. Experimental results for five different omics studies show that the completely open-source approach is competitive with the state-of-the-art in closed-source software. Comparing the same pipeline with REFS and more classic feature selection techniques shows that models created with REFS have a better performance.

Hyperspectral imaging has broad applications, particularly in Earth observation and remote sensing, due to its ability to provide large-scale, non-invasive environmental and agricultural monitoring. However, its high dimensionality and acquisition conditions pose challenges for data transfer, storage, and downstream analysis. Preprocessing algorithms are thus essential for preparing hyperspectral images for further analysis, but they rely on multiple hyperparameters, and their incorrect selection degrades the performance of machine learning models operating on the pre-processed imagery. To address this, we introduce genetic algorithms—both single- and multi-objective—for optimizing pre-processing in multi-target hyperspectral regression. Experiments on real-world hyperspectral data demonstrate that our approach significantly enhances the models for chlorophyll content estimation from hyperspectral images.

Cybersecurity refers to the practice of protecting hardware and software from cyberattacks, unauthorised access, theft, or damage and is becoming an increasing priority for organisations. A key question is the selection of measures (controls) to invest in to reduce the risk of a cybersecurity breach while keeping investments at a minimum. The contributions of this work are to (i) formulate this task as a constrained bi-objective problem, (ii) provide several realistic use cases varying in complexity for algorithm validation, and (iii) investigate the suitability of evolutionary multi-objective optimisation (in our case, MOEA/D) and an augmented epsilon-constraint approach (in CPLEX) to tackle the problem. We find that the augmented epsilon-constraint approach can solve the problem efficiently, capturing a diverse set of Pareto optimal solutions for each scenario. Although the performance of MOEA/D improves as the complexity of the problem increases, it is not able to compete with the augmented epsilon-constraint approach in terms of solutions found and reliability. We hope that the proposed problem and use cases will serve as an interesting test bed to benchmark optimisation algorithms and expand the problem formulation further.

This article proposes the use of connected and automated shuttles (CAS) as a transformative approach to public transportation, which can be also used for delivering parcels to pick-up/drop-off (PUDO) points, located close to bus stops. A multi-objective optimisation framework for CAS systems is designed, focusing on three critical dimensions: Quality of Service (QoS), Transit Network Design (TND), and User Travel Demand (UTD). Additionally, we aim to share passenger transport and last-mile delivery, taking advantage of empty places on shuttles to transport mail baskets optimally filled by parcels. A genetic algorithm is proposed to assign parcels to shuttles taking into account the parcels' size and destination, different shuttles' stops, and space available on them. Our results, obtained from the optimisation of urban transit scenarios, show the framework's applicability and its effectiveness, understanding the trade-offs between competing objectives as well as a reduction in the number of parcels to be delivered by the postal service.

Redundant or questionable states in sequential data can significantly undermine the reliability of data mining. An effective denoising process should adaptively filter these noisy states while preserving essential information, avoiding critical data loss (over-sanitization). The complexity of sequential data poses additional denoising challenges, yet research on adaptive denoising techniques is limited. We propose a novel MOEA-based approach that uses sequential attributes to guide denoising. By selectively incorporating states within sequences, our approach adapts fitness functions to filter noise. Our approach is validated on students' interactions with an Intelligent Tutoring System, our method effectively balances competing objectives and outperforms traditional denoising strategies.

The sixth generation (6G) networks promise transformative advancements in wireless communication, significantly enhancing spectral efficiency and supporting a variety of novel applications. This study investigates the configuration of Reconfigurable Intelligent Surfaces to assist communication efficiency within communication systems serving multiple single-antenna users. We address the multi-objective optimization challenges of balancing different metrics to achieve comprehensive system performance. A novel algorithm is then proposed, which integrates Pareto front grid decomposition with the reproduction operators of differential evolution. Experiments are conducted across various scenarios, particularly under different user density conditions. Numerical results demonstrate and validate the superior performance of the proposed algorithm compared to state-of-the-art multi-objective benchmarks across key metrics comprising Hypervolume and Inverted Generational Distance for practical applications.

An approach to autonomous network defense is proposed that utilizes an evolutionary strategy to optimize default heuristic agents. The default heuristic agent is used to impart knowledge regarding network architecture, i.e. what the key infrastructure and bottlenecks might be. Evaluation takes place using the TTCP CAGE Challenge 2 framework where there are green (normal user), blue (defense), and red (attack) team agents. Unlike the deep learning solutions that have dominated this challenge, we are able to demonstrate that competitive solutions can be evolved that transfer knowledge from a blue team default heuristic. The resulting combined blue team is able to place second relative to the original 17 entries submitted to the TTCP CAGE Challenge 2 competition while maintaining knowledge of the solution.

Classical neural network (NN) compression methods, such as NN pruning and distillation, focus on reducing the NN size. However, these methods often sacrifice accuracy in the process. To address this issue, we propose a novel NN refinement method based on symbolic regression called SR-R. At its core, SR-R employs a symbolic regression method based on Cartesian genetic programming to find a compact mathematical expression that accurately approximates the input-output relationship of a selected module within the NN. SR-R then replaces the targeted module with the discovered mathematical expression. Finally, SR-R fine-tunes the parameters of the remaining modules in the NN. Experiments are conducted on two types of NN benchmarks: multilayer perceptron NNs (MLP) and convolutional NNs (CNN). Experimental results show that, compared with NN pruning and NN distillation, SR-R can effectively reduce the number of NN parameters while maintaining or even enhancing inference accuracy.

Detecting and monitoring chronic wounds is crucial to assess their healing progress and optimize treatment strategies in clinical scenarios. Numerous studies explored chronic wound detection using digital approaches, but most of them operate under the unrealistic assumption that wounds are imaged in the controlled acquisition environment. To address this gap, we propose an approach for detecting chronic wounds using multimodal imaging, coupling a genetic algorithm to identify the most relevant features that contribute to wound assessment with downstream machine learning models. Pruning irrelevant (or even noisy) feature extractors can improve detection quality, and accelerate the entire process, being critical in time-constrained clinics. Our experiments showed that genetically evolved feature subsets allow to build wound detectors that outperform models trained over full feature sets.

Detecting methane in remotely-sensed hyperspectral images is a crucial task in environmental monitoring. It aids in identifying methane leaks and emissions, which is essential for mitigating their impact on the climate change. We tackle this challenge and propose an end-to-end and flexible approach for detecting and locating methane plumes in satellite hyperspectral images. It couples classic machine learning with a genetic algorithm to identify the most important image features that contribute to methane localization. We extract features from superpixels—locally-coherent image areas—and then perform feature selection to identify the most discriminative ones, pruning unnecessary (or even noisy) features. Our experiments performed over the large-scale methane dataset (STAR-COP) indicated that feature subsets optimized using a genetic algorithm allow us to build effective methane detectors that outperform supervised models trained over full feature sets. For reproducibility, we refer to our GitHub repository: https://github.com/smile-research/GeneticAlgorithms4MethaneDetection.git.

Density Functional Theory (DFT) is a widely adopted method in quantum chemistry for investigating the electronic structure of many-electron systems. However, the core Kohn-Sham (KS) equation of DFT contain exchange-correlation approximations that limit the accuracy of DFT calculations. To overcome this limitation, we focus on one-dimensional (1D) DFT and propose a data analytics approach for accurate modeling of the exchange-correlation terms. This approach involves the development of a neural architecture search framework, guided by multi-objective differential evolution (MODE) algorithm, to generate exchange-correlation potential (V_xc) models that are both highly accurate and computationally lightweight. Experimental results demonstrate that the V_xc model derived from this framework not only reduces the number of parameters but also significantly improves the accuracy of the KS equation in predicting the properties of 1D molecules, validating the effectiveness of the proposed method.

Analyzing spectral data is an effective and efficient way to estimate the nutrition of food products. However, spectral data are usually high-dimensional and noisy, which makes spectral data analysis challenging. Data augmentation is an effective method to enhance machine learning models in analyzing spectral data. However, most existing data augmentation methods are designed by human experts, which is tedious and requires extensive expertise. To improve the effectiveness of data augmentation and reduce the dependency on domain knowledge, this paper proposes a genetic programming method to design data augmentation methods automatically. The proposed genetic programming method mimics the real distribution and produces new data instances by adding offsets to the original data. We take a fish spectroscopic dataset as an example to verify the effectiveness of the proposed method. The empirical results show that the data augmentation method designed by genetic programming has a very competitive performance compared to the state-of-the-art manually designed ones and provides good interpretability.

This paper proposes a multimodal ant colony optimization (M-ACO) framework by integrating niching techniques to find multiple different routes for autonomous underwater vehicles (AUV) in complex environments. Unlike existing studies focusing on finding only one optimal route for AUV, M-ACO tries to find multiple different routes with as high quality as possible but meeting a dissimilarity threshold. To this end, M-ACO divides the ant colony into niches with each niche responsible for finding one or several routes. Then, an optimal route preservation strategy is devised to only store those routes whose dissimilarity exceeds the given threshold but fitness has a small discrepancy from the global best route. To validate the effectiveness of M-ACO, this paper instantiates it with five classical ACOs, namely ant system (AS), elitist AS (EAS), max-min AS (MMAS), rank-based AS (ASrank), and ant colony system (ACS). Then, experiments are conducted on different underwater environments with the requirements of finding three optimal routes. The experimental results reveal that MMAS and ACS are the most effective in finding multiple routes for AUV. Between them, MMAS is much better regarding the number of the found optimal routes, while ACS is much better concerning the quality of the found optimal routes.

Particle Swarm Optimization (PSO) is a population-based optimization algorithm inspired by the social behavior of birds, with widespread applications in diverse domains. While PSO demonstrates rapid convergence and resilience against local minima, its performance is susceptible to parameter values and prone to stagnation in complex search spaces. This paper introduces a Hybrid Dynamic Tournament Topology Particle Swarm Optimization with Parameter Independence (HDTT-PSO-PI), integrating a novel velocity update equation and dynamic tournament topology for neighbor selection. The velocity formulation replaces original parameters ω, and ϕ of the DTT-PSO algorithm with α, β, and cs, enabling independent control of particle dynamics and better adaptability across problem landscapes. The HDTT-PSO-PI algorithm further enhances performance by employing genetic operators for increased solution diversity. A comprehensive evaluation of benchmark functions demonstrates the superior performance of HDTT-PSO-PI compared to 15 state-of-the-art evolutionary and swarm algorithms. Parameter optimization experiments highlight the algorithm's robustness across a wide range of settings, significantly improving performance and solution accuracy. These findings confirm the HDTT-PSO-PI algorithm as a promising approach for solving complex, unimodal, and multimodal optimization problems. The results suggest future research opportunities in hybridization and parameter adaptation strategies for swarm-based algorithms.

Mixed-variable optimization problems (MVOPs), involving both continuous and discrete decision variables, are frequently encountered in practical engineering design. The presence of mixed decision variables increases the complexity of the search space, making these problems difficult to solve. Furthermore, recent societal trends have led to an increase in the scale of design targets and the sophistication of design requirements, resulting in a higher number of design and behavioral variables. Consequently, MVOPs are expected to become more complex and large-scale. Particle Swarm Optimization (PSO), developed by Kennedy et al., is widely recognized for its simplicity and high convergence performance. Although originally designed for continuous variables, PSO has been successfully applied to mixed-variable problems, demonstrating its effectiveness. However, most existing PSO approaches for MVOPs focus primarily on handling mixed variables, with applicability limited to problems involving a relatively small number of design variables. This paper presents a novel PSO-based approach to address large-scale MVOPs. The proposed method utilizes three types of dimensionality reduction: one for continuous variables, one for discrete variables, and one for mixed variables, effectively mitigating the complexity of large-scale mixed-variable problems. The capabilities and characteristics of the proposed approach are illustrated through test problems and an engineering design case study.

Swarm intelligence effectively optimizes complex systems across fields like engineering and healthcare, yet algorithm solutions often suffer from low reliability due to unclear configurations and hyperparameters. This study analyzes Particle Swarm Optimization (PSO), focusing on how different communication topologies—Ring, Star, and Von Neumann—affect convergence and search behaviors. Using an adapted IOHxplainer, an explainable benchmarking tool, we investigate how these topologies influence information flow, diversity, and convergence speed, clarifying the balance between exploration and exploitation. Through visualization and statistical analysis, the research enhances interpretability of PSO's decisions and provides practical guidelines for choosing suitable topologies for specific optimization tasks. Ultimately, this contributes to making swarm-based optimization more transparent, robust, and trustworthy.

This paper proposes a hybrid-surrogate-assisted particle swarm optimization (HSAPSO) for high-dimensional expensive optimization problems (EOP) being inherently complex and computationally costly. To address the challenge that a single surrogate model may struggle to provide efficient exploration through the entire evolutionary process, HSAPSO develops strategies consisting of adaptive surrogate selection and hyperparameter estimation. Initially, a linear surrogate facilitates exploration with limited data, later switching to a radial basis function (RBF) surrogate for nonlinear approximation as data grows. Maximum likelihood estimation (MLE) fine-tunes RBF hyperparameters ensuring high accuracy and robustness. Social learning particle swarm optimization with progressive sampling balances exploration and exploitation. Benchmark tests show HSAPSO outperforms four state-of-the-art, demonstrating its effectiveness for high-dimensional expensive optimization.

We study the fractional orienteering problem with mandatory nodes, which aims to design the optimal tourist trip that maximizes the ratio of time spent at places of interest to time spent traveling. Some places of interest are mandatory, while others are optional. Therefore, the problem involves both selecting the optimal set of places to visit and determining the best route between them. We demonstrate how this problem can be efficiently solved using a modified ant colony optimization algorithm. This approach has potential applications in various mobile apps that assist tourists in planning personalized itineraries.

In recent years, swarm intelligence optimization (SIO) algorithms have developed rapidly and are widely applied, particularly in classification tasks. The challenge of imbalanced data is a critical issue in classification, as it negatively impacts classification performance. Resampling techniques have been proposed to address this problem, but their classical approaches leave room for improvement, making applying SIO algorithms to resampling an effective solution. Optimizing resampling results is generally considered a combinatorial optimization process. Therefore, few continuous SIO algorithms have been applied to find the optimal resampling result, making it necessary to propose a unified application framework for them. This paper proposes the Resampling Framework Based on Swarm Intelligence Optimization for Imbalanced Data Classification (R-SIOIC). R-SIOIC supports the application of any continuous SIO algorithm for resampling. It optimizes multiple resampling results in each iteration, ultimately producing the optimal resampling result. This paper selects three continuous SIO algorithms to evaluate the effectiveness of R-SIOIC. The experiments used 13 imbalanced datasets, and compared the results with those from 13 baseline methods and the original data input without resampling. R-SIOIC outperformed all other methods on 11 out of 13 datasets for G-mean and 12 out of 13 datasets for m-AUC, demonstrating its superior performance.

This paper builds a Multiple Tourists Route Planning (MTRP) model by incorporating the traveling cost between scenic spots and the ticket fees of the scenic spots along with the budgets of tourists. The aim of this model is to identify optimal routes for multiple tourists that maximize the traveling experience scores of the multiple tourists and at the same time minimize their traveling experience differences under the given budgets. To effectively solve this problem, this paper adapts the five classical ACOs, namely Ant System (AS), Elitist AS (EAS), Rank-based AS (AS_rank), Min-Max AS (MMAS), and Ant Colony System (ACS) by introducing a new route construction method based on scenic spot pre-selection. Further, a new local search strategy incorporating 2-opt and scenic spot insertion is designed to refine the quality of the found multiple routes. Abundant experiments have been executed on various MTRP instances with different numbers of scenic spots and different numbers of tourists along with different settings of the budgets. The experimental results reveal that the five adapted ACOs are very promising for solving the new MTRP problem and among them. ACS comprehensively performs the best.

Using a limit theorem describing the maximum of independent identically distributed random variables (hereinafter r.v.). in terms of Gumbel distribution, we obtain two claims about the runtime of the (1 + (λ,λ)) GA_μ, which is a modification of the (1 + (λ,λ)) GA from (Doerr, Doerr, Ebel, 2015). The modification consists in starting the (1 + (λ,λ)) GA from a best individual out of μ = n/ln n randomly sampled individuals. The population size λ = ω(1) is deterministic.

In the case of OneMax fitness, limit theorems give us asymptotic distribution of fitness increment in the stage of mutation and crossover of the (1 + (λ,λ)) GA_μ, which leads to [EQUATION] bound on the expected runtime, given suitable parameters settings.

In the case when the fitness is given by OneMax with random disturbances of order [EQUATION] (a "frozen noise"), using limit theorems, we show that with probability tending to 1, the runtime of the (1 + (λ,λ)) GA_μ is at most [EQUATION] as n → ∞, if the disturbance probability at each point is ρ2^-n, ρ = O(n^β), ^β ∈ (0, 1).

The relationship between evolution, which drives fitness enhancement, and ageing, which leads to a decline in fitness, remains an unresolved puzzle in biology. Intuitively, random changes—the primary mechanism of evolution—are expected to be more harmful than beneficial, causing widespread detrimental effects on fitness. The Evolvable Soma Theory of Ageing (ESTA) proposes that ageing results from the cumulative impact of these harmful effects, which primarily cause bodily damage, while a few lead to beneficial adaptations that evolution can harness. This work compares ESTA with mutation accumulation, antagonistic pleiotropy, and disposable soma theories, collectively referred to as the Standard Evolutionary Ageing Theory (SEAT). While SEAT views ageing as a byproduct of diminishing evolutionary pressure, ESTA posits that ageing represents in essence evolution in action. Simulations are performed using a developmental system where genes are linked to onset values that determine their expression, and demonstrate that ESTA achieves superior evo-devo efficiency compared to SEAT. Specifically, our results highlight that the core features of ESTA—fitness evaluation distributed across multiple steps, onset-dependent mutation rates and evolvable gene onsets—are critical for its enhanced performance.

Selective pressure is an evolutionary concept encompassing any factor that causes differential survival and reproduction among individuals within a population. In biological evolution, the intensity of SP largely depends on environmental factors, such as resource scarcity and the favorability of physical conditions. However, it can also be directly influenced by the organisms themselves, for instance, through phenomena like niche construction. In the computational domain, the concept of selective pressure is primarily used within evolutionary computation, where it is typically defined exogenously via a selection operator and its associated hyperparameters. Alternatively, selection can be made self-adaptive, with its level emerging cumulatively from the actions (or "votes") of the individuals. In this paper, we frame a simple form of such a self-adaptive mechanism, based on truncation, as a game in the game-theoretical sense. We then perform simulation experiments using a simple genetic algorithm to investigate the properties of the proposed model.

Evolutionary Algorithms (EAs) have been found successful in the solution of a wide variety of optimization problems. However, EAs are unconstrained search techniques. Thus, incorporating constraints into the fitness function of an EA is an open research area.

Multi-objective evolutionary algorithms (MOEAs) are well established in their application and feature an active field of research. However, when it comes to developing, testing and comparing these algorithms, usually only their performance in the objective space is considered. This results in a lack of understanding when it comes to the dynamics of MOEAs in the search space. The focus of this work is to better understand the behavior of MOEAs by studying its population dynamics. We aim towards finding out which individuals from the initial population contribute in the search towards the Pareto-front. For this, we use the traceable evolutionary algorithm, which allows us to trace the genetic materials and their influence over the evolutionary process. Defining good genetic material for algorithms with more than one objective, however, proves difficult compared to the single-objective case. We evaluate the effects of different known optimal solutions both on the performance and differences in search behavior of MOEAs. Furthermore, we evaluate the population dynamics for different test problems, algorithms, and seed individuals on different locations on the Pareto-front.

In this paper we investigate the fitness landscape and evolutionary dynamics of typical genetic algorithms, applied to a well-known problem. For certain settings, we observe that the population can "evolve to extinction", that is after fast progress over early generations, the population fitness can suddenly drop and never recover. We investigate the settings which give rise to this and show how to avoid it in practice, e.g. by varying selection pressure. However our focus is on understanding the root cause. We identify that the cause is a combination of (1) non-uniform initialisation, leading to evolutionary dynamics driven by a diffusion process; and (2) a cliff-edge landscape in which invalid individuals are neighbours of the global optimum. Based on this, we identify other scenarios where these properties can occur. In particular, we identify that non-uniform initialisation is natural in asymmetric search spaces, which we define as search spaces lacking the property of vertex transitivity.

Evolution Strategies (ESs) are effective randomized heuristics for black-box numerical optimization, known for advanced step-size adaptation and invariance to function transformations and decision space rotations. Typically used for continuous optimization, ESs have been adapted for integer and mixed-integer problems using independent multivariate or truncated continuous mutations. This study explores ESs for nonlinear integer optimization in unbounded search-spaces, based on Rudolph's 1994 convergence and unbiasedness principles, albeit with their application limited to independent Double-Geometric (DG) distributions. In this paper, we extend it and propose a procedure for generating correlated DG-mutations. We hypothesize that such mutations are suitable for integer spaces and can enhance nonseparable problem-solving. To begin, we use the 1/5th success-rule to test the DG mutation distribution in a minimal, elitist single-parent scenario. Then, we validate our hypotheses on an unconstrained quadratic integer test-suite across various dimensions. We show that replacing the conventional Truncated Normal distribution with the DG distribution usually achieves better outcomes in both separable and nonseparable scenarios.

The pdfo library by Tom M. Ragonneau and Zaikun Zhang makes the five derivative-free solvers BOBYQA, COBYLA, LINCOA, NEW-UOA, and UOBYQA—originally written by Michael J. D. Powell—available in Python. In this paper, we are comparing their performance on the bbob test suite with three other solvers from the COCO data archive: CMA-ES from pycma, SLSQP and BFGS from scipy. We also compare the original solvers, written by Powell in Fortran 77, with the current pdfo versions, which saw multiple bug fixes and code improvements by Ragonneau and Zhang.

For the latter comparison, we do not see large effects on performance between the Fortran 77 version and the current pdfo version. The only notable exception is the Bent Cigar function where we observe differences by a factor of 2–5 for BOBYQA, LINCOA, and NEWUOA. Compared to the other baseline algorithms, BOBYQA, LINCOA and NEWUOA perform very similarly over all bbob functions, being about a factor of 5 slower than SLSQP and BFGS while UOBYQA—as the best-performing pdfo solver—outperforms SLSQP and BFGS for larger budgets when compared over all 24 bbob functions. The linear surrogate of COBYLA, on the contrary, is clearly worse over all functions than the other algorithms.

UOBYQA, short for Unconstrained Optimization By Quadratic Approximation, is one of the well-known solvers derived and implemented by Michael J. D. Powell. In each step, the algorithm builds a quadratic surrogate of the objective function, interpolating quadratically many points for which the true function values are known. The model is optimized within the so-called trust region and the resulting solution is evaluated next. Adaptation of the trust region radius allows for fast convergence on a wide range of (noiseless) functions without the need for derivatives.

In this workshop paper, we investigate the effect of (frozen) nonnegative, i.e., worsening noise on UOBYQA with varying probability of solutions being affected by the noise. To this end, we use the COCO platform and its newest addition, the noiser, applied to the classical bbob functions. The numerical benchmarking experiments showcase that UOBYQA is negatively affected by the noise, but surprisingly little over a wide range of noise strengths for some of the bbob functions.

We investigate the impact of outlier noise on the performance of the scipy.optimize implementation of the quasi-Newton BFGS solver. Using the BBOB testbed corrupted with positive—making solution look worse than what they are—or negative—making solutions look better than what they are—outliers simulated with a Cauchy distribution with a probability p, we analyze how the performance is impacted. We show that the impact of positive or negative noise outliers is almost symmetric, that on simple problems BFGS has some robustness to noise, and that for ill-conditionned problems BFGS appears to fail when p or the dimension is too high.

We investigate the robustness to noise and outliers of the Nelder-Mead derivative-free optimization algorithm implemented in the scipy.optimize Python library. Using the noisifier module from the COCO platform, we investigate the impact of adding or subtracting a positive Cauchy noise to the function value with a certain probability p. This probability is varied from 0 till 0.4 allowing to appraise the impact of the noise. We find that Nelder-Mead has highly asymmetric performances with respect to adding a positive noise (i.e. degrading artificially possibly good solutions) or adding a negative noise (i.e. making possibly bad solutions appear good). When adding positive noise, Nelder-Mead shows some robustness in low dimensions (≤ 5). However adding negative noise has very detrimental consequences for the performances of Nelder-Mead, even with a low value of p or in low dimension.

We benchmark a non-elitist CMA-ES algorithm on the BBOB testbed with additive and subtractive noise. In particular, we consider the case where re-evaluated solutions produce the same observed function value. As a comparison, we benchmark a version of CMA-ES with resampling, which aims at reducing the effective noise level. We find CMA-ES to be more sensitive to subtractive noise than to additive noise in dimensions 2, 3, 5, 10, 20 and 40. Resampling for CMA-ES appears to be detrimental for low noise levels, while it is beneficial for high noise levels.

The (1+1) Limited Memory Matrix Adaptation Evolution Strategy, (1+1)-LM-MA-ES, is a minimal elitist variant of the population-based LM-MA-ES, an evolution strategy for efficient optimization in high-dimensional search spaces. We benchmark the algorithm on the large-scale Black-Box Optimization Benchmarking (BBOB) suite of the Comparing Continuous Optimizers (COCO) framework.

We find that the method works well on many unimodal problems. Despite a simple restart mechanism, performance on most multimodal problems remains unsatisfactory. This is expected due to the elitist nature and the minimal population size of one.

In this paper, we propose a comparative benchmark of seven multiobjective optimization methods from the PlatEMO platform using the COCO framework for performance assessment and the bi-objective test suite bbob-biobj. A mix of both standard methods and newer techniques from various sources that were implemented in the PlatEMO framework was selected for the comparison. We find that although the selected methods were overall mostly inferior to the top-performing methods from the bbob-biobj data archive, they performed quite well in certain computational budget ranges and specific function subgroups.

The CMA-ES-PDM is a variant of the CMA-ES algorithm designed for solving mixed-integer black-box optimization (MI-BBO) problems. This algorithm uses probability distribution models, constructed during the search process, to generate the integer components of some candidate solutions. Recently, several novel techniques have been proposed for the CMA-ES-PDM algorithm to enhance its performance. First, the discrete distribution model for the integer variables is fitted to a normal distribution. This fitted distribution is then further smoothed using an initial normal distribution that closely resembles a uniform distribution over the search domain of integer variables. Second, when the upper bound of the probability within the model is reached for certain integer variables, the model is used exclusively for sampling the integer components of the candidate solutions. In this work, we evaluate some improved variants of the CMA-ES-PDM on the bbob-mixint test suite, which includes problems with various properties for MI-BBO. The experimental results show that the variants of CMA-ES-PDM perform well on classes of separable functions, low or moderately conditioned functions, and highly conditioned unimodal functions. Notably, the proposed algorithms outperform other methods on some specific functions.

Rather than obtaining a single good solution for a given optimization problem, users often seek alternative design choices, because the best-found solution may perform poorly with respect to additional objectives or constraints that are difficult to capture into the modeling process. Aiming for batches of diverse solutions of high quality is often desirable, as it provides flexibility to accommodate post-hoc user preferences. At the same time, it is crucial that the quality of the best solution found is not compromised.

One particular problem setting balancing high quality and diversity is fixing the required minimum distance between solutions while simultaneously obtaining the best possible fitness. Recent work by Santoni et al. [arXiv 2024] revealed that this setting is not well addressed by state-of-the-art algorithms, performing in par or worse than pure random sampling.

Driven by this important limitation, we propose a new approach, where parallel runs of the covariance matrix adaptation evolution strategy (CMA-ES) inherit tabu regions in a cascading fashion. We empirically demonstrate that our CMA-ES-Diversity Search (CMA-ES-DS) algorithm generates trajectories that allow to extract high-quality solution batches that respect a given minimum distance requirement, clearly outperforming those obtained from of-the-shelf random sampling, multi-modal optimization algorithms, and standard CMA-ES.

This paper presents BEACON, a novel methodology for generating bi-objective benchmark problems with explicitly controlled correlations in continuous spaces. Although numerous benchmark problems exist, continuous benchmarks lack systematic mechanisms to control objective correlations, critical in real-world optimisation. Our approach utilises Gaussian Process samples approximated via Random Fourier Features and a Cholesky-based correlation transformation to generate problems with tunable correlation values ranging from perfectly negative to perfectly positive. Experiments with three popular multi-objective evolutionary algorithms (NSGA-II, SMS-EMOA, MOEA/D) across varying correlation levels and decision space dimensions reveal that algorithm performance depends on the interplay between correlation structure and dimensionality rather than either factor in isolation. Our framework bridges the gap between discrete benchmarks with correlation control and continuous benchmarks without it, enabling systematic study of correlation effects on optimisation dynamics and supporting the development of algorithms that can adapt to different correlation structures found in real-world problems.

Optimal Mixing (OM) is a variation operator that integrates local search with genetic recombination. EAs with OM are capable of state-of-the-art optimization in discrete spaces, offering significant advantages over classic recombination-based EAs. This success is partly due to high selection pressure that drives rapid convergence. However, this can also negatively impact population diversity, complicating the solving of hierarchical problems, which feature multiple layers of complexity. While there have been attempts to address this issue, these solutions are often complicated and prone to bias. To overcome this, we propose a solution inspired by the Gene Invariant Genetic Algorithm (GIGA), which preserves gene frequencies in the population throughout the process. This technique is tailored to and integrated with the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA), resulting in GI-GOMEA. The simple, yet elegant changes are found to have striking potential: GI-GOMEA outperforms GOMEA on a range of well-known problems, even when these problems are adjusted for pitfalls - biases in much-used benchmark problems that can be easily exploited by maintaining gene invariance. Perhaps even more notably, GI-GOMEA is also found to be effective at solving hierarchical problems, including newly introduced asymmetric hierarchical trap functions.

Over the years, MOEA/D has proven to be a highly effective and efficient algorithm for solving complex problems. Consequently, several studies have focused on extending MOEA/D to address constrained multi-objective optimization problems. In this article, we introduce a dynamic penalty function into the MOEA/D framework to handle these constraints. This penalty function is based on the method of annealing penalties, modified to exhibit linear behavior when interacting with feasible and infeasible solutions during the search process. The proposed approach enables MOEA/D to manage constraints effectively. To assess the performance of our method, we evaluated it on the well-known complex problems from the CEC'2009 benchmark set, while comparing it gainst several state-of-the-art algorithms. Our empirical results show that the proposed method delivers competitive solutions and, in some cases, outperforms the MOEAs included in the comparative study.

In the context of eXplainable Artificial Intelligence (XAI), describing the rationale behind a Machine Learning (ML) model's decisions is crucial to user understanding and acceptability. One way to facilitate this is through visualization of the model's behavior and its resulting decisions. In this paper, we present a novel Visual-based XAI (vXAI) framework that co-designs the model with its graphical representation. Specifically, we consider a training phase in which a classification task is solved separately on two training datasets. For each dataset, we select the best among different trained classifiers, on which we then perform feature selection. Next, visualizations of the classifiers' decision maps are presented to users, who rank them based on clarity of explanation. Interactive Constrained MAP-Elites is then used to optimize an aggregate score that weighs five visual metrics inspired by Gestalt cognitive principles, which all correlate with a clearer visual understanding of the model's decisions. The learned weights are then used to predict the clearest visualization on three unseen datasets. Finally, an end-user evaluation conducted through questionnaires with a sample of 36 individuals with different backgrounds shows that users agree that the visual explanations help to understand (and detect sources of, e.g., bias in) the classifiers' decisions.

Machine learning (ML) has been playing a crucial role in drug discovery, mainly through quantitative structure-activity relationship models that relate molecular structures to properties, such as absorption, distribution, metabolism, excretion, and toxicity (ADMET) properties. However, traditional ML approaches often lack customisation to a particular biochemical task and fail to generalise to new biochemical spaces, resulting in reduced predictive performance. Automated machine learning (AutoML) has emerged to address these limitations by automatically selecting the suitable ML pipelines for a given input dataset. Despite its potential, AutoML is underutilised in cheminformatics, and its decisions often lack interpretability, reducing user trust - especially among non-experts. Accordingly, this paper proposes an evolutionary AutoML method for biochemical property prediction that outputs an interpretable model for understanding the evolved ML pipelines. It combines grammar-based genetic programming with Bayesian networks to guide search and enhance the searched pipelines' interpretability. The evaluation on 12 benchmark ADMET datasets showed that the proposed AutoML method obtained similar or better results than three existing methods. Additionally, the interpretable Bayesian network identified, among the ML pipelines' components generated by the AutoML method (i.e. components like biochemical feature extraction methods, preprocessing techniques and ML algorithms), which components affect the ML pipelines' predictive performance.

Transport administrators make decisions about road infrastructure and traffic management that significantly impact people's lives. To improve efficiency, decision makers complement their expertise with the automated insight afforded by robust and reliable computational models of traffic. To produce such models, we propose an innovative intelligent algorithm that combines Symbolic Regression with Transfer Learning and Neural Networks. The algorithm learns historical and real time traffic patterns from several areas of the road network and transfers that knowledge to the location where a prediction is needed (i.e., the target zone), by injecting it into the model trained on local data. We enhanced our evolutionary algorithm with a Deep Learning component that automates the selection of areas to transfer knowledge from (i.e., the source zones). Its role is to identify those regions of the road network where pretraining models significantly increases predictive accuracy at target locations, providing decision makers with reliable foresight into traffic dynamics which is conducive to sounder road management strategy. Preliminary experiments show our approach is more likely to identify adequate transfer learning sources than algorithm variants where source selection is manual and, respectively, performed by a standard Artificial Neural Network.

Many real-world optimization problems are black-box optimization (BBO) problems. In the last decades, various algorithms have been designed to solve the complex BBO problems. These algorithms demonstrate great performance complementarity in practice, which means that different algorithms outperform on different problem instances. Consequently, how to realize Algorithm Selection (AS) emerges to be an important problem, which has attracted considerable attention. Unfortunately, despite the various methods proposed by researchers, including classification, regression, and ranking, there is still no consensus on which specific method is superior. To pave the researches of algorithm selection in the community, in this work, we employ Exploratory Landscape Analysis (ELA) for feature extraction and neural network as the selection model to study the effectiveness of different algorithm selection approaches. We implement various formulation methods and conduct extensive experiments to analyze their strength and weakness.

Our results reveal that classification-based approaches have significant advantages on selection accuracy, while regression-based approaches have better overall performance on the metrics. Meanwhile, the methods that utilize order information can generally serve as a compromise between classification-based methods and regression-based methods. For the convenience of reproduction and following works, we open-source our code at https://zenodo.org/records/14877548.

The velocity update function in Particle Swarm Optimization (PSO) governs the movement of particles and significantly impacts algorithm performance. Numerous variants of the PSO velocity update function have been proposed, ranging from manually designed rules based on heuristic modifications to functions evolved through evolutionary algorithms. Among the latter, approaches based on Genetic Programming (GP) have been used to generate symbolic velocity expressions. However, most existing GP-based methods focus on optimizing performance on specific benchmark functions, with limited emphasis on generalization. This paper introduces a method for evolving velocity update functions using tree-based GP, with a focus on generalization across heterogeneous optimization problems. Each GP individual represents a velocity function that maps particle-level and swarm-level descriptors to a velocity vector. Experiments are conducted on shifted and rotated functions from the CEC 2005 benchmark suite across varying dimensionalities and evaluated on a different set of benchmark functions. Results indicate that evolved functions can outperform the standard PSO update rule and generalize to previously unseen problems and on different dimensionalities. Furthermore, the best evolved solutions share common structures and dynamic behaviors.

In this paper the idea of automatic improvement of existing heuristic optimization algorithms using genetic programming is investigated. In particular, the Push genetic programming system is used to generate new local search heuristics for the multi-swarm quantum swarm optimization method using the generalized moving peaks benchmark. The best designed heuristic is then applied to a more advanced dynamic optimizer, the adaptive multi-population particle swarm optimization algorithm. The results indicate that the generated heuristic, being unlike any known, allows significant improvement of algorithm performance on most of the test problems of the CEC 2025 competition on dynamic optimization generated by generalized moving peaks benchmark.

It is easy to point out why a method should not be a black box, but it is hard to define what would make it sufficiently transparent.

In more practical terms, the aims behind explainability are not commonly agreed upon, and evaluating a novel XAI method is challenging. This is especially true in the case of explanations relating to metaheuristics, since much of the XAI literature focuses on machine learning, whereas this work is of particular interest to the evolutionary computation community.

This paper will discuss the design of a user study to investigate if our explanatory material is useful to a user working with an optimization problem solved by a metaheuristic.

The participants are presented with the solution produced by the algorithm and are tasked to modify it to satisfy new constraints. The resulting fitness of the new solutions is recorded, and additionally the users answer questions about their trust in the algorithm and in their decision.

While the study is in its early stages, preliminary results show that the users found our explanations helpful.

In Symbolic Regression (SR), achieving a proper balance between accuracy and interpretability remains a key challenge. The Genetic Programming variant of the Gene-pool Optimal Mixing Evolutionary Algorithm (GP-GOMEA) is of particular interest as it achieves state-of-the-art performance using a template that limits the size of expressions. A recently introduced expansion, modular GP-GOMEA, is capable of decomposing expressions using multiple subexpressions, further increasing chances of interpretability. However, modular GP-GOMEA may create larger expressions, increasing the need to balance size and accuracy. A multi-objective variant of GP-GOMEA exists, which can be used, for instance, to optimize for size and accuracy simultaneously, discovering their trade-off. However, even with enhancements that we propose in this paper to improve the performance of multi-objective modular GP-GOMEA, when optimizing for size and accuracy, the single-objective version in which a multi-objective archive is used only for logging, still consistently finds a better average hypervolume. We consequently analyze when a single-objective approach should be preferred. Additionally, we explore an objective that stimulates re-use in multi-objective modular GP-GOMEA.

Real-world problems are often dependent on multiple data modalities, making multimodal fusion essential for leveraging diverse information sources. In high-stakes domains, such as in healthcare, understanding how each modality contributes to the prediction is critical to ensure trustworthy and interpretable AI models. We present MultiFIX, an interpretability-driven multimodal data fusion pipeline that explicitly engineers distinct features from different modalities and combines them to make the final prediction. Initially, only deep learning components are used to train a model from data. The black-box (deep learning) components are subsequently either explained using post-hoc methods such as Grad-CAM for images or fully replaced by interpretable blocks, namely symbolic expressions for tabular data, resulting in an explainable model. We study the use of MultiFIX using several training strategies for feature extraction and predictive modeling. Besides highlighting strengths and weaknesses of MultiFIX, experiments on a variety of synthetic datasets with varying degrees of interaction between modalities demonstrate that MultiFIX can generate multimodal models that can be used to accurately explain both the extracted features and their integration without compromising predictive performance.

Evolutionary computation (EC) methods are effective optimisation algorithms, but their random nature and sensitivity to noise make their behaviour difficult to interpret, limiting real-world use. This paper introduces the novel visualisation tools Noisy Local Optima Networks (Noisy LONs) and Noisy Search Trajectory Networks (Noisy STNs) to illustrate algorithm behaviours and fitness landscapes affected by noise. We evaluated (1+1)-EA, UMDA, and PCEA on the OneMax and Knapsack combinatorial optimisation problems with additive Gaussian noise in fitness evaluations. Results show these visualisations can identify how noise affects algorithm performance, solution paths, and transitions between optima, aiding the explanation of why algorithms may succeed or fail in noisy environments. Further work should improve the clarity and scalability of visualisations to support application to a wider range of problems and noise types, as well as further investigate the predictive power of visualisation features.

Robustness is emerging as a key issue in modern AI systems for computer vision, robotic manipulation, and other domains. For any such system that interacts with objects in the environment, it is important to generate objects that become progressively more adversarial and complex with each iteration, as in curriculum learning, in a manner agnostic to the particular processing methods used by the AI system. We present a data generator of voxel-based 3D adversarial object geometries for training robotic manipulators and other AI systems, which operates independently of any particular visual encoding/decoding pipeline. Our novel approach uses genetic algorithms and can generate arbitrarily many samples, bounded only by the user-specified voxel resolution. In the particular application area of robotic grasping, the success of our approach is demonstrated in terms of the number of adversarial objects generated, how difficult they are to grasp, and how similar they are to more easily graspable objects.

Generative adversarial networks (GANs) are powerful generative models but remain challenging to train due to pathologies such as mode collapse and instability. Recent research has explored co-evolutionary approaches, in which populations of generators and discriminators are evolved, as a promising solution. This paper presents an empirical analysis of different coevolutionary GAN training strategies, focusing on the impact of selection and replacement mechanisms. We compare (μ, λ), (μ+λ) with elitism, and (μ+λ) with tournament selection coevolutionary schemes, along with a non-evolutionary population based multi-generator multi-discriminator GAN baseline, across both synthetic low-dimensional datasets (blob and gaussian mixtures) and an image-based benchmark (MNIST). Results show that full generational replacement, i.e., (μ, λ), consistently outperforms in terms of both sample quality and diversity, particularly when combined with larger offspring sizes. In contrast, elitist approaches tend to converge prematurely and suffer from reduced diversity. These findings highlight the importance of balancing exploration and exploitation dynamics in coevolutionary GAN training and provide guidance for designing more effective population-based generative models.

This article presents multiobjective evolutionary approaches for searching the latent space of Generative Adversarial Networks for human face generation, considering similarity, gender, and race attributes. The problem is relevant to address and improve the robustness of automatic recognition systems. Three variants of Evolutionary Strategy optimization are proposed and compared using multiobjective optimization metrics, quality of generated images, and capability of deceiving the recognition system. Results indicate that the enhanced version of the hybrid evolutionary strategy using an adaptive grid to keep and promote diversity computes the most accurate solutions and proper coverage of the Pareto front. The outcomes of the research hold practical significance in enhancing the resilience of facial recognition systems.

This paper explores a novel approach to generative image creation by evolving prompt embeddings—the internal conditioning tensors used by diffusion models—rather than optimizing prompt text. Using SDXL-Turbo and a real-valued Genetic Algorithm within an Island Model setup, distinct artistic styles are assigned to separate islands, which evolve independently and interact via migration to stimulate stylistic influence.

The goal is not to optimize a fixed objective but to explore the prompt embedding space in an open-ended manner. Evolution is guided by the Aesthetics Predictor V2 to maintain baseline visual quality, while selection pressure is kept intentionally low to preserve diversity.

Image-based results demonstrate how the embedding space is traversed over generations, producing varied and sometimes unexpected combinations of artistic traits. Outputs are visualized through PCA and UMAP projections, and ancestry tracking highlights stylistic evolution. All experiments are reproducible via an open-source Jupyter Notebook accompanying this paper. The method shows that evolutionary algorithms can explore embedding spaces in a structured, interpretable way—enabling creative image generation beyond manual prompt engineering.

In this paper, we introduce pyHMS, a comprehensive open-source Python implementation of the Hierarchic Memetic Strategy (HMS) algorithm, designed to address complex multimodal optimization problems. HMS employs a tree-like structure where multiple populations managed by different metaheuristics operate with limited communication, enhancing solution diversity while balancing exploration and exploitation through hierarchical organization. Our implementation consolidates various HMS advancements from the literature and in some cases provides expanded versions of what was presented. The code architecture is modular and easily extendable, supporting both a high-level interface for practitioners and detailed control for researchers, facilitating experimentation with novel configurations and hybridization of different metaheuristics. The library also provides a set of ready-made tools, which include implementations of niching techniques, widely recognized and novel optimization algorithms, visualization capabilities, and landscape approximation methods. The goal of pyHMS library is to provide a toolbox for tackling complex real-world problems and to encourage the use of this framework as a basis for the creation of novel, hybrid optimization algorithms.

This paper presents a Genetic Programming based framework called logicGP for classification with literal based models and the open source software created and used for the implementation. The used prediction model is a linear combination of logical monomials. The underlying algorithm is designed to be interpretable and to allow for a high degree of predictive ability. The implementation of the algorithm is done in C# with open source code and is designed for high compatibility with Microsoft's ML.NET. The algorithm is presented as an extensible framework and different parameterizations for different tasks are discussed. Additionally, the paper presents the open source code created for the framework and discusses the software architecture used. The algorithm is tested on simulated data for binary classification with three categories (inspired by the analysis of SNP data) and on selected real data for multiclass classification. The experiments show that the algorithm is able to achieve a high degree of predictive ability while maintaining a high degree of interpretability.

We present SEvoBench, a modern C++ framework for evolutionary computation (EC), specifically designed to systematically benchmark evolutionary single-objective optimization algorithms. The framework features modular implementations of Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithms, organized around three core components: (1) algorithm construction with reusable modules, (2) efficient benchmark problem suites, and (3) parallel experimental analysis. Experimental evaluations demonstrate the framework's superior performance in benchmark testing and algorithm comparison. Case studies further validate its capabilities in algorithm hybridization and parameter analysis. Compared to existing frameworks, SEvoBench demonstrates three key advantages: (i) highly efficient and reusable modular implementations of PSO and DE algorithms, (ii) accelerated benchmarking through parallel execution, and (iii) enhanced computational efficiency via SIMD (Single Instruction Multiple Data) vectorization for large-scale problems.

The development of parallel and distributed algorithms has long been an important branch of evolutionary computation research. Whether to balance workloads across multiple computational nodes for enhanced runtime performance, or to enable innovative algorithmic strategies like coevolutionary approaches that optimize convergence behavior, the importance of parallel and distributed computation is undeniable. Although several software projects support parallel and distributed evolutionary computation, there remains potential to enhance the usability, flexibility, and runtime performance in this domain. This paper presents an open-source software system that incorporates an algorithm design language and containerization technology to address these challenges. We present the software's architecture including its graphical user frontend, microservice backend, and the container runtime environment. Further on, we describe application scenarios and results from various tests regarding computational speed and data exchange, which demonstrate the system's applicability and its ability to facilitate future research directions.

This paper proposes to study the morphological and behavioral adaptations exhibited by voxel-based soft robots when evolved for and designed to solve multiple tasks. The voxel-based soft robots of Evolution Gym simulator has been used on Walker+Carrier, Walker+Thrower and Walker+Carrier+BridgeWalker tasks for the proposed study. Unlike the one robot one task practice in Evolutionary Robotics, this study suggests that evolution of robots for multiple tasks discourages the fragile co-adaptation between body and brain and hence deserves more study. The experiments indicate that diverse morphological and behavioral adaptations emerge when the underlying tasks have overlapping morphological and behavioral requirements. When the tasks are dissimilar, though the emerged adaptations have similarity, degrees of variations of such adaptations is still observed. While performance loss of evolved robots for multiple tasks against the single task counterparts have been observed, the emerged adaptations and traits are still encouraging.

Cellular automata have long been celebrated for their ability to generate complex behaviours from simple, local rules, with well-known discrete models like Conway's Game of Life proven capable of universal computation. Recent advancements have extended cellular automata into continuous domains, raising the question of whether these systems retain the capacity for universal computation. In parallel, neural cellular automata have emerged as a powerful paradigm where rules are learned via gradient descent rather than manually designed. This work explores the potential of neural cellular automata to develop a continuous Universal Cellular Automaton through training by gradient descent. We introduce a cellular automaton model, objective functions and training strategies to guide neural cellular automata toward universal computation in a continuous setting. Our experiments demonstrate the successful training of fundamental computational primitives — such as matrix multiplication and transposition — culminating in the emulation of a neural network solving the MNIST digit classification task directly within the cellular automata state. These results represent a foundational step toward realizing analog general-purpose computers, with implications for understanding universal computation in continuous dynamics and advancing the automated discovery of complex cellular automata behaviours via machine learning. ¹

This article critically examines the foundational principles of contemporary AI methods, exploring the limitations that hinder its potential. We draw parallels between the modern AI landscape and the 20^th-century Modern Synthesis in evolutionary biology, and highlight how advancements in evolutionary theory that augmented the Modern Synthesis, particularly those of Evolutionary Developmental Biology, offer insights that can inform a new design paradigm for AI. By synthesizing findings across AI and evolutionary theory, we propose a pathway to overcome existing limitations, enabling AI to achieve its aspirational goals.

Artificial neural networks (ANNs) commonly rely on fixed-weight architectures, limiting their adaptability in dynamic and uncertain environments. In contrast, biological neural systems exhibit plasticity, enabling continuous adaptation to changing conditions. Hebbian learning provides a mechanism for incorporating plasticity into ANNs, offering the potential for improved flexibility in real-world control tasks. However, Hebbian-based models often suffer from instability, making their practical application challenging. This work explores the trade-off between adaptability and stability in Hebbian learning-driven ANNs by introducing a neuro-modulatory term into the standard Hebbian learning formulation, enabling a gradual transition from high plasticity to fixed weights over time. The proposed model, named time-modulated Hebbian learning (tm-HL), was tested on three classical control tasks from the Gymnasium environment, and it was compared to a standard Hebbian learning model and a fixed-weight ANN. An evolutionary algorithm was employed to optimise the Hebbian parameters for the former and the weights of the latter. The proposed approach showed a promising performance, showing higher adaptability over the model with fixed weights in certain scenarios. Moreover, it consistently performed better than the standard Hebbian learning model in all the testing environments.

We introduce the Self-Amendment Game, a simulation framework where Large Language Model (LLM) agents iteratively propose, vote on, and revise the very rules that govern them. Inspired by the self-modifying game Nomic, this system enables agents to operate within a fully amendable environment in which institutional constraints are themselves subject to change. Using leading LLMs, we examine two agent strategies: "Add" agents that focus on introducing new rules, and "Modify" agents that refine existing ones. Add agents tend to generate denser but less stable rule systems, with rapid point accumulation and high leadership turnover. Modify agents foster greater stability, with fewer but more consistent leaders. Analyzing the semantic structure of proposals, we find that varied justification styles often lead to instability, while coherence in reasoning promotes rule adoption. Our findings highlight a crucial trade-off between innovation and governance stability, offering a foundation for studying adaptive, self-governing systems involving both artificial agents and hybrid human-AI institutions.

This paper introduces an attention-based approach to muscle-driven locomotion that allows a single controller to adapt to different body plans. We consider physically simulated agents with bodies modeled as deformable meshes and controllable fibers that act as muscles. Vertices serve as addressable memory, defining keys and values, while muscles generate multi-head queries to extract relevant information from vertex states and produce actuation signals. A key characteristic of our approach is that all muscle fibers share the same attention-based control policy. This enables locomotion controllers that accommodate any number of inputs and outputs while also remaining permutation invariant. We demonstrate the effectiveness of our method by successfully controlling both bipedal and quadrupedal body plans using the same control policy.

Reinforcement learning refers to the ability of an agent to learn from its sequential interactions with the environment to find the optimal behavior that maximizes a particular reward. It is a crucial building block of autonomous intelligent systems. In recent years, there has been increasing attention on techniques for coordinating large numbers of autonomous agents to perform tasks cooperatively. A potentially attractive design strategy is to learn from naturally existing swarm intelligence systems and employ self-organized control paradigms. In this paper, we explore the viability of a self-organized reinforcement learning strategy and aims to solve the multi-agent multi-armed bandit problem for anonymous agents with only spontaneous communications between them. The proposed swarm reinforcement learning approach is compared against the individual implementation of the classical UCB1 algorithm, and the regret generated under different algorithmic and environmental parameter settings are measured and analyzed. The proposed approach is shown to be able to outperform the baseline and also scalable to large decision spaces and swarm sizes.

In developing brains, axonal projections follow chemical gradients shaped by local interactions. This paper asks whether such a process can be inferred from its outcome: For instance, given observed mouse brain connectivity, can one recover the developmental program that produced it? If such developmental programs can be recovered, they not only explain how biological connectivity arises, but also offer a biologically grounded search space for artificial intelligence, in which architectures emerge through the evolution of genetic encodings that produce plausible wiring diagrams. A framework is proposed that uses the biological connectome itself as a beacon to guide this search, referred to as the Connectome-Generating, AI-Generating Algorithm (CONGA). Implemented as neural cellular automata (NCA), a model was trained to reproduce axon-tracing data in the mouse connectome, and its internal representations were compared to gene expression patterns measured in the same spatial coordinates. The result demonstrates how the brain of an intelligent organism may self-assemble through an indirect encoding of connectivity. The model outperformed a static linear baseline, but only when constrained in size, suggesting that compact developmental programs better align with biological mechanisms.

Crossover operators have historically shown limited effectiveness in Cartesian Genetic Programming (CGP), with mutation-only approaches typically dominating the evolutionary process. In this paper, we explore a natural crossover mechanism enabled by Multimodal Adaptive Graph Evolution (MAGE), a multi-chromosome generalization of CGP that groups functions by return type and constrains graph mutation based on type coherence. MAGE's distinct architecture creates an opportunity for a chromosome-level crossover operator that was not previously feasible in traditional CGP. We implement and evaluate this crossover approach on selected problems from the Second Program Synthesis Benchmark Suite (PSB2), comparing it against a mutation-only strategy. Our experiments reveal that chromosome-level crossover offers mixed effectiveness in MAGE, with promising exceptions in problems like GCD and Twitter. This work continues the inquiry into effective crossover methods in graph-based genetic programming, revealing how effectiveness is problem dependent.

In recent years, significant efforts have been made to address graph node classification tasks by applying graph neural networks and methods based on label propagation. Despite the progress achieved by these approaches, their success often hinges on complex architectures and algorithms, sometimes leading to the oversight of crucial technical details. One crucial aspect of the innovative approach in designing artificial neural networks is suggesting a novel neural architecture. Currently used architectures have primarily been developed manually by human experts, which is time-consuming and error-prone. That is why adopting more sophisticated semiautomatic methods, such as Neural Architecture Search, has become commonplace. This paper introduces and assesses a Linear Genetic Programming approach for designing graph neural networks in the context of Node Classification. Our approach aims to systematically define the GCN parameter space, drawing inspiration from recent research on design principles. By doing so, our method seeks to balance achieving satisfactory performance and optimizing memory and computation resources, thus offering a more efficient alternative to conventional approaches from the neural architecture search area.

Genetic Programming (GP) and its variants have proven to be promising techniques for solving problems across various domains. However, GP does not scale well, particularly when applied to symbolic regression in the Boolean domain. To address this limitation, a semantically oriented mutation operator (SOMO) has been proposed and integrated with Cartesian Genetic Programming (CGP). Nevertheless, like standard GP, even SOMO suffers in some cases from bloat - an excessive growth in solution size without a corresponding performance gain. This work introduces SOMO^k-TS, an extension of SOMO that incorporates the so-called Tumor Search strategy to identify and preserve reusable substructures. By managing diversity through an immune-inspired mechanism, SOMO^k-TS promotes the reuse of substructures, thereby reducing computational overhead. It achieves significantly lower execution times while maintaining or improving solution compactness, highlighting its potential for scalable and efficient evolutionary design.

We propose a novel, type-consistent representation for programs manipulating arbitrary data types, that we call typed token processing networks (TTPNs). A TTPN is a network of interconnected stateless gates defining typed ports and processing functions: during the execution, data flows through the network as typed tokens carrying values. TTPNs favor interpretability as they can visually reveal the overall structure of a program and also highlight the way data is processed at runtime—enabling decomposability and simulatability, respectively. Moreover, like other graph representations, TTPNs enable component reuse. We evolve programs in the form of TTPNs from examples, i.e., we do program synthesis, with a simple genetic algorithm and ad hoc genetic operators. Our preliminary results show successful evolution of simple programs from small example sets involving diverse types, though some instances fail. We hypothesize that the particularly rugged fitness landscape imposed by our representation and, more in general, by the program synthesis scenario, may hinder convergence. We propose some directions for tackling these issues.

This work presents a comparative analysis of thermal models for photovoltaic modules using Grammatical Evolution (GE) and Differential Evolution (DE) across four photovoltaic (PV) technologies: crystalline silicon (c-Si), amorphous silicon (a-Si), cadmium telluride (CdTe), and organic (OPV), under three sky conditions: sunny, cloudy, and diffuse. Temperature data were collected through a monitoring system in a photovoltaic cube, measuring temperatures on the horizontal face (top PV module) as well as environmental parameters (irradiance, ambient temperature, wind speed and direction, relative humidity). Three empirical models from the literature (Sandia, Faiman, and Obiwulu) were compared with 10 models generated by GE+DE using a Global Performance Index (GPI) to evaluate the accuracy of the models, considering five statistical metrics. The results show that in 11 out of 12 scenarios, the generated models outperform the empirical models, highlighting the importance of relative humidity in model accuracy. This work extends previous research, providing more accurate predictive models for the operating temperature of photovoltaic modules.

In this study, the Coverage Path Planning (CPP) problem is addressed, which aims to find the best flight path for a unmanned aerial vehicle (drone) to completely cover a given area of interest. Arbitrary areas containing obstacles (e.g. buildings, towers, trees or hills) are considered. The CPP is modeled as a Traveling Salesman Problem, where the drone must visit all non-obstacle points of the area to be covered. Battery power is the main resource that limits a drone's flight time or distance. It is known that, battery consumption is higher when a drone makes turns and altitude changes. To minimize the drone's energy consumption, we consider minimizing the total distance traveled, altitude variations and direction changes made during its route. As the CPP problem is NP-hard, in this work we propose a heuristic based on the GRASP meta-heuristic. The GRASP heuristic repeatedly constructs a solution using the cheapest insertion algorithm and this solution is improved by a local search procedure. The solutions determined by the proposed GRASP are compared with solutions generated by the Mixed-Integer Linear Programming model (solved by GUROBI solver). The results show that the GRASP heuristic determines excellent quality solutions using significantly less CPU time than GUROBI.

This work presents a nested multi-objective optimisation approach for constructing a digital twin of an aircraft's wingtail section from a high-dimensional finite element model (FEM). While FEMs are widely used in engineering for dynamic analysis, they may not always accurately represent physical structures due to simplifying assumptions employed in their development. In this study, an FEM is calibrated to measured wingtail data through model updating, a process where its parameters are adjusted to better match real-world observations. Conventional approaches to model updating require multiple evaluations of the FEM, which might not be viable for Large FEMs that are computationally expensive to evaluate. In this study, this is mitigated using a projection-based reduced-order model (ROM), which is also calibrated. The choice of ROM affects both the accuracy of the model in representing measured data and its computational efficiency—two critical objectives for digital twins. To optimise these conflicting objectives, a nested multi-objective optimisation constructs a set of effective ROMs. Results show that these ROMs significantly outperform those built using conventional methods. These findings demonstrate the potential for real-time applications of digital twins with finite element models, offering a flexible and efficient tool for model updates that adapt to varying operational conditions.

Efficient traffic signal timing is essential for smooth urban traffic flow, but traditional methods struggle with unpredictable conditions. This paper introduces a Memory-Assisted Genetic Algorithm (MGA) to optimize signal timing in such complex environments. The MGA incorporates two key features to enhance its performance. First, it leverages historical traffic data for more informed initial estimates, speeding up the optimization process. Second, it uses immigrants to introduce new solutions in each iteration, maintaining a balance between exploitation with learning from existing solutions patterns and exploring new possibilities to better map with the dynamicity of the traffic network. Tests on a realistic traffic model in SUMO show that the MGA outperforms standard Genetic Algorithm and Webster, delivering efficient and more effective solutions. It significantly reduces average waiting times and lowers fuel consumption. The approach is demonstrated on a real-world city network taken from the UK. These results highlight the MGA's potential as a powerful tool for dynamic and adaptable traffic signal control in urban settings.

Transportation in urban areas is becoming a challenge due to pollution, congestion, and difficulty in expanding current roads. By using existing waterways, autonomous electric vessels have become a sustainable maritime alternative to road transportation. For autonomous electric ferries to become a viable mode of public transportation, they must not only be more convenient, but also provide comfort and be completely safe to use. As these vessels navigate intricate water channels, sharing routes with traditional maritime traffic and responding to dynamic environmental conditions, a robust form safety validation is needed. However, performing such a safety validation is a complex task.

Maritime adaptive stress testing (MAST) is a novel testing method designed to perform safety validation of autonomous maritime systems by revealing the most likely sequences of events resulting in failure. Although promising, existing MAST methods have certain limitations, including the limited variety found among scenarios leading to failures, including collisions. In order to address these limitations, we integrate MAST with an evolutionary algorithm (EA), creating a novel EA-MAST method. Using simulations with two different collision avoidance systems for an autonomous electric ferry, we demonstrate the benefit of EA-MAST, including its capability to create novel and surprising stress test scenarios.

The Job Shop Scheduling Problem (JSSP) is a widely studied NP-hard optimization problem with significant academic and industrial relevance, particularly in the context of Industry 4.0, where efficient scheduling algorithms are crucial for improving decision-making in increasingly automated production systems. Despite extensive theoretical advancements, a gap remains between academic research and real-world implementation, as most studies either focus on theoretical aspects or emphasize numerical advantages while neglecting practical deployment challenges, including those related to computational constraints. To fill this gap, we propose a hybrid optimization approach, hcpga, which integrates a state-of-the-art Constraint Programming (CP) solver, cp-sat, with a custom Genetic Algorithm (ga). The CP solver generates feasible solutions, which are then used to initialize the ga's population. The ga further optimizes the schedule, minimizing the makespan. Our experimental evaluation on 74 JSSP benchmark instances of varying sizes demonstrates that, while standalone cp-satand hcpga achieve comparable makespan results, the latter significantly reduces the time and memory required to find a good solution. This makes our approach highly valuable for industrial applications. To our knowledge, this is the first attempt to combine an evolutionary approach with an exact solver for solving the JSSP, specifically addressing the need for computational efficiency.

In this paper, we used real data to predict the position of the floating wind turbines due to three external forces: wind, wave and current. We analysed data provided by energy company Equinor and applied two machine-learning techniques: Multilayer Perceptron and Random Forest. After demonstrating that machine learning models failed, we used a simple linear regression model and optimisation approach to solve the multi-objective optimisation problem. We minimised the area of the wind farm and maximised its power output by applying the multi-objective optimisation algorithm NSGA-II. We also investigated how changing the length of mooring lines affected the optimisation. We used hypervolume to measure the algorithm's performance. We have shown that the results are very similar for fixed and floating wind farms. However, we have found that in complex wind conditions, i.e., when the wind does not blow only from one direction, for many wind turbines, the floating wind farms were a better solution than the fixed ones.

Transformer neural networks have gained popularity in recent years, demonstrating remarkable performance across many application domains. However, inference on resource-constrained embedded hardware remains challenging due to Transformers' substantial computational demands. We aim to address this problem by focusing on exploiting the inherent parallelism opportunities presented by the multi-head self attention operations of Transformers, to achieve a speedup in processing on embedded hardware. In this paper, we present an evolutionary-based scheduling approach for distribution and allocation of Transformer operations across systolic array-based hardware accelerators used for execution. Our methodology takes as input specifications of the Transformer workload and the target systolic array architecture and explores the large mapping space to identify an efficient plan of operation-to-array assignments. The plans are evaluated against a hardware-aware cost model, capturing the cost of computational cycles for a given operation and systolic array, with the objective to minimize the total sum across all operations. Through extensive experimental evaluations across diverse systolic array dimensions, we demonstrate that our evolutionary-based scheduler surpasses conventional heuristics and is able to find plans offering up to 33.8% average reduction in overall cycle count.

This study investigates recent advances in Anticipatory Learning Classifier Systems (ALCSs) designed to address the aliasing problem that arises when multiple environmental states produce identical perceptions. Four ALCS-based algorithms, ACS2, PEPACS, BACS, and BEACS, are described and rigorously evaluated. The performance of these algorithms is assessed using a comprehensive set of 26 aliased and non-aliased maze environments, with an in-depth analysis of the results. Despite the significant progress made by the BEACS algorithm in mitigating the aliasing issue, several limitations persist, including suboptimal decision policies and model aliasing, which occurs when the algorithm produces overly general rules. These shortcomings are critically examined, with illustrative examples and quantitative metrics provided to underscore the need for further refinement.

With the ever increasing capabilities of modern AI systems comes a greatly growing interest among various non-technical stakeholders in employing "AI" to improve their existing systems or workflows. This rise is especially present in industrial settings, e.g. manufacturing, where—in the past—the usage of AI has usually been limited due to various challenges surrounding the gathering of data. However, there have been concentrated efforts to automate machinery that come with an increase in usable data, which—paired with the wish of some stakeholders to automate through "AI"—makes new applications of AI available. Nevertheless, many stakeholders, especially those that will interact with the system on a daily basis, will not sufficiently trust AI models, hindering their adoption. This issue can be alleviated by using explainable models that can create trust through their transparency, rather than solely through statistical evaluations.

In this extended abstract, past work on how to determine specific requirements of various stakeholder groups on the model structure is reintroduced and one result from a real-world case study is discussed. Additionally, an approach to design a Learning Classifier System that delivers such models is highlighted.

Learning classifier systems (LCS) are often regarded as complex and challenging to master despite the community's ongoing efforts to provide simplified educational models and detailed algorithmic descriptions. In this position paper, we argue that such perceived complexity is due to how LCSs are explained, which is still based on the narrative used to present the early models almost 50 years ago. Such a narrative centers around the system's interaction with the environment and how the information streams from detectors to actuators, creating increasingly focused classifier sets. Accordingly, it blends core LCS concepts with elements universal to all value-based reinforcement learning algorithms that are never included in the descriptions of competing methods. We suggest another, possibly leaner, narrative based on the view of XCS as an approximator of state-action value functions to solve reinforcement learning tasks. We show how abandoning the traditional narrative may result in a simpler description of XCS that can be easily extended to integrate known reinforcement learning extensions and tackle classification and regression problems. Our approach can be seamlessly applied to one-step and multi-step scenarios without modifications. It also provides guidelines for developing LCS implementations that might be more accessible to people approaching LCS for the first time.

Originally, the XCS Classifier System, seen as the most popular and most researched Learning Classifier System (LCS), was designed to learn and solve Reinforcement Learning (RL) problems. As has become clear over time, known weaknesses and the curse of dimensionality of Michigan-style LCSs severely limit its applicability to RL problems. As a result, visual RL problems generally appear to be outside the scope of XCS variants. We target this class of RL benchmarks by combining XCSF, XCS with hyperrectangle conditions and computed linear prediction, with dimensionality reduction methods. In particular, we combine deep variational autoencoders (VAE) with XCSF using an automatic dataset collection scheme and offline training of the VAE and online training for the combined system to target several visual RL problems. Our results show that XCSF is able to learn visual RL problems in the latent space of deep VAEs. Further experiments confirm that simple downscaling of images can also enable XCSF to learn several visual RL problems. Our results do not only indicate that XCSF is better at RL than its reputation, but show that significantly more RL problems might be within the scope of XCSF and motivate further investigation of dimensionality reduction methods for LCSs.

This paper presents an extension to the EVOTER (Evolution of Transparent Explainable Rule Sets) framework, previously introduced to promote transparency and explainability in AI through the evolution of interpretable rule sets. While EVOTER demonstrated strong performance in generating compact and understandable rule-based models using a list-based grammar, the current work, Accelerated Evolutionary Rule-based Learning (AERL), builds upon this foundation by addressing scalability challenges. Specifically, AERL leverages GPU-accelerated computation and back-propagation fine-tuning within a PyTorch framework to significantly enhance the efficiency of rule evaluation and evolution. By introducing a tensorized numerical representation of rules and incorporating gradient-based optimization, AERL achieves superior computational speed and improved search-space exploration. Experimental results confirm that the approach is effective, achieving faster convergence and similar accuracy. It thus offers a scalable path forward for explainable AI.

Conventional classifier systems in evolutionary machine learning often struggle to detect and generalize hierarchical patterns, and thus cannot solve complex real-world problems. Inspired by lateralization and modularity in the biological brain, this extended abstract introduces the developed lateralized classifier system that evolves modular abstractions by decomposing problems into reusable knowledge components. The lateralized system consists of two complementary modules: one (Left Hemispheric Stratagem Module) focused on learning fine-grained, constituent patterns and the other (Right Hemispheric Stratagem Module) on extracting abstract, holistic relationships. Knowledge is encoded using disjunctive normal form-based code fragments and organized into hierarchical concepts stored in a heterogeneous knowledge pool. This structure enables recursive composition and facilitates efficient transfer of building-block knowledge across tasks. Experimental evaluations using complex Boolean problems demonstrate that the lateralized system significantly outperforms conventional learning classifier systems for solving complex problems such as the n-bit Parity problems and 18-bit hierarchical multiplexer problems.

We present a preliminary study investigating the application of fitness landscape analysis to malware evolution. This type of analysis, though widely used in evolutionary computation, has been underutilised in understanding the optimization processes underlying malware adaptation. We examine two types of evolving malware: Android and Windows-based programs, and we analyse an existing evolutionary algorithm from the literature for each setting. To gain deeper insights into the algorithm behaviour we construct, visualise, and analyse search trajectory networks. Our findings suggest that the two considered algorithms are associated with markedly different fitness landscape structure. We notice from the results that current search operators may struggle to effectively navigate malware fitness landscapes. In particular, further consideration of the presence of neutrality and plateaus may be needed in this domain.

When applying evolutionary computation for multimodal multiobjective optimization, it is crucial to balance exploration and exploitation: exploring the design space to identify regions that contain Pareto optima and exploiting these regions to converge towards the Pareto optima. When it comes to benchmarking for multi-objective optimization, however, it has been difficult to ensure such a landscape with desired properties. We thus propose to pre-determine the landscape and implement it as a benchmark problem. This framework is named the Benchmarking Based on Basin Connectivity (3BC) and targets continuous optimization. The 3BC suite includes an instance with recursively nested basins, forming a funnel structure, and another instance without nesting. Our implementation is publicly available at https://github.com/dsakurai/benchmark-visualizer.

The Adam optimiser is a popular adaptive gradient-based learning algorithm used to train neural networks. Adam uses adaptive learning rates (estimated per neural network weight) to increase the speed of convergence. While Adam is claimed to automatically perform step size annealing, it is not immune to oscillations, i.e., updating weights in inconsistent directions. This paper investigates the oscillatory behaviour of Adam in the context of computer vision classification tasks under different batch sizes. We confirm that Adam is indeed highly susceptible to oscillations. Further, we study starting gradient and magnitude of randomly initialised weights as predictors of weight saliency. Conversely to common belief, we discover that the initial gradient is not a reliable predictor of weight saliency. We attribute this finding to inherent oscillations. We also discover that larger batch sizes are more likely to yield inactive weights, bearing important implications for weight pruning.

This study investigates the feasibility and effectiveness of integrating Large Language Models (LLMs) as mutation operators within Genetic Programming (GP) frameworks so as to evolve agent behaviors in multi-agent systems (MAS) and provide benchmarks that evaluate the efficacy of LLM-generated code in multi-agent domains. Our approach leverages the sophisticated code-generation capabilities of LLMs to introduce semantically meaningful variations during the evolutionary process. Specifically, we explore and systematically compare these different prompting strategies: zero-shot, one-shot, and two-shot prompting as well as prompting the generation of commented code to assess their impact on the quality of evolved agent behaviors. Additionally, we propose a novel methodology where evolution operates at a higher abstraction level by mutating pseudocode representations of agent behaviors, subsequently converting them into executable code through another LLM-mediated step. This strategy capitalizes on the extensive natural language training data of LLMs, potentially enabling the discovery of more innovative solutions. Our results indicate that LLM-driven mutation with comment generation enhances agent performance while mutating pseudocode representations yields reduced performance. This research contributes valuable insights regarding the integration of LLM-driven GP techniques into MAS, highlighting both the potential and limitations of these approaches. All code is open-sourced at https://github.com/can-gurkan/LEAR.

Guiding biological systems toward desired states, such as morphogenetic outcomes, remains a fundamental challenge with far-reaching implications for medicine and synthetic biology. While large language models (LLMs) have enabled natural language as an interface for interpretable control in AI systems, their use as mediators for steering biological or cellular dynamics remains largely unexplored. In this work, we present a functional pipeline that translates natural language prompts into spatial vector fields capable of directing simulated cellular collectives. Our approach combines a large language model with an evolvable neural controller (Prompt-to-Intervention, or P2I), optimized via evolutionary strategies to generate behaviors such as clustering or scattering in a simulated 2D environment. We demonstrate that even with constrained vocabulary and simplified cell models, evolved P2I networks can successfully align cellular dynamics with user-defined goals expressed in plain language. This work offers a complete loop from language input to simulated bioelectric-like intervention to behavioral output, providing a foundation for future systems capable of natural language-driven cellular control.

The application of Large Language Models (LLMs) for Automated Algorithm Discovery (AAD), particularly for optimisation heuristics, is an emerging field of research. This emergence necessitates robust, standardised benchmarking practices to rigorously evaluate the capabilities and limitations of LLM-driven AAD methods and the resulting generated algorithms, especially given the opacity of their design process and known issues with existing benchmarks. To address this need, we introduce BLADE (Benchmark suite for LLM-driven Automated Design and Evolution), a modular and extensible framework specifically designed for benchmarking LLM-driven AAD methods in a continuous black-box optimisation context. BLADE integrates collections of benchmark problems (including MA-BBOB and SBOX-COST among others) with instance generators and textual descriptions aimed at capability-focused testing, such as generalisation, specialisation and information exploitation. It offers flexible experimental setup options, standardised logging for reproducibility and fair comparison, incorporates methods for analysing the AAD process (e.g., Code Evolution Graphs and various visualisation approaches) and facilitates comparison against human-designed baselines through integration with established tools like IOHanalyser and IOHexplainer. BLADE provides an 'out-of-the-box' solution to systematically evaluate LLM-driven AAD approaches. The framework is demonstrated through two distinct use cases exploring mutation prompt strategies and function specialisation.

The recent and rapid progress in large language models (LLMs) has markedly influenced research efforts in the automated design and configuration of metaheuristic algorithms. A common limitation of contemporary LLMs is their finite context window, which constrains the amount of information they can effectively utilize during generation. In this study, we investigate the role of conversational context in the metaheuristic design process. This study explores two distinct aspects of LLM-based metaheuristic design: (1) the effect of conversational context on the performance of generated optimizers, and (2) its influence on the validity of generated code. Both are investigated using the EASE framework. The findings yield several unexpected insights, which are discussed in detail in the paper, offering a deeper understanding of how context affects the reliability and effectiveness of LLM-assisted algorithm generation.

We study how large language models (LLMs) can be used in combination with evolutionary computation techniques to automatically discover optimization algorithms for the design of photonic structures. Building on the Large Language Model Evolutionary Algorithm (LLaMEA) framework, we introduce structured prompt engineering tailored to multilayer photonic problems such as Bragg mirror, ellipsometry inverse analysis and solar cell antireflection coatings. We systematically explore multiple configurations of Evolution Strategies, including (1+1), (1+5), (2+10) and others, to balance exploration and exploitation. Our experiments show that LLM-generated algorithms, generated using small-scale problem instances, can match or surpass established methods like Quasi-oppositional Differential Evolution on large-scale realistic real-world problem instances. Notably, LLaMEA's self-debugging mutation loop, augmented by automatically extracted problem-specific insights, achieves strong anytime performance and reliable convergence across diverse problem scales. This work demonstrates the feasibility of domain-focused LLM prompts and evolutionary approaches in solving optical design tasks, paving the way for rapid, automated photonic inverse design. Such an approach is broadly applicable and can transform design processes across a wide range of scientific and engineering domains.

In machine learning, Neural Architecture Search (NAS) requires domain knowledge of model design and a large amount of trial-and-error to achieve promising performance. Meanwhile, evolutionary algorithms have traditionally relied on fixed rules and pre-defined building blocks. The Large Language Model (LLM)-Guided Evolution (GE) framework transformed this approach by incorporating LLMs to directly modify model source code for image classification algorithms on CIFAR data and intelligently guide mutations and crossovers. A key element of LLM-GE is the "Evolution of Thought" (EoT) technique, which establishes feedback loops, allowing LLMs to refine their decisions iteratively based on how previous operations performed. In this study, we perform NAS for object detection by improving LLM-GE to modify the architecture of You Only Look Once (YOLO) models to enhance performance on the KITTI dataset. Our approach intelligently adjusts the design and settings of YOLO to find the optimal algorithms against objective such as detection accuracy and speed. We show that LLM-GE produced variants with significant performance improvements, such as an increase in Mean Average Precision from 92.5% to 94.5%. This result highlights the flexibility and effectiveness of LLM-GE on real-world challenges, offering a novel paradigm for automated machine learning that combines LLM-driven reasoning with evolutionary strategies.

Deep neuroevolution is a highly scalable alternative to reinforcement learning due to its unique ability to encode network updates in a small number of bytes. Recent insights from traditional deep learning indicate high-dimensional models possess intrinsic, low-rank structure. In this work, we introduce low-rank, factorized neuroevolution-an indirect encoding through which we can search a small space of low-rank factors that enforce underlying structure across a network's weights. We compare our approach with non-factorized networks of similar and smaller size to understand how much performance can be attributed to the smaller search space. We evaluate our method on a language modeling task using transformers, as well as continuous and discrete vision-based reinforcement learning tasks. Our study shows that low-rank, factorized neuroevolution outperforms or is competitive with non-factorized neuroevolution, performing notably well on language modeling. Our results also suggest deleterious factorized mutations have a stronger negative impact on performance than deleterious non-factorized mutations, which significantly reduces the runtime on environments with early termination for bad performers. More broadly, these results show how we can use insights from backpropgation-based methods to enhance neuroevolution.

This paper proposes an enhanced approach to Simple Contrastive Graph Clustering (SCGC) by utilizing Cartesian Genetic Programming (CGP) to evolve neural network architectures. The evolutionary algorithm dynamically optimizes the structure and hyperparameters of SCGC, including the number and size of linear layers, optimizer choice (such as Adam, RMSprop, or SGD), learning rates, weight decay, and loss functions, tailored specifically to the given datasets. Using CGP, we automate both the design and training of SCGC architectures, evolving optimized neural networks with minimal manual intervention. Experimental results conducted across multiple generations on ten benchmark datasets demonstrate that our evolved SCGC consistently achieves superior clustering performance compared to state-of-the-art methods, with notable improvements in accuracy, F1-score, and computational efficiency. The evolutionary process not only optimizes the network topology, but also systematically refines hyperparameters, resulting in robust, highly adaptive, and computationally efficient clustering solutions.

This study explores a novel encoding approach for optimizing Liquid State Machines (LSMs) in a Neuroevolution (NE) context. By leveraging a Genetic Algorithm (GA), two components of LSM design, neuron configurations and neuron positions, are used. Three variants were evaluated to assess their individual contributions: the complete proposal considering both components, one encoding with only neuron configurations, and another focusing on neuron positions. Experiments were conducted on varying complexity synthetic classification tasks, demonstrating that neuron configurations significantly influence performance, while neuron positions alone were less effective. Statistical analysis using the Shapiro-Wilk, Kruskal-Wallis, and Dunn's post hoc tests validated these findings. The results highlight the importance of configuration-driven encodings in LSM optimization and suggest the need for refined evolutionary strategies to exploit positional information better.

In this paper we present a Variational Quantum Algorithm (VQA) for the Permutation Flow Shop Scheduling Problem (PFSSP). This scheduling problem is challenging to be solved with a quantum algorithm because the objective function is quite difficult to be expressed by means of a Hamiltonian, and a large number of qubits is generally required. For this reason, we propose to use a variational approach where the solution is represented with a limited number of qubits and the objective function can be computed without explicitly synthesizing a Hamiltonian operator. The algorithm has been implemented and tested on a simulator; the preliminary experimental results demonstrate that our solution could represent a viable alternative to solve the PFSSP on real quantum devices.

A recent work has proposed a revolutionary approach to optimize the Travelling Salesman Problem (TSP) using a single Quantum Bit (QuBit), by invoking the principle of quantum parallelism. Specifically, a quantum version of the classical Brachistochrone algorithm was presented, claiming to solve TSP with more accurate solutions, than existing quantum algorithms. More importantly, it was argued that, using the proposed method, potential speed-up of polynomial time over classical algorithms is achievable. In this work, we critically analyze these claims, with the main argument that the single-qubit approach is still, algorithmically, stochastic. We analyze the level of randomization of the single-qubit method, and develop an equivalently random Quantum Genetic Algorithm (QGA). We compare the optimality of our solution results with that obtained by the single-qubit method. We show that similar accuracy levels can be obtained, using our QGA, even with orders of magnitude fewer optimization iterations, which experimentally refutes some of the major claims within the single-qubit method proposal.

QAOA is a hybrid quantum-classical algorithm to solve optimization problems in gate-based quantum computers. It is based on a variational quantum circuit that can be interpreted as a discretization of the annealing process that quantum annealers follow to find a minimum energy state of a given Hamiltonian. This ensures that QAOA must find an optimal solution for any given optimization problem when the number of layers, p, used in the variational quantum circuit tends to infinity. In practice, the number of layers is usually bounded by a small number. This is a must in current quantum computers of the NISQ era, due to the depth limit of the circuits they can run to avoid problems with decoherence and noise. In this paper, we show mathematical evidence that QAOA requires exponential time to solve linear functions when the number of layers is less than the number of different coefficients of the linear function n. We conjecture that QAOA needs exponential time to find the global optimum of linear functions for any constant value of p, and that the runtime is linear only if p ≥ n. We conclude that we need new quantum algorithms to reach quantum supremacy in quantum optimization.

The Steiner Traveling Salesman Problem (STSP) is a variant of the classical Traveling Salesman Problem. The STSP involves incorporating steiner nodes, which are extra nodes not originally part of the required visit set but that can be added to the route to enhance the overall solution and minimize the total travel cost. Given the NP-hard nature of the STSP, we propose a quantum approach to address it. Specifically, we employ quantum annealing using D-Wave's hardware to explore its potential for solving this problem. To enhance computational feasibility, we develop a preprocessing method that effectively reduces the network size. Our experimental results demonstrate that this reduction technique significantly decreases the problem complexity, making the Quadratic Unconstrained Binary Optimization formulation, the standard input for quantum annealers, better suited for existing quantum hardware. Furthermore, the results highlight the potential of quantum annealing as a promising and innovative approach for solving the STSP.

We consider the encoding in Quadratic Unconstrained Binary Optimization (QUBO) of binary comparison constraints, that is, constraints of the form x < y + c, x ≤ y + c, and x = y + c, where x and y are two integer variables and c is an integer constant. For the sake of simplicity, we will consider that x and y are bounded and belong to the same interval {1,..., n}. We will show that such constraints can be encoded without the need of any extra-variable, conversely to the general scheme for linear inequations, which requires between n - 1 and ⌈log₂(n - 1)⌉ extra-variables, depending on the encoding chosen for integers. Limiting the number of extra-variables needed in QUBO formulations is important as each Boolean QUBO variable will be implemented as a (logical) qubit on a quantum device and the number of such qubits is limited in quantum annealing systems such as D-Wave machines.

Flow Shop Scheduling Problems (FSP) represent a challenging class of combinatorial optimization tasks with significant relevance across diverse domains ranging from manufacturing and logistics to service operations. Recent advances in quantum annealing and quantum-inspired approaches have opened avenues for tackling such problems via Quadratic Unconstrained Binary Optimization models. However, their performance depends strongly on how the problem is encoded as a QUBO. In this study, we perform a comparative evaluation of manually formulated QUBOs versus those automatically produced by the AutoQUBO framework. We test both formulations on D-Wave's hybrid and qbsolv solvers and the InfinityQ solver, exploring the effect of QUBO-solver-specific behaviors and sensitivity, and fine-tuning strategies on the quality of the solution. While carefully crafted manual QUBOs typically yield stronger solution fidelity, they demand greater domain expertise and computational overhead. In contrast, automated approaches greatly expedite modeling at the cost of certain performance trade-offs. We further observe that solver fine-tuning and hardware selection substantially shape outcomes, with certain solvers favoring domain-tailored encodings. These insights demonstrate the necessity of solver-aware QUBO design, offering practical guidance on QUBO construction and solver choice to solve the FSP using quantum and quantum-inspired hardware.

Customer segmentation is strategic for increasing business revenues, as it allows a company to offer tailored products and services. Companies have access to vast amounts of information to generate customer clusters. In the banking sector, for instance, transactional data may reveal several hidden customer characteristics. The lookalike clustering problem aims to expand an initial cluster by detecting similar customers from a larger set. In this work, we model the lookalike clustering problem as a Quadratic Unconstrained Binary Optimization problem and solve it by means of a Quantum Annealer (QA). We tune the penalization parameters of the QA through an adaptive subgradient-inspired algorithm. We then compare QA performance against those obtained by a Simulated Annealing and the classical integer programming solver Gurobi. The results show that QA, when properly tuned, is able to find the optimal solution for small instances of the problem, even when the number of variables exceeds the number of couplers of QA. It fails, instead, for larger ones, due to the high level of noise. The results also show that QA requires a very short time to generate feasible and optimal solutions compared to classical algorithms, thus proving its potential for the solution of fully connected graphs.

Quantum computing, leveraging principles such as superposition and entanglement, has shown remarkable potential in solving complex optimization problems. Quantum annealing (QA) is particularly effective for combinatorial optimization and has gained increasing attention in financial applications. However, financial decision-making problems typically involve conflicting objectives, such as the trade-off between minimizing risk and maximizing returns, posing challenges for current QA approaches in efficiently encoding multi-objective problems and constraints. To address this gap, we propose the first quantum annealing framework for bi-objective weighted portfolio optimization based on the trend ratio model, integrating D-Wave's latest constrained quadratic model (CQM) hybrid solver. Our approach offers flexibility to accommodate diverse investor preferences. Experimental evaluations using real-world U.S. stock market data demonstrate the effectiveness of our method, showing higher-quality solutions and faster runtimes compared to classical multi-objective optimization algorithms. These promising results highlight the significant potential of quantum computing in practical financial optimization scenarios.

Combinatorial optimization is essential across numerous disciplines. Traditional metaheuristics excel at exploring complex solution spaces efficiently, yet they often struggle with scalability. Deep learning has become a viable alternative for quickly generating high-quality solutions, particularly when metaheuristics underperform. In recent years, quantum-inspired approaches such as tensor networks have shown promise in addressing these challenges. Despite these advancements, a thorough comparison of the different paradigms is missing. This study evaluates eight algorithms on Weighted Max-Cut graphs ranging from 10 to 250 nodes. Specifically, we compare a Genetic Algorithm representing metaheuristics, a Graph Neural Network for deep learning, and the Density Matrix Renormalization Group as a tensor network approach. Our analysis focuses on solution quality and computational efficiency (i.e., time and memory usage). Numerical results show that the Genetic Algorithm achieves near-optimal results for small graphs, although its computation time grows significantly with problem size. The Graph Neural Network offers a balanced solution for medium-sized instances with low memory demands and rapid inference, yet it exhibits more significant variability on larger graphs. Meanwhile, the Tensor Network approach consistently yields high approximation ratios and efficient execution on larger graphs, albeit with increased memory consumption.

The desirability function approach is an established and widely adopted method in industry for optimizing multiple response processes. It is seldomly used in multi-criteria hyperparameter tuning. This article fills this gap. It provides an introduction to the desirability function approach to multi-objective optimization (direct and surrogate model-based), and multi-objective hyperparameter tuning. This work is based on the paper by Kuhn [17]. It presents a Python implementation of Kuhn's R package desirability. After the desirability-function approach is introduced, two examples are given that demonstrate how to use desirability functions for classical optimization via response surface modeling and hyperparameter tuning of a neural network, which is implemented in PyTorch. The article discusses the following research questions: (a) How can the desirability function approach be used for multiobjective optimization and hyperparameter tuning? (b) What are advantages and disadvantages of the desirability function approach compared to other multi-objective optimization methods? (c) How can the desirability function approach be improved?

Surrogate-assisted evolutionary algorithms often implement regression models to approximate fitness values. In this paper we introduce new approaches using classification-based surrogate models that predict relative solution quality rather than exact fitness values. We introduce three classification-based surrogate models to improve the efficiency of JADE which is one of the best-performing optimization methods. We demonstrate the efficiency of the considered classification-based surrogate model assisted JADE by benchmarking on the CEC 2013 benchmark suite and comparing the results with the regression-based surrogate model, and with the plain JADE.

Recent work on expensive single-objective Computational Fluid Dynamics (CFD) design problems has identified a trio of surrogate assisted evolutionary algorithms (LSADE, TS-DDEO and ESA) as being particularly strong performers. In this work, we contrast their performance on multi-objective optimisation, embedding eight different popular scalarising functions within their pipelines to facilitate their use in this domain, and compare them to a Bayesian optimisation (BO) alternative on a range of synthetic problems. We find that for bi-objective problems ESA and TS-DDEO outperform the others, but as the number of objectives increases the ranking reverses and BO becomes the dominant performer. Interestingly, the older scalarisation approaches tend to perform better in the configurations used, though again performance is seen to vary as the number of objectives increases. We introduce a new real world multi-objective CFD design benchmark, that of optimising a sand trap geometry, and observe that performance on the collection of synthetic test functions is not predictive on this practical problem — highlighting the need to add such practical test cases to the benchmarking suits in this domain.

Surrogate models provide efficient alternatives to computationally demanding real-world processes but often require large datasets for effective training. A promising solution to this limitation is the transfer of pre-trained surrogate models to new tasks. Previous studies have investigated the transfer of differentiable and non-differentiable surrogate models, typically assuming an affine transformation between the source and target functions. This paper extends previous research by addressing a broader range of transformations, including linear and nonlinear variations. Specifically, we consider the combination of an unknown input warping—such as one modeled by the beta cumulative distribution function—with an unspecified affine transformation. Our approach achieves transfer learning by employing a limited number of data points from the target task to optimize these transformations, minimizing empirical loss on the transfer dataset. We validate the proposed method on the widely used Black-Box Optimization Benchmark (BBOB) testbed and a real-world transfer learning task from the automobile industry. The results underscore the significant advantages of the approach, revealing that the transferred surrogate significantly outperforms both the original surrogate and the one built from scratch using the transfer dataset, particularly in data-scarce scenarios.

Mesh deformation plays a critical role in aerodynamic shape optimisation, enabling efficient geometry modifications without requiring full mesh regeneration. This paper presents a Radial Basis Function (RBF) mesh deformation method, offering a computationally efficient and robust alternative to traditional approaches. The method is integrated into a gradient-free optimisation framework using Bayesian Optimisation (BO), and tested on three case studies. Results show the technique accommodates large shape changes while preserving mesh quality and reducing numerical noise.

This paper presents a surrogate-assisted hyperparameter tuning approach using the Sequential Parameter Optimization Toolbox (SPOT) to improve prediction of compressor performance maps. Accurate prediction is critical for efficiency and reliability in power generation, aerospace and other industries, but experimental data collection is costly and time-consuming. By employing a Kriging-based surrogate model for hyperparameter tuning, the evaluation of the objective function is significantly reduced.

Recurrent Neural Networks are explored as a novel modeling approach for compressor data, leveraging their ability to capture sequential dependencies. Through hyperparameter tuning with SPOT, we compare RNNs, LSTMs, and GRUs while integrating a novel cross-validation strategy to select robust parameter configurations across multiple operating curves. Key contributions include advanced data preprocessing (interpreting data as sequences), a problem-specific network design (supporting variable sequence lengths and bidirectionality), and statistical validation. This benchmark has been cross-validated across multiple compressor maps, and we provide a standardized benchmark (including data and code) for the research community.

The work results from collaboration with MAN Energy Solutions, who contributed expertise and data. This research demonstrates the potential of combining surrogate-based optimization with Recurrent Neural Networks (RNNs, LSTMs, GRUs), leveraging sequential modeling to improve prediction accuracy while reducing computational cost for compressor performance estimation.

Shape-constrained regression aims to fit regression models that adhere to specific constraints regarding the expected shape of the parametric model. Commonly studied constraints include convexity, concavity, symmetry, and monotonicity. These constraints can be used to enforce the desired behavior or incorporate prior knowledge about the studied phenomena, guiding the fitting process towards a more realistic solution. These are particularly useful to ensure proper behavior when extrapolating beyond the training data in cases where only limited training data is available. Also, this helps to reduce the influence of noise, mitigating overfitting. There has been a growing interest in shape-constrained regression, however, no established benchmark currently exists. As a result, many studies lack a direct comparison between methods or focus solely on practical applications. To address this gap, we propose an adaptation of the Feynman benchmark suite for symbolic regression as a general benchmark for shape-constrained regression. The Feynman benchmark suite is an appropriate choice because it is derived from physical phenomena where shape constraints naturally occur. In this benchmark, we evaluate model accuracy, the number of violated constraints, and model behavior when extrapolating data and handling noise. Additionally, we provide a Python interface to facilitate the evaluation of any regression model.

Parkinson's Disease (PD) is a progressive neurodegenerative disorder of the nervous system with a high rate of misdiagnosis. In this paper, we propose a Grammatical Evolution (GE) approach for classifying PD patients, that uses hinge loss as a surrogate fitness function. We compare our approach to standard GE using accuracy as its fitness function. Our results demonstrate that the surrogate fitness approach consistently produces models with better accuracy and reduced complexity. These results highlight the potential of using our approach as a powerful tool for developing trustworthy AI applications in the medical domain.

We revisit the use of the Alternating Pareto Tournament selection strategy, which can efficiently optimize multiple independent fitness objectives. We explore how alternating objectives can be used to exploit a new model curvature estimator in search. We demonstrate this strategy can be used to effectively balance model complexity, accuracy, and model curvature. We further showcase how alternating objectives can be tuned to apply uneven fitness pressure on each objective by changing the frequency each objective is used across generations. We show that considering complexity and curvature during search can improve training efficiency while also improving generalization capabilities.

Symbolic Regression (SR) is a powerful technique for discovering interpretable mathematical expressions. However, benchmarking SR methods remains challenging due to the diversity of algorithms, datasets, and evaluation criteria. In this work, we present an updated version of SRBench. Our benchmark expands the previous one by nearly doubling the number of evaluated methods, refining evaluation metrics, and using improved visualizations of the results to understand the performances. Additionally, we analyze trade-offs between model complexity, accuracy, and energy consumption. Our results show that no single algorithm dominates across all datasets. We propose a call for action from SR community in maintaining and evolving SRBench as a living benchmark that reflects the state-of-the-art in symbolic regression, by standardizing hyperparameter tuning, execution constraints, and computational resource allocation. We also propose deprecation criteria to maintain the benchmark's relevance and discuss best practices for improving SR algorithms, such as adaptive hyperparameter tuning and energy-efficient implementations.

We introduce Hierarchical Multi-view Symbolic Regression (H-MvSR), a novel evolutionary framework that discovers closed-form expressions linking environmental drivers to functional gene abundances across multiple ocean layers. Our method models each depth layer as a separate view while enforcing hierarchical constraints that promote both global structural consistency and local biological specificity. The symbolic models are evolved under multi-objective criteria that balance predictive accuracy, expression simplicity, and cross-view coherence. Furthermore, the framework incorporates pathway-level biological priors, enabling grouped symbolic modeling of molecular functions participating in the same metabolic process. We evaluate H-MvSR using depth-resolved genomic and environmental data from global ocean expeditions and compare its performance against state-of-the-art SR systems. Results show that H-MvSR improves interpretability and multiview consistency while recovering biologically meaningful relationships.

Many machine learning models perform well when making predictions within the training data range, but often struggle when required to extrapolate beyond it. Symbolic regression (SR) using genetic programming (GP) can generate flexible models but is prone to unreliable behaviour in extrapolation. This paper investigates whether adding synthetic data can help improve performance in such cases. We apply Kernel Density Estimation (KDE) to identify regions in the input space where the training data is sparse. Synthetic data is then generated in those regions using a knowledge distillation approach: a teacher model generates predictions on new input points, which are then used to train a student model. We evaluate this method across six benchmark datasets, using neural networks (NN), random forests (RF), and GP both as teacher models (to generate synthetic data) and as student models (trained on the augmented data). Results show that GP models benefit most when trained with synthetic data from NN and RF. The most significant improvements are observed in extrapolation regions, while changes in interpolation areas show only slight changes. We also observe heterogeneous errors, where model performance varies across different regions of the input space. Overall, this approach offers a practical solution for better extrapolation.

With the recent advancements in symbolic regression (SR) enabling search over large function spaces, recovering complex models from data may become attainable. But in what settings can SR algorithms be expected to recover the true data-generating model, or at least the best prediction model? This paper phrases SR as a model selection problem and formalizes the discussion on whether model recovery is possible. For the case of estimating an unknown non-linear conditional expectation function, exhaustive symbolic regression (ESR) is conjectured to select the correct functional form in large samples, given that the true conditional expectation function is in the search space and that a consistent model selection criterion is used. Within the PAC-learning framework, ESR can be phrased as structural risk minimization (SRM) problem, and we indicate that ESR is non-uniformly PAC-learnable under mild assumptions. Finally, we discuss post-selection inference for models selected via SR.

System identification is the task of automatically learning the model of a dynamical system, which can be represented as a system of ordinary differential equations (ODEs), using data points from time-series trajectories. This challenge has been addressed through various methods, including sparse regression, specialized neural networks, and symbolic regression. However, applying standard symbolic regression requires transforming the trajectory data to frame the problem as learning a set of regular equations. This study presents a first comprehensive comparison of the two most common data transformation approaches for system identification, evaluating their performance on a recently published benchmark suite of ODE systems. Our findings reveal that both approaches are highly sensitive to even moderate amounts of added noise, to different degrees. More surprisingly, we also show that data transformations can generate misleading search spaces, even under noise-free conditions. Further analysis indicates that reducing the data sampling step size significantly improves performance, suggesting that both transformation techniques are also affected by sampling frequency, and indicating possible future directions of research for system identification using symbolic regression.

The generation of compact regression models is crucial for interpretability in symbolic regression. Pruning is a well-known technique to compactify models and is usually used in a post hoc fashion as a way to combat bloat and overfitting. This paper introduces a continuous pruning mechanism that simplifies symbolic regression trees during evolution, rather than as a post-processing step. Experiments on regression datasets from the Penn Machine Learning Benchmark show that while this approach reduces overfitting as expected, it also influences the search behavior itself. The impact of pruning depends on the selection procedure, particularly whether children compete with their siblings or their parents. Notably, while pruning is often viewed as a method to combat bloat, our results indicate that its most pronounced effects occur in already depth-constrained contexts, where selection pressure is high, and tree size is inherently limited.

Vehicle Routing Problems are critically important in areas such as logistics, waste collection, and emergency service distribution. Traditionally, designing effective algorithms for these problems requires considerable manual effort and expert knowledge. In this paper, we apply the automatic algorithm design approach to vehicle routing problems using the EMILI (Easily Modifiable Iterated Local Search) framework. EMILI enables a modular strategy for algorithm development by combining various algorithmic components through context-free grammars. When coupled with an automatic algorithm configurator, design decisions can be translated into configurable parameters. Experimental results on classical vehicle routing instances show that the automatically generated algorithms not only achieve competitive solution quality but also outperform state-of-the-art algorithms with significantly less design effort.

Given the rapid advancement of AI across various fields, it is crucial to bridge computational methods and creative poetry generation, pushing the boundaries of what artificial intelligence can achieve in creative domains. This work explores the potential of blending the NSGA-II evolutionary optimization, Gemini 1.5 and Monte Carlo Tree Search to generate and iteratively enhance poems while also incorporating human feedback. Since natural language generation can transform non linguistic inputs like data into expressive text, it opens up avenues to explore innovative poetic form. The results demonstrate the model's better poem generation over traditional methods, showcasing its ability to refine poetic quality dynamically through evolutionary cycles and user feedback, thus setting a new standard for automated poetic creativity. Future work will explore deeper semantic control mechanisms, refined evaluation strategies, and broader linguistic adaptability across diverse poetic traditions.

Efficient waste collection is a significant challenge for urban populations and industrial sectors. This paper models the routing of waste collection using the Family Capacitated Vehicle Routing Problem (F-CVRP), considering different types of waste as families, and refers to this as the Waste Collection Problem (WCP). To solve the WCP, we introduce Q-learning integrated Genetic Algorithm (GA) and Ant Colony Optimization (ACO), denoted as QGA and QACO, respectively. The QGA and QACO models dynamically adjust their parameters, enhancing the balance between exploration and exploitation, thereby improving solution quality and convergence speed. We tested our models on 24 scenarios with varying numbers of vehicles and required visitation points. The Q-learning enhanced Ant Colony Optimization (QACO) algorithm excelled, ranking best in 16 out of 24 cases (67%). Our results demonstrate that QGA consistently outperforms classical GA and QACO surpasses classical ACO, with QACO emerging as the most effective. This highlights capability of QACO to optimize waste collection routes and enhance waste management systems.

Surrogate-assisted evolutionary algorithms (SAEAs) have been widely used for high-dimensional expensive multi-objective optimization problems (EMOPs). However, they often suffer from the curse of dimensionality, inefficiency, and poor adaptability. Hence, we proposes an efficient pretrained model-based SAEA, named Prior-data Fitted Networks-evolutionary algorithm (PFN-EA). By leveraging a pretrained baseline model instead of computationally expensive Gaussian Process (GP) models, PFN-EA significantly reduces training time complexity from O(n³) to O(n²d). It enhances accuracy through domain-adaptive fine-tuning that incorporates cross-domain prior knowledge, while balancing evaluation costs by alternating between real and surrogate-based predictions. Additionally, it combines reference vector-guided selection with dynamic dimensionality reduction for diversity-convergence trade-offs. Experiments on 100- to 200-dimensional DTLZ benchmarks show that PFN-EA outperforms six state-of-the-art SAEAs, achieving top results in 8 out of 14 cases with O(nd) prediction complexity. This work provides a scalable solution for high-dimensional EMOPs and pioneers the use of pretrained models in SAEAs.

This paper evaluates a framework which automatically sets penalty weights in QUBO (Quadratic Unconstrained Binary Optimization) through constraint sensitivity analysis. Combinatorial optimization problems need to be converted to QUBO form before being solved on quantum computers. Traditional QUBO models often use uniform penalty weights across constraints. The challenge of setting multiple penalty weights is that the weight combinations grow exponentially with the number of constraints. The proposed method first applies an exact and sequential method to obtain an initial weight, then adjusts individual weights based on their sensitivity, measured by the effect on the objective function. The constraint sensitivity analysis method was introduced very recently, and only preliminarily tested [10]. In this paper, we extend it to work on multiple (more than 2) constraints and test it on a wider problem benchmark. Experimental evaluations on the Quadratic Assignment Problem, Traveling Salesman Problem, and p-Median Facility Location Problem instances are presented. Results demonstrate that compared with Optuna and existing exact and sequential frameworks, the constraint sensitivity analysis method achieves superior solution quality and lower deviation from the optimal while maintaining acceptable feasibility rates.

Precision livestock farming increasingly relies on data-driven models to improve animal welfare and farm management. However, most existing approaches require manual data processing and result in black-box models that lack transparency for end-users such as veterinarians and farm staff. In this work, we propose an interpretable AutoML framework based on evolutionary computing to address these challenges. At the core of our system is an evolutionary preprocessing pipeline that automatically processes heterogeneous livestock data, including time series and static farm records, to generate compact and meaningful feature sets. To evaluate the pipeline's output, we employ symbolic regression to predict the remaining time to farrowing in sows, a key task to optimize confinement periods and improve welfare. Our approach focuses on producing interpretable models that balance predictive accuracy and simplicity. Initial results demonstrate that evolutionary strategies can successfully identify relevant feature transformations, enabling accurate and understandable farrowing predictions. This study highlights the potential of combining evolutionary preprocessing and symbolic regression to create trustworthy artificial intelligence tools for livestock farming. Future work will extend the pipeline to additional data types and further validate its usability in farm environments.

School Bus Routing can be affected by significant delays, particularly when transporting students with special educational needs and disabilities (SEND). The associated uncertainties can disrupt pickup schedules, negatively impacting students' commuting experience and readiness to learn upon arrival at their schools. These observations were further corroborated by our findings from stakeholders, where delays and unpredictability were consistently identified as significant pain points within existing SBRP solutions. In response to these challenges, this study, conducted in collaboration with an industry partner in North-West England, explores averaging techniques as a noise-handling strategy to mitigate the effects of stochastic disruptions. Specifically, the research investigates implicit and explicit averaging techniques to assess their effectiveness in improving the robustness of bus routes under uncertainty. Our results and findings using real-world datasets suggest that simulating delays and applying averaging techniques throughout the search process helps improve the robustness of solutions. We also examine the computational cost of repeated evaluations and discuss the trade-off with increased robustness. The concluding findings demonstrate the potential of our approach to reduce the effects of random disruptions that can be commonplace when designing school bus routes for pupils with special needs.

Many real-world settings call for multiple autonomous agents to coordinate and work as a collective. In such settings, cooperative coevolution—which trains a policy for each agent in parallel—has emerged as a popular choice. However, providing these coevolving agents only with feedback that evaluates the whole system of agents is often suboptimal, as learning is each individual agent's individual responsibility. This necessitates deriving agent-specific feedback from the system feedback, termed the "multiagent credit assignment problem". Oftentimes, however, such isolation of agent-specific feedback may be computationally expensive, and may not yield commensurate improvements in learning efficiency. In this paper, we present D^flex, an extension of Difference Evaluation that offers tuneable specificity in the feedback computed for each agent. This tuneability—achieved by allowing a subset of coevolving agents to 'share' feedback—allows practitioners to trade between feedback specificity and its compute expense. Our initial results in the multiagent rover exploration problem not only empirically indicate the presence of the feedback specificity vs. compute cost trade-off, but also show D^flex's ability to provide control over it.

Designing quantum circuits is a major challenge due to their sensitivity to noise and the complexity of quantum logic. This paper presents an evolutionary algorithm that balances multiple design criteria, namely fidelity and circuit depth, by combining them into a single scalarised fitness function. This approach enables efficient optimisation while avoiding the computational cost of fully multi-objective methods. A novel circuit representation and set of noise-aware genetic operators are introduced, and the technique is applied to evolve implementations of the Quantum Fourier Transform (QFT) for two- and three-qubit systems. Experimental results show that evolved circuits match or exceed ideal fidelity and outperform textbook QFT implementations under simulated noise. These findings highlight the potential of hardware-aware evolutionary design for producing circuits that are both accurate and resilient on near-term quantum hardware.