GECCO '23 Companion: Proceedings of the Companion Conference on Genetic and Evolutionary Computation

Efficient energy management is critical to building inclusive, safe, resilient, and sustainable cities and human settlements. Optimizing the operation and planning of smart grids is crucial in this regard and remains an active research area. The "Competition on Evolutionary Computation in the Energy Domain" has been held annually since 2017. Its 2023 edition focuses on two problems: Risk-based optimization of energy resource management considering the uncertainty of high penetration of distributed energy resources, and Long-term transmission network expansion planning. In this paper, we apply the RCED-UMDA algorithm to solve these problems, and our experimental results demonstrate its superiority over the top three algorithms of the 2022 and 2021 competition editions.

The Vehicle Routing Problem with Time Windows (VRPTW) is an extension of VRP that introduces time window constraints to the routing optimization process. Scaling Evolutionary Computation algorithms for VRPTW to handle large-scale problems poses significant challenges. Machine Learning assisted Evolutionary Computation strategy have been proposed to enhance optimization algorithms' efficiency and effectiveness. This study proposes a machine-learning model that exploits the graphical nature of VRP to design and improve evolutionary computational methods. The aim is to improve the resilience and efficiency of VRPTW optimization and provide better-quality solutions for practical applications.

Vehicle routing problems have attracted increasing attention because of the rapid development of transportation. Companies want to reduce the cost by lowering the number of vehicles and the total distances, which can be considered as a combinatorial optimization problem. The ant colony algorithm shows great potential in solving vehicle routing problems. However, it suffers from a low convergence speed due to the randomly initialized pheromone, which may cause a waste of computational resources in the early search process. To address this problem, a graph neural network is pre-trained to provide prior knowledge to initialize the pheromone in the ant colony algorithm, which can boost the convergence process. In addition, some classic local research methods are applied to balance the exploration and exploitation of the evolutionary process.

Vehicle routing problem with time windows (VRPTW) is a typical class of constrained path planning problems in the field of combinatorial optimization. VRPTW considers a delivery task for a given set of customers with time windows, and the target is to find optimal routes for a group of vehicles that can minimize the total transportation cost. The traditional heuristics suffer from several limitations when solving VRPTW, such as poor scalability, sensitivity to hyperparameters and difficulty in handling complex constraints. Recent advance in machine learning makes it possible to enhance heuristic approaches via learned knowledge. In this paper, we propose a graph Q-learning assisted ant colony optimization algorithm named GQL-ACO to solve VRPTW. Compared to vanilla ant colony optimization (ACO), our proposed method first employs the learned heuristic values by using graph Q learning, instead of handcrafted ones, to define the hyperparameters of ACO. Second, we design a collaborative search strategy by combining ACO and Q-learning effectively, which can adaptively adjust the hyperparameters of ACO based on the search experiences.

This article summarises recent work in the domain of feature-free algorithm selection that was published in the Journal of Heuristics in January 2023, with the title 'Automated Algorithm Selection: from Feature-Based to Feature-Free Approaches'. Specifically, we consider domains in which there is implicit sequential information encapsulated in the data, e.g., in online bin-packing.

We train two types of recurrent neural networks (RNN) to predict a packing heuristic in online bin-packing that use the sequence of item-sizes as input, i.e. no features are derived to describe the instance. This contrasts to typical approaches to algorithm-selection. The RNN approaches are shown to be capable of achieving within 5% of the oracle performance on between 80.88 and 97.63% of the instances, depending on the dataset. They are also shown to outperform classical machine learning models trained using derived features. In order to explain the observed result, we suggest that our methods perform well when the instances exhibit some implicit structure. To provide evidence for this, 14 new datasets with controllable levels of structure are generated, indicating that a critical threshold of structure is required before algorithm-selection delivers benefit.

We propose a two-stage surrogate-assisted evolutionary approach to address the computational issues arising from using Genetic Algorithm (GA) for feature selection in a wrapper setting for large datasets. The proposed approach involves constructing a lightweight qualitative meta-model by sub-sampling data instances and then using this meta-model to carry out the feature selection task.

We define "Approximation Usefulness" to capture the necessary conditions that allow the meta-model to lead the evolutionary computations to the correct maximum of the fitness function. Based on our procedure we create CHC_QX a Qualitative approXimations variant of the GA-based algorithm CHC (Cross generational elitist selection, Heterogeneous recombination and Cataclysmic mutation). We show that CHC_QX converges faster to feature subset solutions of significantly higher accuracy, particularly for large datasets with over 100K instances. We also demonstrate the applicability of our approach to Swarm Intelligence (SI), with results of PSO_QX, a qualitative approximation adaptation of the Particle Swarm Optimization (PSO) method. A GitHub repository with the complete implementation is available².

This paper for the Hot-off-the-Press track at GECCO 2023 summarizes the original work published at [3].

SonOpt is an open source application that generates sound to facilitate a better understanding of the algorithmic behaviour of bi-objective population-based optimisation algorithms. At each generation of an algorithmic search process, SonOpt receives the current Pareto front approximation (the approximation set) and the hypervolume contributions of the approximation set points. It then produces three distinctive sound streams encapsulating information about the evolving shape of the approximation set, recurrence of approximation set points across generations and their location within the approximation set, and the distribution of hypervolume contributions within the approximation set. In turn, this information provides insights about convergence/stagnation of an algorithm, diversity in the approximation set, and relative importance of approximation set points. In practice, SonOpt is used alongside visualisation methods to facilitate multi-modal monitoring of the algorithmic search process. We demonstrate SonOpt's responsiveness via a numerical and audio analysis performed on a range of bi-objective optimisation problems using several well-known optimisation algorithms (NSGA-II, MOEA/D, multi-objective random search). SonOpt is available for download at https://github.com/tasos-a/SonOpt-2.0, and a range of videos is available at https://tinyurl.com/sonopt2 for live demonstrations of SonOpt. This is an extended abstract of [1].

Very recently, the first mathematical runtime analyses of the multiobjective evolutionary optimizer NSGA-II have been conducted. We continue this line of research with a first runtime analysis of this algorithm on a benchmark problem consisting of multimodal objectives. We prove that if the population size N is at least four times the size of the Pareto front, then the NSGA-II with four standard ways to select parents, bit-wise mutation, and crossover with rate less than one, optimizes the OneJumpZeroJump benchmark with jump size 2 ≤ k ≤ n/4 in time O(Nn^k). When using fast mutation instead of bit-wise mutation this guarantee improves by a factor of k^Ω(k). Overall, this work shows that the NSGA-II copes with the local optima of the OneJumpZeroJump problem at least as well as the global SEMO algorithm.

This paper for the Hot-off-the-Press track at GECCO 2023 summarizes the work Benjamin Doerr, Zhongdi Qu: A first mathematical runtime analysis of the NSGA-II on a multimodal problem. IEEE Transactions on Evolutionary Computation, to appear. DOI: 10.1109/TEVC.2023.3250552 [10].

Due to the more complicated population dynamics of the NSGA-II, none of the existing runtime guarantees for this algorithm is accompanied by a non-trivial lower bound. Via a first mathematical understanding of the population dynamics of the NSGA-II, that is, by estimating the expected number of individuals having a certain objective value, we prove that the NSGA-II with suitable population size needs Ω (Nn log n) function evaluations to find the Pareto front of the OneMinMax problem and Ω(Nn^k) evaluations on the OneJumpZeroJump problem with jump size k. These bounds are asymptotically tight (that is, they match previously shown upper bounds) and show that the NSGA-II here does not even in terms of the parallel runtime (number of iterations) profit from larger population sizes. For the OneJumpZeroJump problem and when the same sorting is used for the computation of the crowding distance contributions of the two objectives, we even obtain a runtime estimate that is tight including the leading constant.

This paper for the Hot-off-the-Press track at GECCO 2023 summarizes the work Benjamin Doerr, Zhongdi Qu: From understanding the population dynamics of the NSGA-II to the first proven lower bounds. Proceedings of AAAI 2023, to appear [7].

Very recently, the first mathematical runtime analyses for the NSGA-II, the most common multi-objective evolutionary algorithm, have been conducted. Continuing this research direction, we prove that the NSGA-II optimizes the OneJumpZeroJump benchmark asymptotically faster when crossover is employed. Together with a parallel independent work by Dang, Opris, Salehi, and Sudholt (also at AAAI 2023), this is the first time such an advantage of crossover is proven for the NSGA-II. Our arguments can be transferred to single-objective optimization. They then prove that crossover can speed up the (μ + 1) genetic algorithm in a different way and more pronounced than known before. Our experiments confirm the added value of crossover and show that the observed advantages are even larger than what our proofs can guarantee.

This paper for the Hot-off-the-Press track at GECCO 2023 summarizes the work Benjamin Doerr, Zhongdi Qu. Runtime analysis for the NSGA-II: Provable speed-ups from crossover, Conference on Artificial Intelligence, AAAI 2023. AAAI Press, to appear. [13].

Symbolic Regression (SR) is the task of finding closed-form analytical expressions that describe the relationship between variables in a dataset. In this work, werethink SR and introduce mechanisms from two perspectives: morphology and adaptability. Morphology: Man-made heuristics are typically utilized in SR algorithms to influence the morphology (or structure) of candidate expressions, potentially introducing unintentional bias and data leakage. To address this issue, we create a depth-aware mathematical language model trained on terminal walks of expression trees, as a replacement to these heuristics. Adaptability: We promote alternating fitness functions across generations, eliminating equations that perform well in only one fitness function and as a result, discover expressions that are closer to the true functional form. We demonstrate this by alternating fitness functions that quantify faithfulness to values (via MSE) and empirical derivatives (via a novel theoretically justified fitness metric coined MSEDI). Proof-of-concept: We combine these ideas into a minimalistic evolutionary SR algorithm that outperforms a suite of benchmark and state of-the-art SR algorithms in problems with unknown constants added, which we claim are more reflective of SR performance for real-world applications. Our claim is then strengthened by reproducing the superior performance on real-world regression datasets from SRBench. This Hot-of-the-Press paper summarizes the work K.S. Fong, S. Wongso and M. Motani, "Rethinking Symbolic Regression: Morphology and Adaptability in the Context of Evolutionary Algorithms", The Eleventh International Conference on Learning International Conference on Learning Representations (ICLR'23).

Mitigating algorithmic bias during the development life cycle of AI-enabled software is crucial given that any bias in these algorithms is inherited by the software systems using them. At the Hot-off-the-Press GECCO track, we aim at disseminating our article Multi-objective search for gender-fair and semantically correct word embeddings. Applied Soft Computing, 2023 [5]. In this work, we exploit multi-objective search to strike an optimal balance between reducing gender bias and improving semantic correctness of word embedding models, which are at the core of many AI-enabled systems. Our results show that, while single-objective search approaches are able to reduce the gender bias of word embeddings, they also reduce their semantic correctness. On the other hand, multi-objective approaches are successful in improving both goals, in contrast to existing work which solely focuses on reducing gender bias. Our results show that multi-objective evolutionary approaches can be successfully exploited to address bias in AI-enable software systems, and we encourage the research community to further explore opportunities in this direction.

Despite initial indifference towards boundary control methods (BCM) in the context of metaheuristic algorithm design, benchmarking, and execution, our research demonstrates their critical importance. This study investigates how the choice of a particular BCM can profoundly influence the performance of competitive algorithms. We analyzed the top three algorithms from the 2017 and 2020 IEEE CEC competitions, posing the following question: Could a change in BCM usage alter an algorithm's overall performance and, consequently, its ranking among competitors? Our findings reveal that paying attention to BCMs can lead to significant improvements.

The experiments revealed that BCM selection can significantly impact an algorithm's performance and, in some instances, its competition rank. However, most authors omitted to mention the implemented BCM, resulting in poor reproducibility and deviating from recommended benchmarking practices for metaheuristic algorithms.

The conclusion is that the BCM should be considered another vital metaheuristics input variable for unambiguous reproducibility of results in benchmarking and for a better understanding of population dynamics.

Many real-world optimization problems may be classified as Large-Scale Global Optimization (LSGO) problems. When these high-dimensional problems are continuous, it was shown effective to embed a decomposition strategy into a Cooperative Co-Evolution (CC) framework. The effectiveness of the method that decomposes a problem into subproblems and optimizes them separately may depend on the decomposition accuracy and cost. Recent decomposition strategy advances focus mainly on Differential Grouping (DG). However, when a considered problem is nonadditively separable, DG-based strategies may report some variables as interacting, although the interaction between them does not exist. Monotonicity checking strategies do not suffer from this disadvantage. However, they suffer from another decomposition inaccuracy - monotonicity checking strategies may miss discovering many existing interactions. Therefore, Incremental Recursive Ranking Grouping (IRRG) is a new proposition that accurately decomposes both additively and nonadditively separable problems. The decomposition cost of IRRG is higher when compared with Recursive DG 3 (RDG3). Since the higher cost was a negligible part of the overall computational budget, optimization results of the considered CC frameworks were affected mainly by the decomposition accuracy.

Optimizing functions without access to gradients is the remit of black-box methods such as evolution strategies. While highly general, their learning dynamics are often times heuristic and inflexible --- exactly the limitations that meta-learning can address. Hence, we propose to discover effective update rules for evolution strategies via meta-learning. Concretely, our approach employs a search strategy parametrized by a self-attention-based architecture, which guarantees the update rule is invariant to the ordering of the candidate solutions. We show that meta-evolving this system on a small set of representative low-dimensional analytic optimization problems is sufficient to discover new evolution strategies capable of generalizing to unseen optimization problems, population sizes and optimization horizons. Furthermore, the same learned evolution strategy can outperform established neuroevolution baselines on supervised and continuous control tasks. As additional contributions, we ablate the individual neural network components of our method; reverse engineer the learned strategy into an explicit heuristic form, which remains highly competitive; and show that it is possible to self-referentially train an evolution strategy from scratch, with the learned update rule used to drive the outer meta-learning loop.

Lottery tickets in Deep Learning [2] refer to highly sparse neural network initializations, which train to the performance level of their dense counterparts The existence of such sparse trainable initializations has previously been documented for a variety of gradient-based training settings. But is the lottery ticket phenomenon an idiosyncrasy of stochastic gradient descent or does it generalize to evolutionary optimization? In this paper we establish the existence of highly sparse trainable initializations for evolution strategies (ES) and characterize qualitative differences compared to gradient descent (GD)-based sparse training. We introduce a novel signal-to-noise (SNR) iterative pruning procedure, which extracts evolvable sub-networks and incorporates loss curvature information into the network pruning step. We demonstrate the existence of highly sparse evolvable initializations for a wide range of network architectures, evolution strategies and task settings. Furthermore, we find that these initializations encode an inductive bias, which transfers across different evolution strategies, related tasks and even GD-based training. Finally, we compare the local optima resulting from the different optimization paradigms and sparsity levels. In contrast to GD, ES explore diverse and flat local optima and do not preserve linear mode connectivity across sparsity levels and independent runs. The full paper was accepted at the ICML conference [4].

This paper proposes a technique combining machine learning and an evolutionary algorithm for solving a graph-based multiobjective optimization problem related to epidemics control. In the studied problem, graph nodes can be protected, by vaccinations, against a simulated epidemic. To solve this problem, a classifier-based multiobjective evolutionary algorithm is proposed, in which population initialization, crossover, mutation and local search are guided by a previously trained machine learning model (a classifier). In the experiments, several machine learning models were considered: the multilayer perceptron (MLP) neural network, the Naïve Bayes classifier, the Support Vector Machine (SVM) and several simpler classifiers. The multilayer perceptron (MLP) neural network was found to be the best performing classifier. The proposed method outperformed an evolutionary optimizer not using any classifier-based components. Results of the experiments shown that knowledge can be transferred from smaller problem instances to larger ones using trained machine learning models. The MLP classifier trained on data collected from instances with 1000 graph nodes maintained good performance when used on instances with up to 20000 nodes.

This Hot-off-the-Press paper summarizes our recently published work, "Matchmaker, Matchmaker, Make Me a Match: Geometric, Variational, and Evolutionary Implications of Criteria for Tag Affinity" [8]. This work appeared in Genetic Programming and Evolvable Machines. Genetic programming systems commonly use tag matching to decide interactions between system components. However, the implications of criteria used to determine affinity between tags with respect evolutionary dynamics have not been directly studied. We investigate differences between tag-matching criteria with respect to geometric constraint and variation generated under mutation. In experiments, we find that tag-matching criteria can influence the rate of adaptive evolution and the quality of evolved solutions. Better understanding of the geometric, variational, and evolutionary properties of tag-matching criteria will facilitate more effective incorporation of tag matching into genetic programming systems. By showing that tag-matching criteria influence connectivity patterns and evolutionary dynamics, our findings also raise fundamental questions about the properties of tag-matching systems in nature.

This Hot-off-the-Press abstract aims at disseminating our recent work titled "MEG: Multi-objective Ensemble Generation for Software Defect Prediction" published in the proceedings of the 16th ACM/IEEE International Symposium on Empirical Software Engineering and Measurement (ESEM) [4]. We believe this work is of interest for the GECCO community as it proposes a novel way to automatically generate ensemble machine learning models leveraging the power of evolutionary computation: MEG introduces the concept of whole-ensemble generation as opposed to the well known Pareto-ensemble generation. While we evaluate the effectiveness of MEG for Software Defect Prediction in our work, MEG can be applied to any classification or regression problem and we invite both researchers and practitioners to further explore its effectiveness for other application domains. To this end, we have made MEG's source code publicly available.

Siamese Neural Networks (SNN) are known to perform well in resource-constrained scenarios where computation and data availability are limited. They utilise the similarity space of a given dataset to extract distinguishing features between dissimilar data samples. Such features have also been utilised for classification tasks. Though several works on enhancing the accuracies and inference times using such similarity spaces have been reported, there is still scope for investigations that can yield more efficient strategies. The Biological Immune System (BIS) is known for employing such a transformation to recognise and contain antigenic attacks. Concepts from a BIS can thus, aid in boosting the classification performance of SNNs. This paper summarizes such an attempt made in our work "Immuno-Inspired Augmentation of Siamese Neural Network for Multi-class Classification" [8] presented at IVCNZ 2022, first published in Lecture Notes in Computer Science, 2023, vol 13836, pages 486--500 by Springer. A novel SNN-based multi-class classification method augmented with an immuno-inspired approach that allows an SNN to plug class-specific characteristics into its architecture is presented herein. The empirical analyses and results conducted on three benchmark datasets, clearly indicate that this method delivers higher accuracies and lower inference times when compared to recent SNN-based multi-class classification techniques.

Analysing Neuroevoution algorithms often proves to be challenging from a fitness performance standpoint. We argue that our Neuroevolution Trajectory Networks (NTNs) visualisation technique, based on the use of complex networks, can effectively highlight the idiosyncratic differences and peculiarities of this family of evolutionary algorithms. This work deploys NTNs specifically to analyse the transfer of knowledge, from different benchmark classification datasets. Here, the knowledge transferred, is considered as the inheritance of evolutionary units representing the layers (and learning optimisers) forming the architecture of Convolutional Neural Networks (CNNs), incrementally developed and generated by Fast-Deep Evolutionary Network Structured Representation. Our approach highlights salient characteristics about this transfer learning paradigm, as well as exceptional findings, which help consolidate our understanding of Neuroevolution and Deep learning. This Hot-off-the-Press paper summarises the work awarded "Best Paper" entitled: "Under the Hood of Transfer Learning for Deep Neuroevolution" by Stefano Sarti, Nuno Lourenço, Jason Adair, Penousal Machado, Gabriela Ochoa; published in Applications of Evolutionary Computation. EvoApplications 2023. https://doi.org/10.1007/978-3-031-30229-9_41

Previously, in a GECCO 2022 Hot-off-the-Press paper [1], we presented a comprehensive survey of the modeling and prediction of Web service (WS) quality of service (QoS) time series [2]. Based on the exhaustive investigation in [2], this research subject has already been deeply and widely studied for over a decade; for the one-step-ahead version of this problem, which can be considered its most primitive problem form, overall, our proposed and developed genetic programming (GP)-based solution outperforms competitors in terms of both modeling and forecasting accuracy, according to our ongoing study, which has been reported in [3] [4] [5]. Nevertheless, as argued in [6], for the long-term use and rental of cloud-based WSs, multi-step-ahead QoS time series prediction of these services is needed. Thus, the authors employed and revised the two most widely used single-predictor-based time series methods, namely, autoregressive integrated moving average (ARIMA) models and exponential smoothing (ES), to address this latest version of the problem.

For this multi-step-ahead variant of the problem, in Y. Y. Fanjiang, Y. Syu and W. L. Huang, "Time Series QoS Forecasting for Web Services Using Multi-Predictor-based Genetic Programming", IEEE Transactions on Services Computing (TSC), Vol. 15, P.P. 1423--1435, 2022, we devise and employ a multipredictor-based approach to genetic programming. First, due to its superiority in our past work for the basic (i.e., one-step-ahead) version of the problem, we investigate the performance of GP on this newly emerged (multi-step-ahead) form of the problem. Second, instead of using a single model for predictions regarding multiple future time points, which is the method commonly adopted in prior research [2], we evolve and apply a dedicated GP-generated predictor for each targeted future time point and its projection. Furthermore, two different strategies for the consumed predictor inputs are tested to determine their differences and influence on accuracy so that a better strategy can be empirically determined. In addition, we propose in the reported paper [7] two disparate techniques to further enhance the resulting performance of our multi-predictor-based GP method.

As in our previous GECCO Hot-off-the-Press paper [1], this abstract paper presents to the GECCO community a verified application of GP on a more difficult and challenging type of WS QoS time series forecasting. Our purpose is to enable the GECCO community to use this application of GP, to try to improve GP to obtain more accurate and better results, and to investigate other potential evolutionary paradigms and techniques for this issue.

The capacitated arc routing problem (CARP) aims at scheduling a fleet of vehicles with limited capacities to serve a set of tasks in a graph. The dynamic CARP (DCARP) optimization focuses on updating the vehicles' service routes when unpredicted dynamic events happen and deteriorate the current service plan. Due to the outside vehicles are still being in their service when dynamic events happen and being located at different positions of the graph with different remaining capacities, the optimization algorithms for static CARP are unsuitable for solving the DCARP instance. However, in the existing literature, almost all proposed algorithms for DCARP were designed only for specific dynamic events instead of generic dynamic events such as the changing of traversing costs, the changing of the task's demand, and the changing of the task's number. Moreover, these algorithms are unable to benefit from the wealth of contributions provided by the existing CARP literature. In this work, we proposed a novel generalized meta-heuristic framework which enables all algorithms designed for static CARP to be capable of solving DCARP instances. Our experimental results demonstrated that the proposed framework significantly improves over state-of-the-art dynamic optimization algorithms in terms of the quality of obtained solution within the limited computational time.

This paper for the Hot-off-the-Press track at GECCO 2023 summarizes the work Hao Tong, Leandro L. Minku, Stefan Menzel, Bernhard Sendhoff, and Xin Yao: A Novel Generalized Meta-heuristic Framework for Dynamic Capacitated Arc Routing Problems published in IEEE Transactions on Evolutionary Computation [10].

As a search-based software engineering (SBSE) user (researcher or practitioner), do you wonder which multi-objective search algorithm(s) (MOSAs) to use to solve your SE problem? If so, instead of just following the crowd and picking the more commonly used MOSA, in this paper, we provide evidence-based guidance to SBSE users to select one or more MOSAs given that they know which qualities they are looking for in the solutions, either in the form of quality indicators (QIs) or quality aspects. To collect the evidence, we performed a large-scale experiment using six MOSAs, eight QIs, and 18 SBSE search problems. In particular, we studied the preferences among MOSAs and QIs in SBSE. Some key findings of our experiment are: (1) each MOSA prefers a specific QI and vice-versa; (2) in general, all the QIs prefer two MOSAs the most, i.e., NSGA-II and SPEA2; (3) the characteristics of the search problems affect the preferences; (4) in terms of quality aspects if some QIs cover the same quality aspect(s) that does not mean that they have the same MOSA preferences. Based on the analysis of the results, we provide guidance for the users in selecting MOSAs.

This is an extended abstract of the paper [1]: J. Wu, P. Arcaini, T. Yue, S. Ali, and H. Zhang, "On the Preferences of Quality Indicators for Multi-Objective Search Algorithms in Search-Based Software Engineering", in Empirical Software Engineering, 27, 144 (2022).

This Hof-off-the-Press paper summarizes our recently published work, "SR-Forest: A Genetic Programming based Heterogeneous Ensemble Learning Method," published in IEEE Transactions on Evolutionary Computation [4]. This paper presents SR-Forest, a novel genetic programming-based heterogeneous ensemble learning method, which combines the strengths of decision trees and genetic programming-based symbolic regression methods. Rather than treating genetic programming-based symbolic regression methods as competitors to random forests, we propose to enhance the performance of random forests by incorporating genetic programming as a complementary technique. We introduce a guided mutation operator, a multi-fidelity evaluation strategy, and an ensemble selection mechanism to accelerate the search process, reduce computational costs, and improve predictive performance. Experimental results on a regression benchmark with 120 datasets show that SR-Forest outperforms 25 existing symbolic regression and ensemble learning methods. Moreover, we demonstrate the effectiveness of SR-Forest on an XGBoost hyperparameter performance prediction task, which is an important application area of ensemble learning methods. Overall, SR-Forest provides a promising approach to solving regression problems and can serve as a valuable tool in real-world applications.

Automated Guided Vehicles (AGVs) are common elements of contemporary industry. Their continuous operation, and thus detection of anomalies in their operational cycles, is critical for uninterrupted production flow. Prediction of signals, such as momentary power consumption (MPC), is used in most anomaly detection methods. Feature engineering - selection or weighting - can significantly improve prediction quality. In this work, we use a genetic algorithm (GA) to optimize weights for features from AGV telemetry. A 2-layer Long Short-Term Memory (LSTM) network was used to predict MPC. Our primary goal was identifying the most effective weighting strategy for enhancing predictive accuracy. We examined different schemes of population initialization. The performance of each was compared to baseline models. Results show a significant improvement in prediction quality compared to the baseline. Our application of GA optimization in feature engineering contributes to the growing body of knowledge on developing more reliable AGV systems, which can lead to reduced operational costs and enhanced sustainability in various industrial settings.

Tackling complex transportation problems is a core issue in intelligent transportation systems, logistics, and planning. Such discrete problems commonly deal with multiple transportation goals mapping them into the objectives targeted by the optimization algorithm. We introduce the parallel co-evolutionary memetic algorithm for the vehicle routing problem with time windows, being one of the most widely-adopted rich vehicle routing problems. Our approach benefits from the parallel evolution of several subpopulations, each intensifying a specific optimization aspect of the local search phase in the underlying memetic algorithm, and from the process of migrating the best individuals across subpopulations. The extensive computational experiments indicate that our technique outperforms a parallel memetic algorithm in which the parallel populations use the same local search procedures.

People with diabetes need to control their blood glucose levels to avoid dangerous situations such as getting into hypoglycemia or hyperglycemia, which can lead to long-term and short-term complications. One of the most important daily tasks of people with diabetes is to estimate or predict the glucose in a near future as a consequence of medication, eating, or insulin administration events. We present a parameterized hardware implementation of a blood glucose level predictor generator. The design was implemented over a Field Programmable Gate Array and uses as input variables a set of data from the person (blood glucose levels, carbohydrates, and insulin units). Our implementation produces personal devices the patient can use whenever new readings of the variable are available. Moreover, it could be combined with insulin pumps and continuous glucose monitoring systems to develop an artificial pancreas. For the model generation, we designed a novel technique based on grammars, cartesian genetic programming with an evolutionary strategy (1+λ) and a fitness function based on the Clarke Error Grid Analysis. Preliminary results show that our hardware implementation achieved higher speeds and lower power consumption than its software counterparts while preserving or even improving the accuracy of the predictions.

People with diabetes need to have their glucose levels under control, and it is essential for them to be able to know or estimate their glucose levels at any time. Continuous glucose monitors are commonly used, which measure interstitial glucose, an approximation of blood glucose, by means of a small catheter. Although most devices are not very intrusive, they do present some discomfort, and it would be preferable if these glucose levels could be estimated non-invasively, for example, through other physiological measurements collected in a simple way. This abstract describes our research on the performance of different grammatical evolution techniques to obtain accurate estimations of actual subcutaneous glucose values from non-invasive physiological measures, steps, calories and heart rates obtained with commercial smartwatches.

We analyze the performance of panmictic evolutionary algorithms in byzantine environments in which fitness can be computed by malicious agents. We measure the influence of the rate of unreliability of the environment, and the effect that a simple mechanism based on redundant computation can have on the results attained.

We present the Pareto Late Acceptance Hill Climbing algorithm, a multi-objective optimization algorithm based on the Late Acceptance Hill Climbing. We propose an initial experimental analysis of its behavior applying it to different formulations of the bi-objective Permutation Flowshop Scheduling Problem.

Grammar-guided genetic programming is a type of genetic programming that uses a grammar to restrict the solutions in the exploration of the search space. Different representations of grammar-guided genetic programming exist, each with specific properties that affect how the evolutionary process is developed. We propose a new representation that uses a tree structure with non-encoding nodes for the individuals in the population, a.k.a. Tree-Based Grammatical Evolution with Non-Encoding Nodes. Each tree's node has a set of children nodes and an associated number that determines which are used in decoding the solution and which are non-encoding nodes. This representation increases the size and complexity of the individuals while performing a more exhaustive exploration of the solution space. We compare the performance of our proposal with state-of-the-art genetic programming algorithms for the 11-multiplexer benchmark, showing encouraging results.

In this paper, we describe the experience gained when Evolutionary Algorithms were applied to SATB music composition and the impact it is demonstrating in Spanish Professional Music Conservatories for the last three years. To our knowledge, this is the first time that an EA-inspired tool has been used at a national level in music conservatories.

We study the behaviour of particle swarm optimisation (PSO) with increasing problem dimension for the Alpine 1 function as an exploratory and preliminary case study. Performance trends are analysed and the tuned population size for PSO across dimensions is considered. While performance generally decreases monotonically with scale, there is an unexpected improvement in performance part way along the trend. This also appears to coincide with a counterintuitive transition from large to small populations being preferred, and underlines the challenge, and importance of, selecting the right algorithm and configuration for the problem at each increase in dimensionality.

Pathfinding Algorithms are used in many research areas in different combinations and settings. In most cases, they are used for path planning, while another interesting problem class is path paving. This class represents road or railway construction, needle injection, mining, or metro planning. Finding the shortest or quickest path or minimizing energy consumption are often the objectives of current pathfinding problems. However, the influence on the environment which is induced when paving a path is not regarded in those problems so far. The proposed problem is an epistasis problem. In this work, we introduce the concept of path-influenced environments (PIEs), outline various paving strategies and give a detailed outlook on future research.

This study investigates whether a genetic algorithm (GA) can improve the performance of machine learning for sarcopenia diagnosis. An essential aspect of applying feature selection to machine learning for diagnosing sarcopenia is the selection of features that directly affect the diagnosis. To determine whether the GA can perform this logic effectively, we performed feature selection using the Korean Longitudinal Study of Aging (KLoSA) survey data. This study is significant because it implements feature selection using GA and shows that diagnosis performance is improved compared to other machine learning methods without feature selection. In addition, the results showed that GAs could improve the diagnosis of sarcopenia in future research.

Obesity is a significant public health concern that affects millions of people worldwide. As a complex condition influenced by various factors, modeling the transmission dynamics of obesity is crucial for developing effective interventions and public health policies. In recent years, there has been a growing interest in using epidemiological techniques to model the spread of obesity within populations. However, these techniques have limitations when accurately describing the available data, especially when considering uncertainties and inaccuracies. To address this issue, this paper proposes a novel approach to modeling the evolution of obesity as a transmission disease. Specifically, we use multi-objective dynamic structured grammatical evolution to generate models that accurately describe available data while considering their uncertainties and inaccuracies. Our approach is based on a synthetic dataset that tracks the evolution of a population divided into three groups according to the Body Mass Index of its individuals. Using this technique, we aim to identify lower-impact relationships often overlooked in standard models, which can improve the accuracy and understanding of the transmission dynamics of obesity. Our work aims to support the development of more effective public health policies and interventions for reducing obesity.

Using a case study of forecasting the recent, volatile electricity price from the Polish day-ahead market, the paper compares two different approaches to finding Temporal Convolutional Network configurations of high performance. First, the CMA-ES[1] was evaluated, and later, the MoTPE[4] was examined. For the same 24-h price forecast task and using the same training and test sets, the first, evolutionary approach resulted in both better prediction performance and, more importantly, significantly shorter computation time. The search through 10³ different hyperparameter combinations was completed in less than an hour, and the short-period evaluation resulted in sMAPE of 12.9 and rMAE of 0.31.

Quantifying the drought resistance of potato cultivars plays a key role in precision agriculture, and it may lead to the development of new varieties of plants that are more resistant to harsh environmental conditions. In this work, we tackle the issue of extracting such information in a non-invasive way by acquiring in-field hyperspectral measurements of the potato leaves. Then, we exploit an array of machine learning models to classify plants into three wilting classes based on such data, with those classes corresponding to their drought resistance. We show that evolutionary band selection can dramatically reduce the dimensionality of hyperspectral data while improving classification accuracy. Our experimental study revealed that the evolutionarily-optimized models offer high-quality performance with the impartial r_ϕ reaching 0.784, accuracy: 0.867, and a 30% improvement over the baseline models which do not benefit from band selection.

Selecting an appropriate neural network architecture and hyper-parameters to optimize performance for a given application is a difficult task. To overcome this challenge, Neural Architecture Search (NAS) and Hyperparameter Optimization (HPO) have been introduced. However, these techniques are often computationally-expensive and require significant amounts of execution time. To address this issue, we propose a semi-automated NAS approach that optimizes pre-existing architectural structures using genetic algorithms and eliminates unsuccessful combinations through shallow network training. The effectiveness of our technique was verified through an experiment that produces a family of AlexNet-like neural networks comprising 1296 models for image classification tasks. The computational study was conducted with five runs of a genetic algorithm, resulting in the deep models with mean loss of 0.7044 and accuracy of 0.7334, both with low standard deviations, outperforming the original AlexNet model with a significant margin.

This paper introduces a symbolic regression based filter transform for convolutional neural network using CGP (Cartesian Genetic Programming). Symbolic regression is a powerful technique to discover analytic equations that describe data, which can lead to explainable models and the ability to predict unseen data. In contrast, neural networks have achieved amazing levels of accuracy on image recognition and natural language processing tasks, but they are often seen as black-box models that are difficult to interpret and typically extrapolate poorly. symbolic regression approaches to deep learning are underexplored.

Surrogate-assisted evolutionary algorithms (SAEAs) aim to use efficient computational models with the goal of approximating the fitness function in evolutionary computation systems. This area of research has received significant attention from the specialised research community in different areas, for example, single and many objective optimisation or dynamic and stationary optimisation problems. An emergent and exciting area that has received little attention from the SAEAs community is in neuroevolution. This refers to the use of evolutionary algorithms in the automatic configuration of artificial neural network (ANN) architectures, hyper-parameters and/or the training of ANNs. However, ANNs suffer from two major issues: (a) the use of highly-intense computational power for their correct training, and (b) the highly specialised human expertise required to correctly configure ANNs necessary to get a well-performing network. This work aims to fill this important research gap in SAEAs in neuroevolution by addressing these two issues. We demonstrate how one can use a Kriging Partial Least Squares method in place of the well-known Kriging method, which normally cannot be used in neuroevolution due to the high dimensionality of the data.

This study experiments the integration of the zero-cost proxy metric Synaptic Flow with the Gene-pool Optimal Mixing (GOM) crossover to efficiently generate new candidates during an evolutionary neural architecture search (ENAS). Our experiments demonstrate that the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) with Synaptic Flow can obtain top-performing architectures with a small additional overhead compared to a classic Genetic Algorithm. Code is available at: https://github.com/ELO-Lab/SF-GOMENAS.

There are a lot of types of PSO to make conventional PSO as effective as possible. Basically, PSO is quite easy, and it is known as effective in any type of problems within several numbers of design variables. However, requirements of industrial problems become complicated that the number of design variables raise these days, and the following shortcoming make conventional PSO difficult to apply to such problems. The performance of conventional PSO depends on setting three parameters, and most of them set them priori to execution. This makes it impossible to search according to the situation of convergence. Once velocities become close to zero, those individuals lost ways to get out from local minimum. Therefore, we need some procedure like mutation in Genetic Algorithms. In large scale problems, there are some sort of dependencies in design variables. The effectiveness of PSO does not lose if the variable relationships and sets of relatively small numbers of design variables in problems are found. In this paper, we propose a new method Forked Divergence Particle Swarm Optimization (PSO) in order to overcome problems in conventional PSO. In the experiment, the effectiveness of the proposed method is validated through two types of benchmark functions.

Constructing a finite set of candidates for each node has been proved that it is an effective means in ant colony optimization (ACO) for solving the travelling salesman problem (TSP). However, some neighbor nodes in the optimal routes are two nodes with large separation distance. To solve this problem, this paper proposes an ACO with pre-exploration of outliers (ACO-EO). The techniques in ACO-EO include: a) the outliers selection, b) pre-exploration adjacent nodes for outliers. To verify the effectiveness of the ACO-EO, a number of experiments are conducted using 30 benchmark instances (ranging from 101 nodes to 1784 nodes in topologies) taken from the well-known TSPLIB. From the comparison with state-of-the-art ACO-based methods, ACO-EO outperforms these competitors in terms of convergence and solution accurancy.

Behavioural diversity has been demonstrated as beneficial in biological social systems, such as insect colonies and human societies, as well as artificial systems such as large-scale software and swarm-robotics systems. Evolutionary swarm robotics is a popular experimental platform for demonstrating the emergence of various social phenomena and collective behaviour, including behavioural diversity and specialization. However, from an automated design perspective, the evolutionary conditions necessary to synthesize optimal collective behaviours (swarm-robotic controllers) that function across increasingly complex environments (difficult tasks), remains unclear. Thus, we introduce a comparative study of behavioural-diversity maintenance methods (swarm-controller extension of the MAP-Elites algorithm) versus those without behavioural diversity mechanisms (Steady-State Genetic Algorithm), as a means to evolve suitable degrees of behavioural diversity over increasingly difficult collective behaviour (sheep-dog herding) tasks. In support of previous work, experiment results demonstrate that behavioural diversity can be generated without specific speciation mechanisms or geographical isolation in the task environment, although the direct evolution of a functionally (behaviorally) diverse swarm does not yield high task performance.

Our topic is performance differences between using random and chaos for particle swarm optimization (PSO). We take random sequences with different probability distributions and compare them to chaotic sequences with different but also with same density functions. This enables us to differentiate between differences in the origin of the sequences (random number generator or chaotic nonlinear system) and statistical differences expressed by the underlying distributions. Our findings (obtained by evaluating the PSO performance for various benchmark problems using statistical hypothesis testing) cast considerable doubt on previous results which compared random to chaos and suggested that the choice leads to intrinsic differences in performance.

Texture defect detection is the process of identifying and locating defects in a texture-based product or material, such as textiles, paper, or metal surfaces. This paper presents a novel approach for texture defect detection using statistical features and a bio-inspired algorithm. The use of statistical features for the detection of texture defects has proven to be an effective approach in many applications. The features of images are extracted using GLCM and GLRLM of textures, and combined to form a unified feature set. The Bat Algorithm (BAT) is then used for feature selection, in combination with a novel fitness function. The selected features are used to train a LGBM and MLPClassifier to classify the images as defective or non-defective. The proposed method was evaluated on a dataset of KolektorSDD2 images, which is a benchmark dataset for texture defect detection. Results demonstrate that the proposed method outperforms traditional feature selection methods and improves the overall accuracy of the defect detection system when LGBM classifier is used instead of MLPC. The proposed approach has potential applications in various texture-based industries and further research can be done to improve the method and test it on other datasets and applications.

Dynamic optimization problem (DOP) is a kind of problem that contains a series of static problems with different problem characteristics. The main idea of the existing dynamic optimization algorithms is to continuously locate and track changing optimal solutions using limited computational resources. Hence, how to strengthen the exploration ability for locating the optimum of the static problem in an environment and how to improve the adaptation ability to the changing optima in different environments are two key issues for efficiently solving DOP. To address these issues, we propose a diversity-driven multi-population particle swarm optimization (DMPSO) algorithm. First, we propose a center information-based update strategy to strengthen the exploration ability of the PSO algorithm in each subpopulation. Second, a stagnant subpopulation activation strategy is proposed to activate the stagnant subpopulations, and a random walk strategy is proposed to improve the optima tracking capability of the best-performing subpopulation. Third, an archive-based initialization strategy is proposed to reinitialize the population. Experimental studies are conducted on the moving peaks benchmark to compare the DMPSO algorithm with some state-of-the-art dynamic optimization algorithms. The experimental results show that the proposed DMPSO algorithm outperforms the contender algorithms which validate the effectiveness of the proposed algorithm.

We propose Multi-Task Multi-Behavior MAP-Elites, a variant of MAP-Elites that finds a large number of high-quality solutions for a large set of tasks (optimization problems from a given family). It combines the original MAP-Elites for the search for diversity and Multi-Task MAP-Elites for leveraging similarity between tasks. It performs better than three baselines on a humanoid fault-recovery set of tasks, solving more tasks and finding twice as many solutions per solved task.

We address the problem of promoting diversity in online embodied evolution of heterogeneous robot swarms. We argue that it is not easy to adapt existing diversity algorithms from traditional evolutionary robotics to this context and describe a method in which selection is based on originality and which allows a swarm of heterogeneous agents to maintain a high degree of diversity in behavioral space. We also describe a behavioral distance measure that compares behaviors in the same conditions to provide reliable measurements in online and distributed contexts. We test the selection scheme on an open-ended survival task and show its effectiveness. Without any other pressure besides that of the environment, the evolved strategies tend toward simplicity, exploiting the existing affordances. An additional external pressure enables the emergence of rich and diverse behaviors.

In complex network systems, the problem that how to select members with considerable information-spreading ability, i.e., the influence maximization (IM) problem, is a current research hotspot. In practice, networked systems are extremely vulnerable to interferences from external sources or even human sabotages, which cause direct disturbances on the topology. One of the common attacks is cascading failures. To cope with the IM problem under cascading failures, a new metric R_S-cf is defined to evaluate the performance of seeds under this attack model. Guided by this, a Memetic algorithm, named MA-RIM_cf, is devised to determine those nodes with both robustness and influential ability. The reasonableness and effectiveness of the algorithm are verified by experiments on synthetic network data. These solutions are expected to solve the influence maximization problem in realistic environments.

Multi-agent systems are often presented as a solution for dangerous missions, such as search-and-rescue and disaster relief, which require timely decision-making. However, the corresponding environments rarely allow for long range communication or control, and often come with a lack of crucial information for autonomous decision-making (e.g. topology of the area, or number and priority of targets).

In this paper, we present a fast collective decision-making framework for robotic swarms, which requires no external infrastructure or pre-existing knowledge. This method is based on running an abstract decision-making model simultaneously with an ad-hoc navigation strategy. We demonstrate the scalability of our proposed method with respect to the swarm size, and its flexibility regarding the number and quality of alternatives, in simulated experiments.

Inspired by biological and cultural evolution, there have been many attempts to explore and elucidate the necessary conditions for open-endedness in artificial intelligence and artificial life. Using a continuous cellular automata called Lenia as the base system, we built large-scale evolutionary simulations using parallel computing framework JAX, in order to achieve the goal of never-ending evolution of self-organizing patterns. We report a number of system design choices, including (1) implicit implementation of genetic operators, such as reproduction by pattern self-replication, and selection by differential existential success; (2) localization of genetic information; and (3) algorithms for dynamically maintenance of the localized genotypes and translation to phenotypes. Simulation results tend to go through a phase of diversity and creativity, gradually converge to domination by fast expanding patterns, presumably an optimal solution under the current design. Based on our experimentation, we propose several factors that may further facilitate open-ended evolution, such as virtual environment design, mass conservation, and energy constraints.

Real-world problems are often comprised of many objectives and require solutions that carefully trade-off between them. Current approaches to many-objective optimization often require challenging assumptions, like knowledge of the importance/difficulty of objectives in a weighted-sum single-objective paradigm, or enormous populations to overcome the curse of dimensionality in multiobjective Pareto optimization. Combining elements from Many-Objective Evolutionary Algorithms and Quality Diversity algorithms like MAP-Elites, we propose Many-objective Optimization via Voting for Elites (MOVE). MOVE maintains a map of elites that perform well on different subsets of the objective functions. On a 14-objective image-neuroevolution problem, we demonstrate that MOVE is viable with a population of as few as 50 elites and outperforms a naive single-objective baseline. We find that the algorithm's performance relies on solutions jumping across bins (for a parent to produce a child that is elite for a different subset of objectives). We suggest that this type of goal-switching is an implicit method to automatic identification of stepping stones or curriculum learning. We comment on the similarities and differences between MOVE and MAP-Elites, hoping to provide insight to aid in the understanding of that approach - and suggest future work that may inform this approach's use for many-objective problems in general.

Evolutionary transitions, where replicating units combine to form more complex units, are a major source of the complexity found in nature. In this paper we aim to find conditions that promote egalitarian major transitions in a digital artificial ecology. We identify major transitions in this context by observing changes in fitness across different levels of organization. Fitness increases primarily at the community level suggest the occurrence of major transitions. We employ a genetic algorithm using lexicase selection to find regions of parameter space that promote community-level fitness increases. This approach successfully finds multiple ecological community structures that appear to support major transitions. These results illustrate the power of evolutionary computation for exploring the parameter space of complex simulations and push us closer to an understanding of the factors that lead to egalitarian major transitions.

The design process of complex engineering systems may involve problems in which the number and type of design variables and constraints vary throughout the optimization process based on the values of dimensional variables. This category of problems is called Variable-Size Design Space optimization. A well-known application is the optimal layout problem which requires to place a variable number of components into a container. The dual objective is here to optimize the list of components in addition to their placements within the container. In this paper, a two-level algorithm is described to solve the aforementioned optimal layout problems. This algorithm combines the strength of a Swarm Intelligence algorithm based on a virtual-force system and a discrete Bayesian Optimization algorithm purposely adapted to tackle the dimensional aspect of this problem. The implementation of the two-level algorithm is discussed and the proposed approach is applied to the layout optimization of a satellite module. The performance of the algorithm is then analyzed with respect to several occupation rates of the system. This approach is also compared with a Hidden-Genes Genetic Algorithm.

Neuroevolution (NE) has recently proven a competitive alternative to learning by gradient descent in reinforcement learning tasks. However, the majority of NE methods and associated simulation environments differ crucially from biological evolution: the environment is reset to initial conditions at the end of each generation, whereas natural environments are continuously modified by their inhabitants; agents reproduce based on their ability to maximize rewards within a population, while biological organisms reproduce and die based on internal physiological variables that depend on their resource consumption; simulation environments are primarily single-agent while the biological world is inherently multi-agent and evolves alongside the population. In this work we present a method for continuously evolving adaptive agents without any environment or population reset. The environment is a large grid world with complex spatiotemporal resource generation, containing many agents that are each controlled by an evolvable recurrent neural network and locally reproduce based on their internal physiology. The entire system is implemented in JAX, allowing very fast simulation on a GPU. We show that NE can operate in an ecologically-valid non-episodic multi-agent setting, finding sustainable collective foraging strategies in the presence of a complex interplay between ecological and evolutionary dynamics.

Automata chemistries are a field within Artificial Life that studies how populations of self-replicating programs control their own evolution. Nanopond is an automata chemistry that until now had no publications available to document its features, no studies on what its outputs are, and no comparisons with other systems. Yet it is relatively easy to set up and compile; it runs very quickly, and can be parallelised; and it produces graphical results that suggest a level of emergent complexity worthy of scientific study. In this work, the emergent complexity observable in Nanopond is characterised and placed in the context of similar systems, notably Tierra, Avida, Amoeba and Stringmol. Premliminary results are presented which show how several common self-replicating attractor states in the emergent patterns exhibited by Nanopond are related to the distribution of energy around the system, demonstrating important properties of emergent complexity.

Robotic grasping refers to making a robotic system pick an object by applying forces and torques on its surface. Despite the recent advances in data-driven approaches, grasping still needs to be solved. In this work, we consider grasping as a Diversity Search problem, where we attempt to find as many solutions as possible that verify a sparse binary criterion. We propose a variant of a state-of-the-art QD method for grasping based on a divide-and-conquer paradigm to handle grasping discontinuities. Experiments conducted on 3 different robot-gripper setups and several standard objects show that this variant outperforms state-of-the-art for generating diverse repertoires of grasping trajectories.

The use of MAP-Elites in high-dimensional behavioral spaces requires a scalable method for dividing the space into regions of equal volume. So far, the recommended approach to generate these regions has been the Centroidal Voronoi Tesselation (CVT), but this algorithm has a significant computational cost (typically a few minutes for more than 50 dimensions). In this paper, we investigate alternative approaches to generate regions of equal volumes for MAP-Elites. In particular, we experiment with generating region centroids with low-discrepancy sequences (Sobol, Halton), pseudorandom numbers, and a simple blue noise generator. Our results show that, for spaces with 100 dimensions, most methods perform similarly, including pseudo-random numbers. For spaces with dimensions between 5 and 50, a CVT generates significantly better centroids. In lower dimensions (1--5), a scrambled Sobol sequence generates well-spread centroids in a few milliseconds.

In this work, we investigate whether differential (unequal) resource access promotes social stratification (the partitioning of a population into hierarchical groups based on socioeconomic factors). We achieve this by conducting scenario experimentation with Neo-COOP, an ABM that utilizes a Cultural Algorithm to simulate the evolution of resource sharing preferences in an artificial society. By varying the agents' initial resource sharing beliefs, the intensity of differential access, and the frequency at which the agents experience environmental stress. We find that while social stratification does increase when differential access increases, the effect is attenuated at the extremes with agents instead favouring an increase in selfish behaviour across the social strata. We also show that the severity (magnitude) of social stratification is most prominent in societies with initially selfish agents regardless of the intensity of differential access. Interestingly, our results also suggest that heterogeneous populations (agents with greater diversity of resource sharing beliefs) exhibit emergent social stratification to a lesser degree than homogenized populations (even in populations where agents are initialized to be altruistic).

In environments that vary frequently and unpredictably, bet-hedgers can overtake the population. Diversifying bet-hedgers have a diverse set of offspring so that, no matter the conditions they find themselves in, at least some offspring will have high fitness. In contrast, conservative bet-hedgers have a set of offspring that all have an in-between phenotype compared to the specialists. Here, we use an evolutionary algorithm of gene regulatory networks to de novo evolve the two strategies and investigate their relative success in different parameter settings. We found that diversifying bet-hedgers almost always evolved first, but then eventually got outcompeted by conservative bet-hedgers. We argue that even though similar selection pressures apply to the two bet-hedger strategies, conservative bet-hedgers could win due to the robustness of their evolved networks, in contrast to the sensitive networks of the diversifying bet-hedgers. These results reveal an unexplored aspect of the evolution of bet-hedging that could shed more light on the principles of biological adaptation in variable environmental conditions.

This paper introduces a user-driven evolutionary algorithm based on Quality Diversity (QD) search. During a design session, the user iteratively selects among presented alternatives and their selections affect the upcoming results. We implement a variation of the MAP-Elites algorithm where the presented alternatives are sampled from a small region (window) of the behavioral space. After a user selection, the window is centered on the selected individual's behavior characterization, evolution selects parents from within this window to produce offspring, and new alternatives are sampled. Essentially we define an adaptive system of local QD search, where the user's selections guide the search towards specific regions of the behavioral space. The system is tested on the generation of architectural layouts, a constrained optimization task, leveraging QD search through a two-archive approach.

Learning algorithms, like Quality-Diversity (QD), can be used to acquire repertoires of diverse robotics skills. This learning is commonly done via computer simulation due to the large number of evaluations required. However, training in a virtual environment generates a gap between simulation and reality. Here, we build upon the Reset-Free QD (RF-QD) algorithm to learn controllers directly on a physical robot. This method uses a dynamics model, learned from interactions between the robot and the environment, to predict the robot's behaviour and improve sample efficiency. A behaviour selection policy filters out uninteresting or unsafe policies predicted by the model. RF-QD also includes a recovery policy that returns the robot to a safe zone when it has walked outside of it, allowing continuous learning. We demonstrate that our method enables a physical quadruped robot to learn a repertoire of behaviours in two hours without human supervision. We successfully test the solution repertoire using a maze navigation task. Finally, we compare our approach to the MAP-Elites algorithm. We show that dynamics awareness and a recovery policy are required for training on a physical robot for optimal archive generation. Video available at https://youtu.be/BgGNvIsRh7Q

Combining a spatiotemporal, multi-agent based model of a foraging ecosystem with linear, genetically programmed rules for the agents' behaviors results in implicit, endogenous, objective functions and selection algorithms based on "natural selection". Use of this implicit optimization of genetic programs for study of biological systems is tested by application to an artificial foraging ecosystem, and compared with established biological, ecological, and stochastic gene diffusion models. Limited program memory and execution time constraints emulate real-time and concurrent properties of physical and biological systems, and stress test the optimization algorithms. Relative fitness of the agents' programs and efficiency of the resultant populations as functions of these constraints gauge optimization effectiveness and efficiency. Novel solutions confirm the creativity of the optimization process and provide an unique opportunity to experimentally test the neutral code bloating hypotheses. Use of this implicit, endogenous, evolutionary optimization of spatially interacting, genetically programmed agents is thus shown to be novel, consistent with biological systems, and effective and efficient in discovering fit and novel solutions.

Automated generation of complex and diverse environments can be achieved through the use of Procedural Content Generation (PCG) algorithms. However, generating content that is both meaningful and reflective of specific intentions and constraints remains a challenge. Recent advances in Large Language Models (LLMs) have demonstrated their effectiveness in various domains. These models can be fine-tuned and information can be reused to accelerate training for new tasks. Our study presents MarioGPT, a fine-tuned GPT2 model that has been trained to generate tile-based game levels for Super Mario Bros. The results demonstrate that MarioGPT can generate diverse levels and can be text-prompted for controllable level generation, addressing a critical challenge in current PCG techniques.

We investigate targeted attacks to important links in scale-free networks and propose simple and efficient heuristics strategies to mitigate the damage. In order to reduce the computational burden, we focus on heuristics that make use of local information for the most part. Using model scale-free networks and under the constraint of an invariant degree distribution, we show by numerical simulation that our approach allows to enhance the network robustness notably, as measured by the integrity of the largest connected component. We also show that the approach is effective on a couple of larger real-world networks.

The spread of contagions has been a central component of research on social networks. An abundance of literature shows that few nodes in the network contribute significantly to the final magnitude of the outbreak. The problem of finding the set of k most influential nodes is called the Influence Maximization Problem. This problem is NP-Hard. Considering the usefulness and difficulty of this problem, there has been a lot of scholarly efforts to solve it. In this paper, we propose a metaheuristic approach for this problem. Specifically, we enhance the simple Genetic Algorithm with a Neighbor-Hop Mutation and demonstrate that it outperforms the Greedy algorithm in all test cases. Furthermore, our proposed algorithm converges in a significantly shorter time, taking only one to two hundred generations compared to the one to four thousand generations required by the simple Genetic Algorithm.

The JuLeS framework (short for Julia Local Search)¹ is a versatile and highly customizable platform for quickly creating Local Search solvers. Developed using the Julia programming language, JuLeS enables efficient implementation of solvers, facilitates the development of new meta-heuristic algorithms, and easily integrates with existing tools. The overhead of the framework with respect to existing C++ frameworks is moderate, but it benefits from a lower programming effort and integrability into the Julia ecosystem. The design, architecture, and features of JuLeS are explained and its effectiveness is demonstrated through three use cases that highlight its design achievements.

Multi-point dynamic aggregation (MPDA) problem is a representative model to describe the task allocation in a multi-robot system. It is a NP-hard problem in which several robots cooperate to finish a set of distributed tasks. Considering the strong exploration ability and simple structure of particle swarm optimization (PSO), in this paper, we propose a new algorithm, called adaptive PSO with local search to solve MPDA effectively and efficiently. Since MPDA is a constraint problem with huge and complex search space, an adaptive initialization method is designed to generate feasible seed solutions guiding the swarm to feasible regions quickly, especially for the situations where robots need to cooperate closely. Meanwhile, an adaptive parameter is set to control the execution of initialization according to the characteristics of the problem. Then, to further reduce the search space, the velocity update rule is modified based on the random keys representation to limit the searching range of particles. Finally, a new local search strategy considering the cooperation relationship between robots is introduced to enhance the exploitation ability of the algorithm. The experimental results show that the proposed algorithm is more effective and efficient than the state-of-the-art methods.

Finding Boolean functions with specific properties is a complex combinatorial optimization problem where the search space grows super-exponentially with the number of input variables. One common property of interest is the nonlinearity of Boolean functions. Constructing highly nonlinear Boolean functions is difficult as it is not always known what nonlinearity values can be reached in practice. In this paper, we investigate the effects of the genetic operators for bit-string encoding in optimizing nonlinearity. While several mutation and crossover operators have commonly been used, the link between the genotype they operate on and the resulting phenotype changes is mostly obscure. The analysis reveals interesting insights into operator effectiveness and indicates how algorithm design may improve convergence compared to an operator-agnostic genetic algorithm.

Solvers for Curriculum-Based Course Timetabling were until recently difficult to configure and evaluate because of the limited number of benchmark instances. Recent work has proposed new real-world instances, as well as thousands of generated ones that can be used to train configurators and for machine learning applications. The less numerous real-world instances can then be used as a test set. To assess whether the generated instances exhibit sufficiently similar behavior to the real ones, we choose to consider a basic indicator: feasibility. We find that 38 % of the artificial instances are infeasible versus 6% of real-world ones, and show that a feasibility prediction model trained on artificial instances performs extremely poorly on real-world ones. The objective of this paper is therefore to be able to predict which generated instances behave like the real-world instances in order to improve the quality of the training set. As a first step, we propose a selection procedure for the artificial training set that produces a feasibility prediction model that works as well as if it were trained on real-world instances. Then, we propose a pipeline to build a selection model that picks artificial instances that match the infeasibility behavior of the real-world ones.

Signed graphs represent interactions between entities with positive and negative edges, which respectively denote attraction and repulsion. Finding a clustering that partitions the nodes of signed graphs into clusters comprising dense positive intra-connections and sparse negative intra-connections is a relevant problem in graph analysis. In this work, we propose and engineer a memetic algorithm based on a novel multilevel approach for this problem. Our experimental results demonstrate that our algorithm outperforms the current state-of-the-art in computing better solutions.

This paper addresses the joint scheduling of production operations, transport tasks, and storage/retrieval activities in flexible job shop systems where the production operations and transport tasks can be done by one of the several resources available. Jobs need to be retrieved from storage and delivered to a load/unload area, from there, they are transported to and between the machines where their operations are processed on. Once all operations of a job are processed, the job is taken back to the load/unload area and then returned to the storage cell. Therefore, the problem under study requires, concurrently, solving job routing, machine scheduling, transport allocation, vehicle scheduling, and shuttle schedule. To this end, we propose a hybrid biased random-key genetic algorithm (BRKGA) in which the mutation operator resorts to six local search heuristics. The computational experiments conducted on a set of benchmark instances show the effectiveness of the proposed mutation operator.

The bounded diameter minimum spanning tree (BDMST) problem aims at obtaining a spanning tree T of minimum cost under the constraint that the diameter of T is no greater than a positive integer parameter. In order to increase the efficiency of creating new solutions for permutation-based solution representation, this paper presents a Simulated Annealing (SA) algorithm for the BDMST problem. Specifically, a biased swap operator is designed to produce neighbor solutions. In the biased swap operator, one of the two swap positions is selected by the K-tournament selection strategy, where smaller positions are preferred. Furthermore, an accelerated evaluation strategy is proposed to efficiently evaluate the cost of neighbor solutions. The effectiveness and efficiency of the biased swap operator and accelerated evaluation strategy are verified by experimental results. The comparison carried out on complete Euclidean graphs shows that the proposed SA algorithm performs significantly better than other well-behaved algorithms and is especially suitable for large-scale instances.

An English language keyboard configuration involves 30 keys - 26 alphabets and four punctuation marks: comma, period, semi-colon, and question mark. Based on the sequence of letters that frequently appear in typing activities, one or more keyboard configurations will be optimal for a specific performance metric. Here, we consider the cumulative distance between two consecutive keystrokes to type out a large piece of text as the optimization objective, as it directly relates to the typing efficiency. The shorter the distance the fingers needs to move between strokes, the faster is the typing speed. When considering such a scenario, researchers often focus on a specific single objective one at a time and come up with the respective optimal keyboard configuration. The complete dissimilarity of these optimal, yet esoteric, keyboards from the current in-practice QWERTY configuration makes the new optimal keyboard configuration harder to learn and deploy on a larger scale. Hence in this study, we look at a multi-objective version of such a problem and consider two objectives - maximizing typing efficiency and maximizing similarity to QWERTY configuration. We make use of the NSGA-II algorithm and produce a Pareto set of keyboard configurations ranging from the most efficient to the most similar configurations. The range of solutions can potentially provide a design innovation path for gradually moving from the popular QWERTY configuration to more efficient configurations as a series of improvements.

This paper proposes applying 2 algorithms to minimize network resources using fix-grid and flex-grid technology in next-generation optical networks. An algorithm based on the (μ + λ) evolutionary algorithm was proposed and compared with an exact method based on Mixed-Integer Linear Programming. The value of the objective function and the computation time was used as the primary metrics for performance evaluation. The performance of the proposed algorithms was investigated for a 10-node network with different node degrees from two to five. The presented results confirm the advantages of the proposed evolutionary approach, especially in terms of computational time, compared to the reference method.

The QUBO framework provides a way to model, in principle, any combinatorial optimization problem and enables the use of Ising machines to solve it. Ising machines are devices designed to quickly find good solutions to QUBO problems. In previous work, Auto-QUBO was designed to automatically generate QUBO formulations from a high-level problem description. We address two shortcomings of this method. It only works on a per-instance basis, making repeated formulations for similar problems inefficient, and relies on the user to specify penalty weights. This work introduces symbolic sampling, which provides QUBO formulations for entire problem classes. We demonstrate the speedup that can be achieved with this approach using instances of the maximum clique problem. Additionally, we use proven methods to compute valid penalty weights automatically to simplify the translation process. By providing a user-friendly way to generate QUBO formulations in an efficient manner, both in terms of time and problem difficulty, we enable more people to use Ising machines for combinatorial optimization.

In this paper, we explore the Multidimensional Multi-way Number Partitioning Problem (MDMWNPP), which is a more complex version of the number partitioning problem. In MDMWNPP, we aim to partition a set of vectors into a given number of subsets, such that the sums of each subset's elements are as close to equal as possible for all vector coordinates. To address this problem, we propose a diploid genetic algorithm (DGA) that maintains population diversity and enhances the performance of genetic algorithms (GA). We also integrate an efficient local search (LS) procedure to guide the search towards promising solution regions. Our approach is compared to the classical (haploid) GA and state-of-the-art results for MDMWNPP on 96 benchmark instances from the literature. The results indicate that our method outperforms the classical GA and is highly competitive with the state-of-the-art approaches.

This paper proposes a new evolutionary strategy - called Evolutionary Abduction (EVA) - designed to target a class of problems called Combinatorial Causal Optimization Problems (CCOP). In a CCOP, the goal is to find combinations of causes that best explain or predict an effect of interest. EVA is inspired by abduction, a powerful form of causal inference employed in many artificial intelligence tasks. EVA defines a set of abductive operators to repeatedly construct hypothetical cause-effect instances, and then automatically assesses their plausibility as well as their novelty with respect to already known instances. Experiments confirm that, given a background knowledge, EVA can construct better hypotheses for a given effect, outperforming alternative strategies based on common metaheurstics previously used for CCOP.

In this paper we are concerned with solving a generalized version of the well-known minimum dominating set problem, the so-called k-domination problem, k ∈ ℕ. This problem is about finding a minimal cardinality subset D of vertices of a graph G = (V, E) such that every υ ∈ V belongs to D or has at least k neighbors from D. The k-domination problem has applications in distributed systems, biological networks etc. We propose a variable neighborhood search (VNS) metaheuristic for solving the k-domination problem. The Vns is equipped with an efficient fitness function that allows it to consider both feasible and infeasible solutions, while appropriately penalizing infeasible solutions. The control parameters of the Vns are tuned using a grid search approach. The method is compared to the best known heuristic approaches from the literature: the beam search and several greedy approaches. Experimental evaluations are performed on a real-world benchmark set whose instances represent the road networks of different cities. The Vns provided new state-of-the-art results for all considered problem instances with k ∈ {1, 2, 4}.

A methodology on how to prepare agents to succeed on a priori unknown logistics problems is presented. The training of the agents is and can only be executed using a small number of test problems that are taken out of a broad class of generalized logistics problems. The developed agents are then evaluated on unknown instances of the problem class. This work has been developed in the context of last year's AbstractSwarm Multi-Agent Logistics Competition. The most successful algorithms are presented, and additionally, all participating algorithms are discussed with respect to the features of the algorithms that contribute to their success. As a result, we conclude that such a broad variety of a priori unknown logistics problems can be solved efficiently if multiple different good working approaches are used, instead of trying to find one optimal algorithm. For the used test problems this method can undercut, trivial as well as non-trivial implementations, for example, algorithms based on machine learning.

In most of the existing benchmark generators for combinatorial optimization, one cannot tune variable importance, making the generation of real-like instances challenging. However, when it comes to the study of optimization algorithms or new problems there is a lack of real-like instances. To achieve more real-like instances, a recently proposed generator, PUBO_i (Polynomial Unconstrained Binary Optimization with importance), includes parameters that directly influence variable weights. The parameters of this generator enable the generation of landscapes with varying properties, such as ruggedness and neutrality levels, yet their global structure and the impact on optimization algorithm behavior remain to be studied. In this work, we use local optima networks to observe the differences in the landscape's global structure according to variable importance. Both the visualization and the metrics highlight how the landscapes are affected by the variable importance parameters of PUBO_i, and that landscapes with variable importance resemble real-like ones previously observed. We also conduct a first performance analysis using two iterated local search algorithms and observe different behaviors on different PUBO_i instances according to variable weights distribution.

Evolutionary multitask algorithms that adopt multitask optimization paradigms have been proposed to tackle multiple problems simultaneously and improve the performance of traditional evolutionary algorithms. One of the most crucial challenges in evolutionary multitasking applied to network design is the lack of an efficient unified representation to encode solutions. This paper presents the first representation based on node-depth encoding for evolutionary multitask algorithms to tackle network design problems. Remarkably, we propose an encoding method to represent solutions modeled by trees of arbitrary graphs in the form of a unified representation and design a corresponding decoding method to reconstruct solutions from a unified search space for each task. To verify the efficiency of our proposed methods, extensive experiments are conducted on well-known network design problems and demonstrate that our approach performs significantly better than previous approaches regarding solution quality.

The uncapacitated facility location problem (UFLP) is an NP-hard problem with a wide range of applications. It aims to choose a set of facilities to serve customers with the lowest total cost. This paper explores the idea of learning good heuristics, which could be regarded as a kind of optimization experiences, over a set of small problem instances. Then the learned heuristics (i.e., gained experiences) are used to generate good solutions for large-scale UFLPs although the large-scale ones are never used during learning. In this paper, we propose a novel facility opening estimation (FOE) heuristic for UFLP. Each facility's opening probability is estimated by a model related to its local apportioned cost (LAC). The model learns from the experience extracted in solving small UFLPs. Then, the model is embedded into the FOE heuristic to generate solutions for large UFLPs. The empirical results and analysis demonstrate that the optimization experience extraction is effective and can assist in generating high-quality solutions for large UFLPs.

Multitask learning has attracted widespread attention to handle multiple tasks simultaneously. Multitask genetic programming has been successfully used to learn scheduling heuristics for multiple multi-objective dynamic flexible job shop scheduling tasks simultaneously. With genetic programming, the learned scheduling heuristics consist of terminals that are extracted from the features of specific tasks. However, how to set proper terminals with multiple tasks still needs to be investigated. This paper has investigated the effectiveness of three strategies for this purpose, i.e., intersection strategy to use the common terminals between tasks, separation strategy to apply different terminals for different tasks, and union strategy to utilise all the terminals needed for all tasks. The results show that the union strategy which gives tasks the terminals needed by all tasks performs the best. In addition, we find that the learned routing/sequencing rule by the developed algorithm with union strategy in one multitask scenario can share knowledge between each other. On the other hand and more importantly, the learned routing/sequencing rule can also be specific to their tasks with distinguished knowledge represented by genetic materials.

Recently, Deep Learning (DL) algorithms have shown state-of-the-art performance in numerous tasks. The design of DL algorithms is time-consuming process that requires expert-level knowledge. To overcome this problem, Neural Architecture Search (NAS) is proposed, which automatically searches for the best neural network architecture for a given task. Indeed, evolutionary NAS has emerged as a widely studied research area, in which evolutionary algorithms are used to design neural networks. In this study, we proposed a novel encoding scheme to represent Convolutional Neural Network (CNN) architectures using continuous representation, which provides a larger search space and potentially finds better solutions compared to discrete representations. Moreover, it allows better exploitation of genetic operators, leading to a quick convergence of individuals. Furthermore, in order to reduce the computational time of the evaluation phase during the search process, surrogate models are used to provide an alternative objective function. To evaluate the effectiveness of the proposal, experiments are performed on CIFAR-10 and multiple datasets from the MedMNIST benchmark. The experimental results demonstrated the effectiveness of the proposed approach compared to several existing state-of-the-art algorithms.

Data stream clustering is essential in machine learning and big data analytics. However, clustering this type of data requires some restrictions in time and memory. This paper proposes a multiobjective data stream clustering algorithm (IMOC-Stream) that addresses these challenges by incorporating time and memory optimization into the clustering process. The goal of IMOC-Stream is to 1) reduce computation time by using idle times to apply genetic operations and enhance the solution. 2) reduce memory allocation by introducing a new tree synopsis. 3) find arbitrarily shaped clusters by using a multi-objective framework. We conducted an experimental study with high-dimensional stream datasets and compared them to well-known stream clustering techniques. The experiments show the ability of our method to partition the data stream into arbitrarily shaped, compact, and well-separated clusters while optimizing time and memory. Our approach also outperformed most of the other stream algorithms.

Text-to-image generation has achieved impressive results, featuring a variety of models trained on extensive datasets comprising text-image pairs. However, some methods depend on pre-trained models, using gradient-based approaches to update latent vectors in the latent space. In this work, we propose the use of Covariance Matrix Adaptation Evolution Strategy to explore the latent space of a Generative Adversarial Network. Our experimental study compares our approach with gradient-based and hybrid strategies, using diverse text inputs for image generation. We adapt an evaluation method that projects the generated samples into a two-dimensional grid to assess the diversity of the distribution. Results evidence that the evolutionary method produces more diverse samples across different grid regions, while the hybrid method combines gradient-based and evolutionary approaches, enhancing result quality.

As a reactive and modular policy control architecture, Behavior Tree (BT) has been used in computer games and robotics for autonomous agents' task switching. However, constructing BTs manually for complex tasks requires expert domain-knowledge and is error-prone. As a solution, researchers have proposed to auto-construct BTs using evolutionary algorithms such as Genetic Programming (GP) and Grammatical Evolution (GE). Nevertheless, their effectiveness in practical situations is in doubt and there are different drawbacks in the application.

In this paper, we present a novel BT evolutionary system that integrates both GE and GP as modules and auto-checks the complexity of a given task to select which module to use. In addition, our system collects BTs that are either previously generated or manually designed by the user, which are utilized to further improve the convergence speed and the quality of generated trees for new tasks.

Quality-Diversity offers powerful ideas to create diverse, high-performing populations. Here, we investigate the capabilities these ideas hold to solve exploration-hard single-objective problems, in addition to creating diverse high-performing populations.

We find that MAP-Elites is well suited to overcome deceptive reward structures, while an Elites-type approach with an unstructured, distance based container and extinction events can even outperform it.

Furthermore, we analyse how the QD score, the standard evaluation of MAP-Elites type algorithms, is not well suited to predict the success of a configuration in solving a maze. This shows that the exploration capacity is an entirely different dimension in which QD algorithms can be utilized, evaluated, and improved on. It is a dimension that does not currently seem to be covered, implicitly or explicitly, by the current advances in the field.

We consider the problem of deriving parameters of the preference model employed in the multiple criteria sorting method called FlowSort. We propose a suite of preference learning algorithms based on differential evolution and simulated annealing, their combinations with mathematical programming, and a dedicated heuristic. They are tested on various monotonic benchmark datasets and compared in terms of 0/1 loss. The evolutionary algorithm and the dedicated heuristic prove competitive against state-of-the-art preference learning methods. The former attains better results when coupled with boundary profiles for all considered datasets. For other methods, there is no clear indication that using the class limits is more advantageous than class prototypes.

Neural networks are a common and powerful tool to approximate highly complex non-linear functions. Most typically, the connection weights of these structures are adapted during training by employing gradient descent techniques. As this is not possible for so-called semiring neural networks, we propose to use a genetic algorithm for training this type of network and present a modern extendable C++-based parallelized implementation of the genetic algorithm Genitor II for this task. We compare our parallelized implementation with a more conventional implementation of the Genitor II algorithm and demonstrate that this novel approach is efficient. As a consequence, this novel implementation allows for the first time efficient and practical training of semiring neural networks even for relatively large network sizes of several hundred units. The source code is publicly available under the MIT license: https://git.informatik.uni-leipzig.de/ml-group/semiring-nn/parallelized-c-implementation.

Random Forest (RF) is one of the most popular and effective machine learning algorithms. It is known for its superior predictive performance, versatility, and stability, among other things. However, an ensemble of decision trees (DTs) represents a black-box classifier. On the other hand, interpretability and explainability are ones of the top artificial intelligence trends, to make predictors more trustworthy and reliable. In this paper, we propose an evolutionary algorithm to extract a single DT that mimics the original RF model in terms of predictive power. The initial population is composed of trees from RF. During evolution, the genetic operators modify individuals (DTs) and exploit the initial (genetic) material. e.g., splits/tests in the tree nodes or more expanded parts of the DTs. The results show that the classification accuracy of a single DT predictor is not worse than that of the original RF. At the same time, and probably most importantly, the resulting classifier is a single smaller-size DT that is almost self-explainable.

Modern machine learning (ML) models are capable of impressive performances. However, their prowess is not due only to the improvements in their architecture and training algorithms but also to a drastic increase in computational power used to train them.

Such a drastic increase led to a growing interest in distributed ML, which in turn made worker failures and adversarial attacks an increasingly pressing concern. While distributed byzantine resilient algorithms have been proposed in a differentiable setting, none exist in a gradient-free setting.

The goal of this work is to address this shortcoming. For that, we introduce a more general definition of byzantine-resilience in ML - the model-consensus, that extends the definition of the classical distributed consensus. We then leverage this definition to show that a general class of gradient-free ML algorithms - (1, λ)-Evolutionary Search - can be combined with classical distributed consensus algorithms to generate gradient-free byzantine-resilient distributed learning algorithms. We provide proofs and pseudo-code for two specific cases - the Total Order Broadcast and proof-of-work leader election.

To our knowledge, this is the first time a byzantine resilience in gradient-free ML was defined, and algorithms to achieve it - were proposed.

Learning Classifier Systems (LCSs), a series of rules-based evolutionary computation techniques, which have solved a wide range of discrete-feature-based applications over their 40 years of history. Yet, adapting LCSs to complicated continuous-feature-based domains is still an unsolved challenge. This paper proposes new LCS methods specialized for continuous problems. Concretely, phenotype-orientated Absumption, Subsumption, and Mutation are proposed and employed to form and revise rules directly in a single iteration according to the target problems' inherent data distribution, allowing rules to be released from the burden of directly carrying the information of previous instances. Furthermore, a novel representation format supporting fine-grained generalization degree modification is also proposed. Experiments demonstrate for the first time that LCSs are promising techniques in efficiently producing models with satisfactory prediction performance for complicated continuous problems.

Adaptive Markov Chain Monte Carlo (MCMC) adapts the covariance of the proposal distribution to improve the efficiency of Metropolis Hastings (MH). Adaptive Metropolis (AM) is the prime example. Some stochastic optimisation techniques adapt the co-variance of the search distribution. Some examples are Gaussian Adaptation (GaA) and (1+1)-Covariance Matrix Adaptation Evolution Strategy (CMAES) that can be turned into MCMC samplers in a straightforward way. However, the adaptation rational used by these samplers differ. AM estimates the covariance of the target distribution based on the generated samples. GaA adapts the covariance such that the entropy of the proposal is increased/decreased when the candidate sample is accepted/rejected while adaptation in CMAES increases the likelihood of generating better search points. We compare the performance of AM, GaA and (1+1)-CMAES samplers on a test suite of target distributions to understand the effectiveness of the adaptation mechanism used.

Cluster analysis is a popular technique used to identify patterns in data mining. However, evaluating the accuracy of a clustering task is a challenging process which remains to be an open issue. In this work, we focus on two factors that significantly influence clustering performance: the optimal number of clusters and the subset of relevant attributes. While the former has been extensively studied, the latter has received comparatively less attention, especially in relation to its equivalent in supervised learning. Despite their clear interdependence, these factors have rarely been studied together. In this context, we propose an evolutionary algorithm that simultaneously optimizes both factors using ad-hoc variations of internal validation indices as a fitness function.

A key component of automated algorithm selection and configuration, which in most cases are performed using supervised machine learning (ML) methods is a good-performing predictive model. The predictive model uses the feature representation of a set of problem instances as input data and predicts the algorithm performance achieved on them. Common machine learning models struggle to make predictions for instances with feature representations not covered by the training data, resulting in poor generalization to unseen problems. In this study, we propose a workflow to estimate the generalizability of a predictive model for algorithm performance, trained on one benchmark suite to another. The workflow has been tested by training predictive models across benchmark suites and the results show that generalizability patterns in the landscape feature space are reflected in the performance space.

The configuration of Evolutionary Algorithm (EA) parameters is a significant challenge. While previous studies have examined methods for configuring EA parameters, there remains a lack of a general solution for optimizing these parameters. To overcome this, we propose DEMOCA, an automated Deep Reinforcement Learning (DRL) method for online control of multi-objective EA parameters. When tested on a multi-objective Flexible Job Shop Scheduling Problem (FJSP) using a Genetic Algorithm (GA), DEMOCA was found to be as effective as grid search while requiring significantly less training cost.

This article presents a multiobjective evolutionary approach for coevolutionary training of Generative Adversarial Networks. The proposal applies an explicit multiobjective optimization approach based on Pareto ranking and non-dominated sorting over the co-evolutionary search implemented by the Lipizzaner framework, to optimize the quality and diversity of the generated synthetic data. Two functions are studied for evaluating diversity. The main results obtained for the handwritten digits generation problem show that the proposed multiobjective search is able to compute accurate and diverse solutions, improving over the standard Lipizzaner implementation.

Deep learning is a cutting-edge methodology that has been widely used in real-world applications to solve computer vision tasks. Deep learning models are typically seen as black boxes, opaque, and difficult to interpret. Recently, attention-based vision transformers have been introduced to overcome the black-box behavior of deep networks. However, the decision-making process of the vision transformer is still not interpretable. Moreover, these models require a large amount of memory, huge computational resources, and enormous training data.

Learning classifier systems is a state-of-the-art rule-based evolutionary machine learning technique that stands out for its ability to provide interpretable decisions. These systems generate niche-based solutions, require less memory, and can be trained using small data sets. We hypothesize to wangle attention in learning classifier systems to identify critical components of the problem instance, link features to create simple patterns, and model hierarchical relationships in the data. The experimental results for binary-class image classification (cat and dog) tasks demonstrate that the novel system successfully ignores the irrelevant parts and pays attention to the salient features of cats and dogs. Crucially, the novel system exhibits almost the same performance accuracy as that of the state-of-the-art learning classifier systems.

This paper introduces two enhancements that apply to evolution strategies such as Augmented Random Search (ARS). These improvements target generalizable tasks with widely varying initial conditions, such as legged robot locomotion where the robot starts off in a random joint configuration. The first innovation builds upon the mirrored sampling feature of ARS. It mitigates the detrimental effect of unexplained variance on training stability by forcing the simulator to use the same random seed for both mirrored pairs. The second innovation is a multi-phase end tournament procedure performed right after the ARS method is complete. This tournament helps to ensure that the final product of training, a single model selected from the population, performs well over a wide range of random initial conditions. Improved results are demonstrated using MuJoCo simulations of legged robots.

Learning classifier tables (LCTs) are lightweight, classifier based, hardware implemented reinforcement learning (RL) building blocks which enable self-adaptivity and self-optimization properties in multicore systems. LCTs are deployed per-core to learn and optimize potentially conflicting objectives and constraints. Experience replay (ER) is a replay memory technique in RL, where agents experiences are stored in a buffer and are used to improve the learning process. Implementing an ER buffer in hardware requires memory and is expensive. We introduce LCT-DER: LCT with dynamic-sized experience replay, where the classifier population and experiences share the same memory by exploiting the concept of macro-classifiers. LCT-DER performing DVFS achieves 44.5% and 4.5% lower number of power budget overshoots and IPS difference compared to a standard LCT without requiring additional memory.

Perceptual aliasing is one of the most important problems in Robot-navigation as a robot cannot distinguish its state via its immediate observations leading to poor decision-making. Frames-of-References-based XCS learns policies comprising of constituent-level paths (that may be aliased) integrated into a holistic-level path that has unique patterns of the environment leading to improved policy performance. However, unique references are required to identify an aliased state such that is impractical to learn a policy in an environment with multiple, sequential, aliased states, e.g., a long, uniform, corridor. This paper introduces methods for hierarchical references, which concatenate sequential aliased states to form a discrete unique state and references them using the end-of-the-series state. The experiments investigated the performance of the proposed system in partially observable environments with complex aliasing patterns, including sequential aliased states. The results showed that the proposed system overcomes the state-of-the-art system's issues in the tested problems; learning in sequential aliased states, unlike the previous system.

For many real-world decision-making tasks, a key feature is decision explainability. Hence, the so-called glass-box models offer full explainability and are still prevalent. An important area of application is the classification of imbalanced data. We require that the proposed classifiers not make errors on the minority class while minimizing errors on the majority class. This paper proposes a method for preprocessing imbalanced data by generating minority class objects. We use a multi-criteria optimization method (NSGA-II) to avoid optimizing a single aggregate criterion. The method returns a group of non-dominated solutions from which the end user can choose the best solution from his point of view. The automatic solution selection from a Pareto front is also proposed for comparison purposes. The proposed method returns good-quality classifiers, often surpassing the quality of baseline single-objective methods, and is additionally characterized by full interpretability.

Many real world robotics problems, where the mission needs or environmental conditions change suddenly, require robots to identify deficiencies and adapt their behaviors in order to satisfy the new task requirements. Quality Diversity (QD) methods can generate diverse sets of behaviors that augment a robot's initial skills; however, they require many training runs and result in hundreds or thousands of candidate behaviors the robot would need to try. We introduce Knowledge Shaped MAP-Elites, which exploits the knowledge past policies no longer work to shape a small number of niches in the behavior space; this generates new behaviors without any direct information of the target task. Knowledge Shaped MAP-Elites reliably finds behaviors that work on an unknown target task in an order of less magnitude computation compared to state-of-the-art QD approaches.

The wide usage of tensor computation in deep neural networks (DNNs) has boosted the high demand for high-performance and flexible library implementation on different hardware platforms, which is time-cost and inefficient. Deep learning compilers (DLCs) are therefore proposed, such as Ansor, to search the optimization computation combinations automatically. Ansor can generate high-performance tensor programs by employing Genetic Algorithm (GA) in its auto-tuning process. However, the structure information of an individual is easily destroyed by the uniform crossover operator, which leads to low search efficiency. In this paper, we propose a two-point crossover operator applied in Ansor called Ansor-TPC, which can optimize tensor computation with higher efficiency. The tensor expression can be computed with random schedules regarded as individuals. When performing the crossover operator, Ansor-TPC exchanges parent genes at two points instead of every point, which can preserve the structure information of programs and find the optimal schedule combination in the large search space. A high-performance program is generated for targeted hardware based on the optimized schedule configuration. Ansor-TPC is compared with the benchmarks at different levels. In terms of average performance, Ansor-TPC achieves 1.07--23.2× performance speedup. In terms of the best performance, Ansor-TPC outperforms by up to 1.06--23.0×.

Artificial neural networks (ANNs) can be trained with reinforcement learning (RL) in simulation to control robots. However, changes in the environment resulting in out-of-distribution situations put learned policies at risk of failure. Since the world can change in unpredictable ways, it might be desirable to be able to continue to update the parameters of the ANNs even after deployment, to prevent failures stemming from a distributional shift. However, in order to optimize with RL, a reward signal is needed. This is usually provided in the simulated environment, but might not necessarily always be available after training. We propose a solution to this problem that involves evolving a function that provides a reward signal to an RL algorithm based only on the inputs and outputs of the policy. We call this approach Evolved Internal Reward Reinforcement Learning (EIR-RL) and test it on various control tasks that have different reward structures and difficulty levels. Our method shows improved training stability and speed of the RL agent under standard circumstances, as well as the ability to train the RL agent under circumstances unseen during the initial optimization phase. We discuss how our results could inform future studies on autonomous, adapting agents.

The idea of a circular economy proves promising with the evergrowing need for more sustainable production methods and resource utilization. However, this introduces new challenges compared to the traditional, mostly linear production processes and often leads to a tradeoff between sustainability and costs. In these environments, multi-objective evolutionary algorithms (MOEAs) are a great tool to tackle the increased complexity of supply chains in a circular economy. While MOEAs have been used to optimize circular supply chain models in the past, it was usually done for specific industries and using standard operators. In this paper, we propose a generalized test problem to provide a tool for evaluating MOEAs with respect to a circular supply chain (CSC) problem. In this problem, we try to optimize the product plan as well as the material sourcing at the same time, considering the objectives of maximizing the profit and sustainable resource use.

Hunting of the plark is a complex adversarial multi-agent, asymmetrical, stochastic, and partially observable war game. An aircraft player has the objective to find and destroy a hidden submarine, and the submarine player has the objective of escaping the faster aircraft. This paper demonstrates a statistical forward planning rolling horizon evolutionary algorithm agent, that models enemy behavior using heuristics, and masters the game outperforming other agents including deep reinforcement learning, heuristic, and human players.

In this article, a multi-objective artificial bee colony algorithm with dynamic neighborhood search (MOABC) is employed to address the two-stage assembly flexible job scheduling problem (AFJSP) with transportation and setup times. In the considered problem, there are two stages as follows: 1) in the first stage, the classic flexible job shop scheduling problem (FJSP) with transportation and setup times is considered, and 2) each product is assembled in the second stage, where the setup times between products is embedded. To address the problem, first, a mixed integer linear programming model is developed, wherein makespan and total energy consumption are optimized simultaneously. Second, an effective initialization strategy is designed to generate an initial population with high performance. Next, in the decoding phase, two types of neighborhood knowledge based on the problem characteristics are extracted. Subsequently, to enhance the local search capabilities, a dynamic neighborhood search (DNS) heuristic with five different neighborhood structures in the onlooker stage is proposed. Finally, comprehensive computational comparisons and statistical analysis with state-of-the-art algorithms verified the effectiveness of the proposed algorithm.

Dynamic Multi-objective Optimization problems (DMOPs) can represent formulations of complex realistic scenarios in industrial, logistics and energy domains. Consistent and comparable testing on DMOP benchmarks has seen recent progress in tools for comprehensive and reproducible testing. Ranges of possible dynamic instances of DMOPs can be generated defined by their frequency and severity of change parameters. Here, a combination of machine learning and evolutionary algorithm techniques allow for an efficient determination of algorithm performance limits. An iterative Support Vector Machine model is integrated with the existing Dynamic Parameter Testing Platform (DPTP) for selective (rather than exhaustive) evaluation of dynamic instances to inform on algorithm capability.

Hypervolume is most likely the most often used quality indicator in EMO because of its compatibility with the dominance relation. In the context of EMO one is quite often interested not only in the hypervolume of the final solutions set but also in the evolution of hypervolume during the run of the algorithm. Such evolution of hypervolume may allow for a more detailed analysis of a given EMO algorithm or may be used for on-line convergence detection and on-line stopping criteria. Of course, full recalculation of hypervolume after addition of each new solution would be extremely inefficient. However, one may update hypervolume after generation of a new solution(s) which can be achieved by calculating hypervolume contribution of the new solution. In this paper we evaluate the performance of the quick hypervolume (QHV) and WFG algorithms in on-line hypervolume update using benchmark datasets. We show that especially QHV performs very well in such context with the time needed to process the whole set of solutions in on-line manner being only moderately longer than static calculation of the final hypervolume. Finally, we illustrate how on-line QHV could be used to monitor evolution of hypervolume during runs of a hybrid multiobjective evolutionary algorithm.

Novelty search's ability to efficiently explore the fitness space is gaining attention. Different novelty metrics, however, produce different search results. Here we show that novelty metrics are complementary and a multi-novelty approach improves the performance substantially. Specifically, we propose a multi-novelty search multi/many-objective algorithm (Curious II) that has both Euclidian distance and prediction-error novelty metrics. On the one hand, the Euclidian distance based novelty metric makes the subpopulation explore subspaces with low crowd density and avoids premature convergence. On the other hand, the prediction-error novelty metric guides a subpopulation to explore subspaces with unexpected objective fitness. Experiments reveal that using both novelty metrics in a multi-novelty algorithm has strong benefits. Curious II was compared with two state-of-the-art algorithms and two novelty search-based algorithms on the WFG 1--8 test problem with up to 10 objectives. It outperforms all the others in 28 out of 32 tasks for the HV index and in 27 out of 32 tasks for the IGD index.

There is a growing number of network attacks and the data on the network is more exposed than ever with the increased activity on the Internet. Applying Machine Learning (ML) techniques for cyber-security is a popular and effective approach to address this problem. However, the data which is used by ML algorithms have to be protected. In this paper, we present a framework that combines autoencoder, multi-objective optimization algorithms, and different ML algorithms to encode the network data, reduce its size, and detect and classify the network attacks. The novel element used in this framework, with respect to earlier research, is the application of multi-objective optimization algorithms, such as Multi-Objective Differential Evolution or Non-dominated Sorting Genetic Algorithm-II, to handle the different objectives in the fitness function of the autoencoder (autoencoder decoding error and accuracy of ML algorithm). We evaluated six different ML algorithms for attack detection and classification on network dataset UNSW-NB15. The performance of the proposed framework is compared with single-objective Differential Evolution. The results showed that Multi-Objective Differential Evolution outperforms the counterparts for attack detection, while all the evaluated algorithms showed similar performance for attack classification.

Elitism, which constructs the new population by preserving best solutions out of the old population and newly-generated solutions, has been a default way for population update since its introduction into multi-objective evolutionary algorithms (MOEAs) in the late 1990s. In this paper, we take an opposite perspective to conduct the population update in MOEAs by simply discarding elitism. That is, we treat the newly-generated solutions as the new population directly (so that all selection pressure comes from mating selection). We propose a simple non-elitist MOEA (called NE-MOEA) that only uses Pareto dominance sorting to compare solutions, without involving any diversity-related selection criterion. Preliminary experimental results show that NE-MOEA can compete with well-known elitist MOEAs (NSGA-II, SMS-EMOA and NSGA-III) on several combinatorial problems. Lastly, we discuss limitations of the proposed non-elitist algorithm and suggest possible future research directions.

Expensive multimodal multi-objective problems widely exit in real-world applications, in which multiple Pareto solutions correspond to the same objective values. To tackle the above-mentioned problems, traditional particle swarm optimization algorithms always select a Pareto solution from the archive based on preferences as an exemplar. However, this exemplar may not be the best exemplar for each particle. Therefore, a multi-surrogate assisted particle swarm optimization with multiple exemplars is proposed. Firstly, a multi-surrogate model based on clustering is constructed to fit the many-to-one mapping relationship. Secondly, a surrogate assisted optimization strategy based on multiple exemplars is developed. In this strategy, each particle performs optimization under the guidance of multiple exemplars in the archive, and the optimal exemplar is selected based on the evaluations of the surrogate models. Finally, an archive update strategy based on crowding distance is proposed to balance the diversity both in the decision and objective spaces. The experimental results show that the proposed algorithm is significantly superior to eight state-of-the-art evolutionary algorithms on chosen benchmark problems.

Vehicle routing problem with soft time windows (VRPSTW) is an important logistic problem in the supply chain. Besides minimizing transport costs, how to guarantee fairness among the vehicles is one of the main concerns. This paper investigates a variant of VRPSTW, called VRPSTW with salary balancing(VRPSTWSB). The salary is calculated by travel costs, load, and time window violations. To solve the problem, we first design a clustering algorithm to group the customers, then propose a novel multi-objective local search algorithm to plan the route for each vehicle. The simulation results on the traditional instances show that the proposed algorithm can obtain satisfactory solutions.

In this article, multiobjective optimization of neural models is studied, aimed at making decisions about vaccine distribution in a scenario of a disease spreading among farms, pastures and other locations. The epidemic is simulated using a real-life dataset of animal movements between such premises in Italy in years 2017--2020. Three neural models are studied: multilayer perceptrons (MLP), classical recurrent neural networks (RNN) and Long Short-Term Memory (LSTM) networks with the weights of the networks optimized using the MOEA/D algorithm. In the experiments, MOEA/D with the binary-vector representation optimizing the assignment of vaccinations to the premises was used as a comparison method. In order to assess the generalization capacity of the tested methods, the optimization was performed on data from the years 2017--2019 and the results (optimized neural models, and optimized vaccination assignments, respectively) were used for the year 2020. The two neural models which worked best were the MLP and the LSTM which outperformed both the RNN and MOEA/D optimizing the assignment of vaccinations. The advantage of the MLP and the LSTM is particularly well-visible when the number of vaccinated nodes is low, which may be important in practical applications.

In some real-world multi-objective optimization problems, Pareto optimal solutions with different design parameter values are mapped to the same point with the same objective function values. Such problems are called multi-modal multi-objective optimization problems (MMOPs). For MMOPs, multi-modal multi-objective evolutionary algorithms (MMOEAs) have been developed for approximating both the Pareto front (PF) and the Pareto sets (PSs). However, most MMOEAs use population convergence in the objective space as the primary evaluation criterion. They do not necessarily have a high PS approximation ability. To better approximate both PF and PSs, we propose a decomposition-based MMOEA where an MMOP is transformed into a number of two-objective subproblems. One objective of each subproblem is a scalarizing function defined by a weight vector for the original MMOP, while the other is defined by a decision space diversity. Experimental results show a high approximation ability of the proposed method for both PF and PSs.

To solve sparse large-scale multi-objective optimization problems, this paper proposes to use a matrix to evaluate the variable correlations and perform adaptive updates, which achieve the highest accuracy of sparse relationship mining. Meanwhile, a new genetic operator is proposed to ensure the sparsity of the generated solutions. According to the experimental results of eight benchmark problems, the algorithm outperforms existing evolutionary algorithms in solving sparse LSMOPs problems.

Current business activity scheduling systems are designed to maximise efficiency in terms of business metrics, but rarely take personal preferences into account. The goal of this work is to provide a formalisation and an experimental test of a SCRUM-like personalised scheduling system based on many-objective optimization. We propose a many-objective optimization framework in which the a priori preferences of the human decision makers (DMs) target different regions in the search space, from which the optimization retrieves alternative solutions that allow a posteriori decision making. The implementation of the proposed approach is based on a combination of NSGA-II and two custom operators aimed at proximity-enhanced mutation as well as search-space mapping. Our results show that the proposed method is able to generate diverse schedules. However, the aspiration values (a priori preferences) used in different system configurations notably influence the result characteristics, calling for detailed analysis of the interrelationships between preferences and the shape of the resulting pareto front. The modelling approach is considered as a successful proof of principle for the intended use case at an abstract level.

This paper proposes the partitioning method with edge weight vectors sharing for parallel distributed MOEA/D in a distributed memory environment. Massively parallelization in a distributed memory environment effectively speeds up evolutionary multi-objective optimization algorithms for practical application problems. On the other hand, when MOEA/D is divided for parallelization by focusing on the weight vector in the objective function space, the T-neighborhood is divided and the problem that the solution distribution becomes sparse near the boundary of the divided region arises. Here, we propose a partitioning method to share edge weight vectors among all partitions, and then assign other weight vectors uniformly to each partition. Using the constrained knapsack problem as a benchmark problem, we show that it is possible to eliminate the need for migration processing to correct the value of the ideal point and improve the problem that the T-neighborhood is divided, and the distribution of the solution becomes sparse.

Selection hyper-heuristics (SSHH) are search strategies that can be successfully applied to multi-objective optimization (MOO) problems. They showed resilient results to different types of optimization problems, which may come at the cost of a longer resolution time than other metaheuristics. Learning a single selection rule in MOO might be limiting because the information from the multiple objectives might be unexploited. A novel approach named the multi-policy approach is proposed and discussed to further enhance the searching ability of sequence-based selection hyper-heuristics, together with an ad-hoc learning rule. The availability of a set of problem-specific low-level heuristics is assumed and the resolution of a specific class of combinatorial problems, i.e., vehicle routing problems (VRPs), is considered for a numerical example. The multi-policy approach showed the ability to learn different selection rules for each objective and to change them during the execution of the algorithm, i.e., when solutions are getting closer to the Pareto front. The availability of parallel computation can speed up the calculation since the methodology is suitable for parallelization. The proposed methodology was found to produce production-ready solutions and the approach is expected to be successfully extended to problems different from the VRP.

The enormous search space in large-scale multiobjective optimization presents a significant challenge to the convergence of existing evolutionary algorithms (EAs). It is necessary to further improve the convergence efficiency of the fuzzy decision variables framework (FDV) for large-scale multiobjective optimization. Therefore, this paper proposes a fuzzy decision variables framework based on directed sampling (FDVDS) for large-scale multiobjective optimization. After initializing the population, guided solutions are generated by directed sampling to improve the diversity of the population and speed up the convergence of the population. Finally, some representative EAs are embedded into FDVDS, and the framework's effectiveness is verified by performing comparative experiments on large-scale multiobjective optimization test problems with up to 5000 decision variables.

Predefined reference vectors (RVs) are utilised in decomposition-based algorithms to solve many-objective optimisation problems (MaOPs). Two commonly used creation methods are those proposed by Das and Dennis and Deb and Jain. The former method generates many RVs at lower-order boundaries to create sufficient RVs in the intermediate area. The latter solves this challenge by adopting a layered creation of RVs but often fails in creating RVs on higher-order boundaries. To address these challenges, RVs in this study proposed to be created and categorised in clusters in the intermediate area of the m-dimensional space and the boundaries of various kinds independently. Diverse combinations of RV groups, with a manageable number of vectors each, can be utilised in optimisation. Pareto front in various subregions can be investigated with the desired number of approximations. A separate analysis in each subregion can be performed if needed. The approximations can be combined to form the final PF. The method is readily implemented into existing decomposition-based MaOP algorithms.

Dynamic flexible job shop scheduling (DFJSS) is an important combinatorial optimisation problem that requires handling machine assignment and operation sequencing simultaneously in dynamic environments. Genetic programming (GP) has achieved great success to evolve scheduling heuristics for DFJSS. In manufacturing, multi-objective DFJSS (MO-DFJSS) is more common and challenging due to conflicting objectives. Existing Pareto dominance-based multi-objective GP methods show their limitations of not providing good spreadability and consistency in heuristic behaviour. Multi-objective evolutionary algorithm based on decomposition (MOEA/D) has the potential to provide good spreadability and consistency due to the mechanisms of weights-based subproblems decomposition and neighbours-based evolution. However, it is non-trivial to apply MOEA/D to MO-DFJSS since we need to search in heuristic space. To address these challenges, we propose a multi-objective GP approach based on decomposition (MOGP/D) that incorporates the advantages of MOEA/D and GP to learn scheduling heuristics for MO-DFJSS. A mapping strategy is designed to find the fittest individual for each subproblem. Extensive experiments show that MOGP/D obtains competitive performance with the state-of-the-art methods for MO-DFJSS, and good spreadability and consistency in heuristic behaviour.

Most real world problems are multiobjective by nature and expensive to evaluate. We propose in this work a surrogate assisted approach for multiobjective evolutionary algorithms by building a surrogate model on each objective. However, integrating a surrogate model within an optimization process generates complexity with additional hyper-parameters to tune. Empirical validation on standards MOO benchmark problems of a use case based on NSGA-II and surrogates using SVM regression shows a significant improvement of the optimization cost in terms of true objectives evaluations, especially for low budget. We also discuss the behavior of the proposed algorithm using different values of the parameter calibrating the use of the surrogate model.

Multiobjective Evolutionary Algorithm based on Decomposition (MOEA/D) is effective for solving multi-objective optimization problems. However, in real-world applications, problems with imposed constraints are common. Therefore, research on Constraint Handling Techniques (CHTs) has been done. CHTs focus on improving search performance by utilizing infeasible solutions. Multi-objective-based CHTs are effective in promoting convergence and diversity in solution sets, but existing CHTs for MOEA/D have limitations in terms of flexibility and extensibility (e.g., the scalarization function to be used). To overcome this, this paper proposes a CHT using two sets of weight vectors to make constraints an objective function. The proposed method is flexible and can be used in any MOEA/D variant. It is incorporated into a basic MOEA/D and its effectiveness is demonstrated by comparing it with existing constrained MOEA/D on 2- and 3-objective benchmark problems.

Vectorial Genetic Programming (Vec-GP) extends regular GP by allowing vectorial input features (e.g. time series data), while retaining the expressiveness and interpretability of regular GP. The availability of raw vectorial data during training, not only enables Vec-GP to select appropriate aggregation functions itself, but also allows Vec-GP to extract segments from vectors prior to aggregation (like windows for time series data). This is a critical factor in many machine learning applications, as vectors can be very long and only small segments may be relevant. However, allowing aggregation over segments within GP models makes the training more complicated. We explore the use of common evolutionary algorithms to help GP identify appropriate segments, which we analyze using a simplified problem that focuses on optimizing aggregation segments on fixed data. Since the studied algorithms are to be used in GP for local optimization (e.g. as mutation operator), we evaluate not only the quality of the solutions, but also take into account the convergence speed and anytime performance. Among the evaluated algorithms, CMA-ES, PSO and ALPS show the most promising results, which would be prime candidates for evaluation within GP.

The GKLS generator is one of the most used testbeds for benchmarking global optimization algorithms. In this paper, we conduct both a computational analysis and the Exploratory Landscape Analysis (ELA) of the GKLS generator. We utilize both canonically used and newly generated classes of GKLS-generated problems and show their use in benchmarking three state-of-the-art methods (from evolutionary and deterministic communities) in dimensions 5 and 10. We show that the GKLS generator produces "needle in a haystack" type problems that become extremely difficult to optimize in higher dimensions. We also conduct the ELA on the GKLS generator and then compare it to the ELA of two other widely used benchmark sets (BBOB and CEC 2014), and discuss the results.

In the field of surrogate-assisted evolutionary algorithms (SAEAs), Gaussian Process (GP) is a widely used technique to approximate the objective function. Although a GP model can provide an expected gradient of a function to be approximated, little attention has been paid to the utilization of the gradient information. Thus, this paper presents an expected gradient-based SAEA, in which the expected gradient of the objective function provided by the GP models is utilized to conduct an efficient local search. Specifically, the proposed algorithm first conducts a global search with a differential evolution algorithm to find promising regions of the search space. Then, it builds a GP model for each promising region, and a quasi-Newton method (L-BFGS-B) is executed on its model with guidance from the expected gradient. This gradient-based local search intends to sufficiently search the approximate objective function, by finding various local optimal solutions in an efficient manner. Experimental results show that our algorithm is competitive with state-of-the-art SAEAs on a single-objective optimization benchmark suite.

Exploratory landscape analysis has been at the forefront of characterizing single-objective continuous optimization problems. Other variants, which can be summarized under the term landscape analysis, have been used in the domain of combinatorial problems. However, none to little has been done in this research area for mixed-integer problems. In this work, we evaluate the current state of existing exploratory landscape analysis features and their applicability on a subset of mixed-integer problems.

Evaluating the performance of heuristic optimisation algorithms is essential to determine how well they perform under various conditions. Recently, the BIAS toolbox was introduced as a behaviour benchmark to detect structural bias (SB) in search algorithms. The toolbox can be used to identify biases in existing algorithms, as well as to test for bias in newly developed algorithms. In this article, we introduce a novel and explainable deep-learning expansion of the BIAS toolbox, called Deep-BIAS. Where the original toolbox uses 39 statistical tests and a Random Forest model to predict the existence and type of SB, the Deep-BIAS method uses a trained deep-learning model to immediately detect the strength and type of SB based on the raw performance distributions. Through a series of experiments with a variety of structurally biased scenarios, we demonstrate the effectiveness of Deep-BIAS. We also present the results of using the toolbox on 336 state-of-the-art optimisation algorithms, which showed the presence of various types of structural bias, particularly towards the centre of the objective space or exhibiting discretisation behaviour. The Deep-BIAS method outperforms the BIAS toolbox both in detecting bias and for classifying the type of SB. Furthermore, explanations can be derived using XAI techniques.

In the Music Information Retrieval domain, the concept of time signature detection has been ongoing for some time now. Time signature is being considered as a feature in broader classification problems such as music genre classification. To develop a realistic model that is capable of accurately detecting any time signature from any music track, different techniques are adopted. Based on previous research, two models have been highlighted (Beat and Audio Similarity Matrix) in this study for their potential but not without their limitations. Therefore, a new model was developed with the idea from the previous models. We called this model Mel-Frequency Cepstral Coefficient Similarity Matrix (MFCCSM). It uses Mel-coefficients extracted from audio signals which produce mel-frequency cepstrum coefficients that are eventually optimized. Two optimization techniques, Bayesian optimization and Genetic Algorithm, were considered for optimization, with the latter being the major technique used in the model. In comparison with the previous two models, MFCCSM showed a significant increase in accuracy of about 8% after optimization based on two datasets that were used for the study. Overall, the GA optimization also gives insight into the set of frequencies in each coefficients of the MFCC which can be further explored in future research.

Recently, influence maximization has become a key research area in complex networks, focusing on selecting optimal seed sets for propagation in the network. However, networks often face complex environments with node/link failures or external attacks, making robustness critical for seed nodes. This robust influence maximization problem is not comprehensively addressed by existing approaches, which fail to combine information or knowledge across multiple scenarios. To address this, this paper introduces multi-task optimization theory, designing an evolutionary algorithm, MFEANet, to consider diversity gene information and multiple optimization scenarios simultaneously. MFEANet achieves competitive performance in experimental results compared to existing methods.

Unsupervised learning algorithms are popular as they do not require annotated data. However as per the no-free lunch theorem, the best algorithm to use is not the same for all datasets. This study is the first to automate the composition of an unsupervised image clustering algorithm. This work uses two different techniques to perform automated algorithm composition. The first technique is a genetic algorithm (GA) and the second is a genetic algorithm hyperheuristic (GAHH). A comparison of the two techniques shows that the GA outperforms the GAHH. The GA designs unsupervised clustering algorithms that result in state of the art performance for the Oral lesion, Celebrity faces and COVID-19 datasets.

Relational Bayesian optimization for permutation (RBOP) is a new permutation estimation of distribution algorithm proposed in this paper. RBOP uses binary relations to represent the common property in permutations. Inspired by the Bayesian optimization algorithm, RBOP first builds a Bayesian network using binary relations. Then, RBOP samples genes using the most certain edge in the Bayesian network. In the scenario of black-box optimization, RBOP aims to solve various permutation problems with a limited number of function evaluations. Experiments show that in terms of average relative percentage deviation, RBOP outperforms edge histogram-based sampling algorithm on quadratic assignment problems, permutation flow shop problems and linear ordering problems. Additionally, RBOP also outperforms both node histogram-based sampling algorithm and kernels of Mallows model using Cayley distance on traveling salesman problems, permutation flow shop problems, linear ordering problems and 6 out of 10 instances of quadratic assignment problems.

This paper presents a comparison on performances between the Coarse-Grained Steady-State Genetic Algorithm (SSGA) and the Generational Genetic Algorithm (GGA) on benchmark problems of the Capacitated Vehicle Routing Problem (CVRP). A statistical fractional multi-factorial design of experiments is done to find optimal parameter settings for the SSGA, while the best settings for the GGA were taken from aprevious study. The GAs were compared pairwise on problems of various sizes, with results indicating the SSGA outperforms the GGA on all the problems. A pooled statistical test further support this, with a p-value less than 0.05%, further proving the SSGA is significantly better than the GGA.

State-of-the-art multi-objective evolutionary algorithms (MOEAs) are highly elitist. These algorithms usually employ a deterministic (μ + λ) selection, where only the best individuals are selected for the next generation. However, for certain problems, it could be useful to have greater diversity to explore the search space.

In this work, we aim to study the impact of temporal heterogeneity on the search to find a balance between exploration and exploitation by adding an extra parameter to evolutionary algorithms. This parameter controls the selection pressure going from (μ+λ) to (μ,λ) strategies. We analyzed classical evolutionary algorithms for single and multi-objective optimization (three and five objectives) and tested them on academic benchmarks. Our preliminary results indicate that there is a significant statistical difference at least for single-objective optimization problems. These results indicate that we should adapt the selection pressure for different problems and at different stages of the search.

In optimization, we often encounter expensive black-box problems with unknown problem structures. Bayesian Optimization (BO) is a popular, surrogate-assisted and thus sample-efficient approach for this setting. The BO pipeline itself is highly configurable with many different design choices regarding the initial design, surrogate model and acquisition function (AF). Unfortunately, our understanding of how to select suitable components for a problem at hand is very limited. In this work, we focus on the choice of the AF, whose main purpose it is to balance the trade-off between exploring regions with high uncertainty and those with high promise for good solutions. We propose Self-Adjusting Weighted Expected Improvement (SAWEI), where we let the exploration-exploitation trade-off self-adjust in a data-driven manner based on a convergence criterion for BO. On the BBOB functions of the COCO benchmark, our method performs favorably compared to handcrafted baselines and serves as a robust default choice for any problem structure. With SAWEI, we are a step closer to on-the-fly, data-driven and robust BO designs that automatically adjust their sampling behavior to the problem at hand.

We propose a novel evolutionary algorithm on bit vectors which derives from the principles of information theory. The information-theoretic evolutionary algorithm (it-EA) iteratively updates a search distribution with two parameters, the center, that is the bit vector at which standard bit mutation is applied, and the mutation rate. The mutation rate is updated by means of information-geometric optimization and the center is updated by means of a maximum likelihood principle. Standard elitist and non elitist updates of the center are also considered. Experiments illustrate the dynamics of the mutation rate. In an empirical runtime analysis on OneMax, the elitist and non elitist it-EAs obtain promising results.

Evolutionary algorithms are stochastic algorithms so they tend to find different solutions when run repeatedly. However, it is not just the solutions that vary - the very dynamics of the search that led to finding these solutions are likely to differ as well. It is especially in the algorithms with complex population structures - such as convection selection where a population is divided into subpopulations according to fitness values - where an opportunity for highly diverse dynamics arises. This work investigates the way evolutionary dynamics of subpopulations influence the performance of evolutionary algorithms with convection selection. We employ a demanding task of evolutionary design of 3D structures to analyze the relation between the properties of the optimization task and the features of the evolutionary process. Based on this analysis, we identify the mechanisms that influence the performance of convection selection, and suggest ways to improve this selection scheme.

Performance complementarity of solvers available to tackle black-box optimization problems gives rise to the important task of algorithm selection (AS). Automated AS approaches can help replace tedious and labor-intensive manual selection, and have already shown promising performance in various optimization domains. Automated AS relies on machine learning (ML) techniques to recommend the best algorithm given the information about the problem instance. Unfortunately, there are no clear guidelines for choosing the most appropriate one from a variety of ML techniques. Tree-based models such as Random Forest or XGBoost have consistently demonstrated outstanding performance for automated AS. Transformers and other tabular deep learning models have also been increasingly applied in this context.

We investigate in this work the impact of the choice of the ML technique on AS performance. We compare four ML models on the task of predicting the best solver for the BBOB problems for 7 different runtime budgets in 2 dimensions. While our results confirm that a per-instance AS has indeed impressive potential, we also show that the particular choice of the ML technique is of much minor importance.

This paper investigates the effect of hybridising sampling algorithms with population-based meta-heuristics. Recent literature has shown that alternatives to the traditionally used pseudo-random number generators to generate the initial population of meta-heuristics can improve performance. However, most studies focus on sample sizes that are limited to the size of the initial populations. In contrast, this paper studies the effect of extended random initialisation, which uses relatively large samples and then initialises the meta-heuristics from the points in the sample with the best-found fitness values. A portfolio of three meta-heuristics, four sampling algorithms and three different sampling budgets are analysed from the fixed budget perspective on the BBOB benchmark suite. Statistical analysis of the results shows that the hybrid algorithms converge to better solutions than their non-hybrid counterparts. The results further indicate that large sample sizes can be used to generate landscape analysis features, ensuring reliable approximations of the investigated functions' properties without lessening the meta-heuristics' performance.

Dynamic Optimization Problems (DOPs) are characterized by changes in the fitness landscape that can occur at any time and are common in real world applications. The main issues to be considered include detecting the change in the fitness landscape and reacting in accord. Over the years, several evolutionary algorithms have been proposed to take into account this characteristic during the optimization process. However, the number of available tools or open source codebases for these approaches is limited, making reproducibility and extensive experimentation difficult. To solve this, we developed a component-oriented framework for DOPs called Adjustable Components for Dynamic Problems (AbCD), inspired by similar works in the Multiobjective static domain. Using this framework, we investigate components that were proposed in several popular DOP algorithms. Our experiments show that the performance of these components depends on the problem and the selected components used in a configuration, which differs from the results reported in the literature. Using irace, we demonstrate how this framework can automatically generate DOP algorithm configurations that take into account the characteristics of the problem to be solved. Our results highlight existing problems in the DOP field that need to be addressed in the future development of algorithms and components.

Multimodal functions play a central role in artificial intelligence and evolutionary algorithms. Still, there are several limitations when it comes to existing work on optimization of complex multimodal functions. In this paper, we study the optimization of such functions, in the subset selection problem setting, by carefully integrating different methods: evolutionary algorithms, stochastic local search, clustering, and feedback control. The goal is to carefully balance exploration and exploitation during hybrid evolutionary search by using feedback control to adapt population diversity via crowding. We empirically test our integrated method on complex synthetic combinatorial optimization problems, demonstrating promising results compared to previous work.

In the context of metaheuristic search algorithms, two recent approaches have been proposed to measure algorithm similarity. The first one is based on shared search strategies, such as mutation or selection. The second one involves an empirical analysis that uses a set of performance metrics on benchmark problems. This paper explores whether high Component Similarity corresponds to Performance Similarity by analyzing these two similarity metrics on 9 CMA-ES variants on the COCO benchmark.

We propose DoE2Vec, a variational autoencoder (VAE)-based methodology to learn optimization landscape characteristics for downstream meta-learning tasks, e.g., automated selection of optimization algorithms. Principally, using large training data sets generated with a random function generator, DoE2Vec self-learns an informative latent representation for any design of experiments (DoE). Unlike the classical exploratory landscape analysis (ELA) method, our approach does not require any feature engineering and is easily applicable to high-dimensional search spaces. For validation, the proposed approach is used for three downstream classification tasks. We show that the latent representations can significantly boost performances when being used complementary to the classical ELA features.

We provide an open source framework to experiment with evolutionary algorithms which we call Experimenting and Learning toolkit for Evolutionary Algorithms (ELEA). ELEA is browser-based and allows to assemble evolutionary algorithms using drag-and-drop, starting from a number of simple pre-designed examples, making the startup costs for employing the toolkit minimal. The designed examples can be executed and collected data can be displayed graphically. Further features include export of algorithm designs and experimental results as well as multi-threading.

With the very intuitive user interface and the short time to get initial experiments going, this tool is especially suitable for explorative analyses of algorithms as well as for the use in classrooms.

The container relocation problem is a combinatorial optimisation problem aimed at finding a sequence of container relocations to retrieve all containers in a predetermined order by minimising a given objective. Relocation rules (RRs), which consist of a priority function and relocation scheme, are heuristics commonly used for solving the mentioned problem due to their flexibility and efficiency. Recently, in many real-world problems it is becoming increasingly important to consider energy consumption. However, for this variant no RRs exist and would need to be designed manually. One possibility to circumvent this issue is by applying hyperheuristics to automatically design new RRs. In this study we use genetic programming to obtain priority functions used in RRs whose goal is to minimise energy consumption. We compare the proposed approach with a genetic algorithm from the literature used to design the priority function. The results obtained demonstrate that the RRs designed by genetic programming achieve the best performance.

Genetic programming systems often use large training sets to evaluate candidate solutions, which can be computationally expensive. Down-sampling training sets has long been used to decrease the computational cost of evaluation in a wide range of application domains. Indeed, recent studies have shown that both random and informed down-sampling can substantially improve problem-solving success for GP systems that use lexicase parent selection. We use the PushGP framework to experimentally test whether these down-sampling techniques can also improve problem-solving success in the context of two other commonly used selection methods, fitness-proportionate and tournament selection, across eight GP problems (four program synthesis and four symbolic regression). We verified that down-sampling can benefit the problem-solving success of both fitness-proportionate and tournament selection. However, the number of problems wherein down-sampling improved problem-solving success varied by selection scheme, suggesting that the impact of down-sampling depends both on the problem and choice of selection scheme. Surprisingly, we found that down-sampling was most consistently beneficial when combined with lexicase selection as compared to tournament and fitness-proportionate selection. Overall, our results suggest that down-sampling should be considered more often when solving test-based GP problems.

We present an analysis of the loss of population-level test coverage induced by different down-sampling strategies when combined with lexicase selection. We study recorded populations from the first generation of genetic programming runs, as well as entirely synthetic populations. Our findings verify the hypothesis that informed down-sampling better maintains population-level test coverage when compared to random down-sampling. Additionally, we show that both forms of down-sampling cause greater test coverage loss than standard lexicase selection with no down-sampling. However, given more information about the population, we found that informed down-sampling can further reduce its test coverage loss. We also recommend wider adoption of the static population analyses we present in this work.

When using genetic programming for program synthesis, we are usually constrained by a computational budget measured in program executions during evolution. The computational budget is influenced by the choice of population size and number of generations per run leading to a trade-off between both possibilities. To better understand this trade-off, we analyze the effects of different combinations of population sizes and number of generations on performance. Further, we analyze how the use of different variation operators affects this trade-off. We conduct experiments on a range of common program synthesis benchmarks and find that using larger population sizes lead to a better search performance. Additionally, we find that using high probabilities for crossover and mutation lead to higher success rates. Focusing on only crossover or using only mutation usually leads to lower search performance. In summary, we find that large populations combined with high mutation and crossover rates yield highest GP performance for program synthesis approaches.

Genetic Programming (GP) has the potential to generate intrinsically explainable models. Despite that, in practice, this potential is not fully achieved because the solutions usually grow too much during the evolution. The excessive growth together with the functional and structural complexity of the solutions increase the computational cost and the risk of overfitting. Thus, many approaches have been developed to prevent the solutions to grow excessively in GP. However, it is still an open question how these approaches can be used for improving the interpretability of the models. This article presents an empirical study of eight structural complexity metrics that have been used as evaluation criteria in multi-objective optimisation. Tree depth, size, visitation length, number of unique features, a proxy for human interpretability, number of operators, number of non-linear operators and number of consecutive nonlinear operators were tested. The results show that potentially the best approach for generating good interpretable GP models is to use the combination of more than one structural complexity metric.

Unlike most research of symbolic regression with genetic programming (GP) concerning black-box optimization, this paper focuses on the scenario where the underlying function is available, but due to limited computational resources or product imperfection, the function needs to be approximated with simplicity to fit measured data. Taylor polynomial (TP) is commonly used in such scenario; however, its performance drops drastically away from the expansion point. On the other hand, solely using GP does not utilize the knowledge of the underlying function, even though possibly inaccurate. This paper proposes using GP as a TP enhancer, namely TPE-GP, to combine the advantages from TP and GP. Specifically, TPE-GP utilizes infinite-order operators to compensate the power of TP with finite order. Empirically, on functions that are expressible by TP, TP outperformed both gplearn and TPE-GP as expected, while TPE-GP outperformed gplearn due to the use of TP. On functions that are not expressible by TP but expressible by the function set (FS), TPE-GP was competitive with gplearn while both outperformed TP. Finally, on functions that are not expressible by both TP and FS, TPE-GP outperformed both TP and gplearn, indicating the hybrid did achieve the synergy effect from TP and GP.

The Traveling Salesman Problem (TSP) is a difficult permutation-based optimisation problem typically solved using heuristics or meta-heuristics which search the solution problem space. An alternative is to find sets of manipulations to a solution which lead to optimality. Hyper-heuristics search this space applying heuristics sequentially, similar to a program. Genetic Programming (GP) evolves programs typically for classification or regression problems. This paper hypothesizes that GP can be used to evolve heuristic programs to directly solve the TSP. However, evolving a full program to solve the TSP is likely difficult due to required length and complexity. Consequently, a phased GP method is proposed whereby after a phase of generations the best program is saved and executed. The subsequent generation phase restarts operating on this saved program output. A full program is evolved piecemeal. Experiments demonstrate that whilst pure GP cannot solve TSP instances when using simple operators, Phased-GP can obtain solutions within 4% of optimal for TSPs of several hundred cities. Moreover, Phased-GP operates up to nine times faster than pure GP.

Underspecification happens when there are different plausible hypotheses for a training and validation data set that behave differently when evaluating outside the training domain or distribution. Symbolic regression algorithms are prone to underspecification because of the additional degree of freedom of having to specify the structural component of the regression model. When facing different likely alternatives, some algorithms use the Occam's razor principle of choosing the simplest alternative. But not only there is no guarantee that this is the correct decision but the definition of simplest in symbolic regression is also subjective. In this work we analyse the use diversity control mechanisms to help fight the underspecification problem by providing to the end-user multiple alternative models in a single execution. These alternative models can be used in a post-analysis process when the practitioner has additional knowledge. For this purpose, we implemented a fitness sharing mechanism in the Transformation-Interaction-Rational Symbolic Regression algorithm with a distance function that measures how different two models behave outside the domain of the training data. The results showed that this adaptation is capable of producing multiple alternatives with similar fitness but with distinct behavior outside this domain.

We introduce Leap mapping, a new mapping process for Grammatical Evolution (GE), which spreads introns within the effective length of the genome (the part of the genome consumed while mapping), preserving information for future generations and performing less disruptive crossover and mutation operations than standard GE. Using the exact same genotypic representation as GE, Leap mapping reads the genome in separate parts named 'frames', where the size of each is the number of production rules in the grammar. Each codon inside a frame is responsible for mapping a different production rule of the grammar. The process keeps consuming codons from the frame until it needs to map again a production rule already mapped with that frame. At this point, the mapping starts consuming codons from the next frame. We assessed the performance of this new mapping in some benchmark problems, which require modular solutions: four Boolean problems and three versions of the Lawnmower problem. Moreover, we compared the results with the standard mapping procedure and a multi-genome version.

Recent years saw an increase in the application of genetic programming (GP) as a hyper-heuristic, i.e., a method used to generate heuristics for solving various combinatorial optimisation problems. One of its widest application is in scheduling to automatically design constructive heuristics called dispatching rules (DRs). DRs are crucial for solving dynamic scheduling environments, in which the conditions change over time. Although automatically designed DRs achieve good results, their performance is limited as a single DR cannot always perform well. Therefore, various methods were used to improve their performance, among which ensemble learning represents one of the most promising directions. Using ensembles introduces several new parameters, such as the ensemble construction method, ensemble collaboration method, and ensemble size. This study investigates the possibility to remove the ensemble size parameter when constructing ensembles. Therefore, the simple ensemble combination method is adapted to randomly select the size of the ensemble it generates, rather than using a fixed ensemble size. Experimental results demonstrate that not using a fixed ensemble size does not result in a worse performance, and that the best ensembles are of smaller sizes. This shows that the ensemble size can be eliminated without a significant influence on the performance.

This paper proposes a model-based genetic programming algorithm for symbolic regression, called the ranging-binding genetic programming algorithm (RBGP). The goal is to allow offspring to retain the superiority of their promising parents during evolution. Inspired by the concept of model building, RBGP makes use of syntactic information and semantics information in a program to capture the hidden patterns. When compared with GP-GOMEA, ellynGP, and gplearn, RBGP outperformed the others on average in the Penn machine learning benchmarks, RBGP achieving statistically significant improvements over all other methods on 44% of the problems.

Symbolic Regression (SR) is the task of finding closed-form expressions that describe the relationship between variables in a dataset. Current SR methods tend to neglect a large portion of the search space of 'short' expressions in favor of longer expressions which are less explainable. In contrast to current SR methods, we propose to prioritize expression length over prediction performance. We do so by systematically searching through the search space of 'short' expressions, utilizing K-expressions from Gene Expression Programming. However, the search space of 'short' expressions is large, scaling approximately exponentially with the number of variables in a dataset. To reduce the size of the search space, we propose a method, termed DistilSR, which replaces terminal symbols with weighted linear combinations of variables. We show that DistilSR exactly recovers the ground-truth equation of 16 synthetic datasets 100% of the time, outperforming 14 benchmark SR methods in SRBench. DistilSR also shows outperformance on 14 real-world datasets when compared against 14 benchmark SR algorithms and 4 benchmark non-SR algorithms from SRBench. These equations were also consistently shorter. Finally, to further enforce sparsity of weights, we propose a method of actively setting uninfluential weights to 0, achieving even shorter expressions with competitive prediction performance.

The Fuzzy Adaptive Resonance Theory (ART) algorithm is effective for unsupervised clustering. The Fuzzy ART choice function is an integral part of the Fuzzy ART algorithm. One of the challenges is that different choice functions are effective for different datasets. This work evolves the choice function using GE. The study compares the evolved choice functions to manually created choice functions. This study compares two different grammars for the GE, a basic grammar that includes only functions from the Fuzzy ART algorithm and an extended grammar that includes additional functions. This work also compares different fitness functions for GE. Analysis is done using ten UCI benchmark datasets and three real-world sentiment analysis datasets, it is found that the evolved functions using the extended grammar perform better than the manually created functions. The best fitness function to use for the GE is dataset dependent.

Designing heuristics is an arduous task, usually approached with hyper-heuristic methods such as genetic programming (GP). In this setting, the goal of GP is to evolve new heuristics that generalise well, i.e., that work well on a large number of problems. To achieve this, GP must use a good training model to evolve new heuristics and also to evaluate their generalisation ability. For this reason, dozens of training models have been used in the literature. However, there is a lack of comparison between different models to determine their effectiveness, which makes it difficult to choose the right one. Therefore, in this paper, we compare different training models and evaluate their effectiveness. We consider the well-known Travelling Salesman Problem (TSP) as a case study to analyse the performance of different training models and gain insights about training models. Moreover, this research opens new directions for the future application of hyper-heuristics.

Symbolic regression (SR) is a well-known regression problem, that aims to find a symbolic expression that best fits a given dataset. Linear Genetic Programming (LGP) is a good and powerful candidate for solving symbolic regression problems. However, current LGPs for SR only focus on finding scalar-valued functions, and limited work has been done on finding vector-valued functions with vectorial-based LGP. In addition, a comprehensive dataset for testing vectorial-based GP is still lacking in the literature. To this end, we propose a new extensive benchmark suite for vectorial symbolic regression. Furthermore, we propose a new vectorial LGP algorithm for symbolic regression, which directly deals with high dimensional data using vectorial representation and operations. Experimental results show that the proposed algorithm outperforms another recently published vectorial GP method on the benchmark suite for vector-valued functions and that it also generalizes better on unseen data.

The encoding method of a searchable encryption can significantly impact the performance of a location-based alert system. While there were attempts to design searchable encryption manually, Gray Encoding is considered the most preferable method. However, if the alert zones are scattered unevenly, Gray Encoding fails to achieve token aggregation. In this research, a novel Quadtree-based Genetic Programming (Quadtree-GP) is proposed to iteratively identify superior searchable encryption candidates for the location-based alert system. Quadtree-GP can be effectively applied on customized requirements and different grid maps. Extensive experimental results show that Quadtree-GP is able to find searchable encryption candidates that outperform GP search, random search, and the baseline Gray Encoding in terms of user response time, token remaining percentage, and execution time.

Active learning for genetic programming using model ensemble uncertainty was explored across a range of uncertainty metrics to determine if active learning can be used with GP to minimize training set sizes by selecting maximally informative samples to guide evolution. The choice of uncertainty metric was found to have a significant impact on the success of active learning to inform model development in genetic programming. Differential evolution was found to be an effective optimizer, likely due to the non-convex nature of the uncertainty space, while differential entropy was found to be an effective uncertainty metric. Uncertainty-based active learning was compared to two random sampling methods and the results show that active learning successfully identified informative samples and can be used with GP to reduce required training set sizes to arrive at a solution.

Just over a decade ago, the first comprehensive review on the state of benchmarking in Genetic Programming (GP) analyzed the mismatch between the problems that are used to test the performance of GP systems and real-world problems. Since then, several benchmark suites in major GP problem domains have been proposed over time, which were able to fill some of the major gaps. In the framework of the first review about the state of benchmarking in GP, logic synthesis was classified as one of the major GP problem domains. However, a diverse and accessible benchmark suite for logic synthesis is still missing in the field of GP. In this work, we take a first step towards a benchmark suite for logic synthesis that covers different types of Boolean functions that are commonly used for the evaluation of GP systems. We also present baseline results that have been obtained by former work and in our evaluation experiments by using Cartesian Genetic Programming.

In this paper we present an iterative structure-based genetic programming algorithm for neural architecture search. Canonical genetic programming uses a fitness function to determine where to move the search to in the program space. This research investigates using the structure of the syntax trees, representing different areas of the program space, in addition to the fitness function to direct the search. The structure is used to avoid areas of the search that previously led to local optima both globally (exploration) and locally (exploitation). The proposed approach is evaluated for image classification and video shorts creation. The iterative structure-based approach was found to produce better results then canonical genetic programming for both problem domains, with a slight reduction in computational cost. The approach also produced better results than genetic algorithms which are traditionally used for neural architecture search.

Automated machine learning (AutoML) has allowed for many innovations in biomedical data science; however, most AutoML approaches do not support image or text data. To rectify this, we implemented four feature extractors in the Tree-based Pipeline Optimization Tool (TPOT) to make TPOT with Feature Extraction (TPOT-FE), an automated machine learning system that uses genetic programming (GP) to create ideal pipelines for a classification or regression task. These feature extractors enable TPOT-FE to build pipelines that can analyze non-tabular data, including text and images, which are increasingly common biomedical big data modalities that can contain rich quantities of information. We evaluate this approach on six image datasets and four text datasets, including three biomedical datasets, and show that TPOT-FE is able to consistently construct and optimize classification pipelines on all of the datasets.

Evolutionary differential equation discovery proved to be a tool to obtain equations with less a priori assumptions than conventional approaches, such as sparse symbolic regression over the complete possible terms library. The equation discovery field contains two independent directions. The first one is purely mathematical and concerns differentiation, the object of optimization and its relation to the functional spaces and others. The second one is dedicated purely to the optimizatioal problem statement. Both topics are worth investigating to improve the algorithm's ability to handle experimental data a more artificial intelligence way, without significant pre-processing and a priori knowledge of their nature. In the paper, we consider the prevalence of either single-objective optimization, which considers only the discrepancy between selected terms in the equation, or multi-objective optimization, which additionally takes into account the complexity of the obtained equation. The proposed comparison approach is shown on classical model examples - Burgers equation, wave equation, and Korteweg - de Vries equation.

Linear scaling has greatly improved the performance of genetic programming when performing symbolic regression. Linear scaling transforms the output of an expression to reduce its error. Mean squared error and correlation have been used with scaling, often interchangeably and with assumed equivalence. We examine if this equivalence is justified by investigating the differences between an error-based metric and a correlation-based metric on 11 well-known symbolic regression benchmarks. We investigate the effect a change of fitness function has on performance, individuals size and diversity. Error-based scaling and Correlation were seen to attain equivalent performance and found solutions with very similar size and diversity on the majority of problem, but not all. In order to ascertain if the strengths of both approaches could be combined, we explored a double tournament selection strategy, where two tournaments are conducted sequentially to select individuals for recombination. Double tournament selection found smaller solutions and the best solution in five benchmarks, including finding the best solutions on both real-world dataset used in our experiments.

Context-Free Grammars (CFGs) are used in Genetic Programming (GP) to encode the structure and syntax of programs, enabling efficient exploration of potential solutions and generation of well-formed and syntactically correct programs. Probabilistic Context-Free Grammars (PCFG) can be used to model the distribution of solutions to help guide the search process. Structured Grammatical Evolution (SGE) is a grammar-based GP algorithm that uses a list of dynamic lists as its genotype, where each list represents the ordered indexes of production rules to expand for each non-terminal in the grammar. Two recent variants incorporate PCFG into the SGE framework, where the probabilities of the production rule change during the evolutionary process, resulting in improved performance.

This study examines the impact of these differences on the behavior of SGE and its variants, Probabilistic Structured Grammatical Evolution (PSGE) and Co-evolutionary Probabilistic Structured Grammatical Evolution (Co-PSGE), in terms of population tree depth, genotype size, new solutions generated, and runtime. The results indicate that the use of probabilistic alternatives can affect the growth of tree depth and size and increases the ability to generate new solutions.

We formulate a formal grammar to generate Full Approximation Scheme multigrid solvers. Then, using Grammar-Guided Genetic Programming we perform a multiobjective optimization to find optimal instances of such solvers for a given nonlinear system of equations. This approach is evaluated for a two-dimensional Poisson problem with added nonlinearities. We observe that the evolved solvers outperform the baseline methods by having a faster runtime and a higher convergence rate.

Symbolic regression is a common problem in genetic programming (GP), but the syntactic search carried out by the standard GP algorithm often struggles to tune the learned expressions. On the other hand, gradient-based optimizers can efficiently tune parametric functions by exploring the search space locally. While there is a large amount of research on the combination of evolutionary algorithms and local search (LS) strategies, few of these studies deal with GP. To get the best from both worlds, we propose embedding learnable parameters in GP programs and combining the standard GP evolutionary approach with a gradient-based refinement of the individuals employing the Adam optimizer. We devise two different algorithms that differ in how these parameters are shared in the expression operators and report experimental results performed on a set of standard real-life application datasets. Our findings show that the proposed gradient-based LS approach can be effectively combined with GP to outperform the original algorithm.

One-dimensional cutting stock and packing problems require determining a set of patterns that are applied a number of times each on raw material pieces to produce a number of customer orders. Among many other solving methods, greedy algorithms guided by heuristic rules stand out due to their low computational cost and ability to be adapted to sets of instances with similar structures. In this paper, we use genetic programming (GP) to evolve heuristics for the one-dimensional bin packing problem. We explore two greedy variants taken from the literature; in the first one, termed cut-by-cut, the heuristic rule is used to construct the pattern by selecting the most appropriate item that should be packed. In the second one, denoted as pattern-by-pattern, a number of patterns are randomly generated, and the heuristic selects the most appropriate one to be applied. We thoroughly analysed the problem's features to identify the relevant attributes of each greedy strategy. From these attributes, we exploited GP to evolve a number of heuristics adapted to a well-known benchmark set of one-dimensional bin packing instances. The experimental results provided interesting insights into the problem features and showed that the evolved heuristics are competitive with the state-of-the-art.

Self-supervised learning (SSL) methods have been widely used to train deep learning models for computer vision and natural language processing domains. They leverage large amounts of unlabeled data to help pretrain models by learning patterns implicit in the data. Recently, new SSL techniques for tabular data have been developed, using new pretext tasks that typically aim to reconstruct a corrupted input sample and yielding models which are, ideally, robust feature transforms. In this paper, we pose the research question of whether genetic programming is capable of leveraging data processed using SSL methods to improve its performance. We test this hypothesis by assuming different amounts of labeled data on seven different datasets (five OpenML benchmarking datasets and two real-world datasets). The obtained results show that in almost all problems, standard genetic programming is not able to capitalize on the learned representations, producing results equal to or worse than using the labeled partitions.

Transfer learning has recently gained popularity in the evolutionary algorithms space. Determining a good criteria for how to transfer knowledge can be very challenging. It has been a focus of research to optimize the process of deciding what, when and how to transfer knowledge. Genetic programming is an area of evolutionary algorithms that has benefited greatly from transfer learning. In this paper, a selection hyper-heuristic (SHeTL) has been used to optimize transfer learning, i.e. what to transfer, when to transfer and how to transfer, in genetic programming. The proposed approach has been applied to benchmark and real-world symbolic regression problems. SHeTL produced significant improvements over canonical genetic programming. Furthermore, the hyper-heuristic produced better results than previous transfer learning approaches used in genetic programming.

The search for the optimal treatment plan of a focused ultrasound-based procedure is a complex multi-modal problem, trying to deliver the solution in clinically relevant time while not sacrificing the precision below a critical threshold. To test a solution, many computationally expensive simulations must be evaluated, often thousands of times. The recent renaissance of machine learning could provide an answer to this. Indeed, a state-of-the-art neural predictor of Acoustic Propagation through a human skull was published recently, speeding up the simulation significantly. The utilized architecture, however, could use some improvements in precision. To explore the design more deeply, we made an attempt to improve the solver by use of an evolutionary algorithm, challenging the importance of different building blocks. Utilizing Genetic Programming, we improved their solution significantly, resulting in a solver with approximately an order of magnitude better RMSE of the predictor, while still delivering solutions in a reasonable time frame. Furthermore, a second study was conducted to gauge the effects of the multi-resolution encoding on the precision of the network, providing interesting topics for further research on the effects of the memory blocks and convolution kernel sizes for PDE RCNN solvers.

Quality Diversity (QD) optimization aims at returning a diverse collection of high quality solutions in a single run. Prior work indicated that the optimized collection concentrates in a subspace of the genotype space called the Elite Hypervolume. This suggested that if the Elite Hypervolume is convex, perturbing a solution (elite) towards the direction of another elite would create a solution inside the subspace. To accelerate QD optimization, the IsoLineDD operator was proposed which perturbs a solution along the line that connects it with another elite, both in the forward and the backward direction (i.e., towards and away from another elite), with equal probability. In this work, we hypothesize that the backward direction is mostly useful for exploration, at the beginning of QD optimization, rather than exploitation. To validate our hypothesis, we create a dynamic IsoLineDD operator that modifies its probability of creating solutions in the forward and backward directions, respectively. Our experiments and analysis in the robotic arm repertoire and Rastrigin problems invalidate this hypothesis by demonstrating that the forward and backward directions of vanilla IsoLineDD equally contribute to the optimization of the collection.

During the first part of life, the brain develops while it learns through a process called synaptogenesis. The neurons, growing and interacting with each other, create synapses. However, eventually the brain prunes those synapses. While previous work focused on learning and pruning independently, in this work we propose a biologically plausible model that, thanks to a combination of Hebbian Learning and pruning, aims to simulate the synaptogenesis process. In this way, while learning how to solve the task, the agent translates its experience into a particular network structure. Namely, the network structure builds itself during the execution of the task. We call this approach Self-building Neural Network (SBNN). We compare our proposed SBNN with traditional feed forward neural networks (FFNNs) over three OpenAI classic control tasks. The results show that our model performs generally better than FFNNs. Moreover, we observe that the performance decay while increasing the pruning rate is smaller in our model than with FFNNs.

Quantum Machine Learning (QML) is a recent and rapidly evolving field where the theoretical framework and logic of quantum mechanics are employed to solve machine learning tasks. Various techniques with different levels of quantum-classical hybridization have been proposed. Here we focus on variational quantum circuits (VQC), which emerged as the most promising candidates for the quantum counterpart of neural networks in the noisy intermediate-scale quantum (NISQ) era. Although showing promising results, VQCs can be hard to train because of different issues, e.g., barren plateau, periodicity of the weights, or choice of architecture. This paper focuses on this last problem for finding optimal architectures of variational quantum circuits for various tasks. To address it, we propose a gradient-free algorithm inspired by natural evolution to optimize both the weights and the architecture of the VQC. In particular, we present a version of the well-known neuroevolution of augmenting topologies (NEAT) algorithm and adapt it to the case of variational quantum circuits. We refer to the proposed architecture search algorithm for VQC as QNEAT. We test the algorithm with different benchmark problems of classical fields of machine learning i.e. reinforcement learning and combinatorial optimization.

This work presents the preliminary results of and discusses current challenges in ongoing research of neuroevolution for the task of evolving agents for autonomous cyber operations (ACO). The application of reinforcement learning to the cyber domain is especially challenging due to the extremely limited observability of the environment over extended time frames where an adversary can potentially take many actions without being detected. To promote research within this space The Technical Cooperation Program (TTCP), which is an international collaboration organization between the US, UK, Canada, Australia, and New Zealand, released the Cyber Operations Research Gym (CybORG) to enable experimentation with RL algorithms in both simulated and emulated environments. Using competition to spur investigation and innovation, TTCP has released the CAGE Challenges which for evaluating RL in network defense.[1] This work evolves agents for ACO using the python-based neuroevolution library Evosax[2] which supports high performance, GPU accelerated evolutionary algorithms for the purpose of optimizing artificial neural network parameters. The use of neuroevolution in this paper is a first for the ACO task and benchmarks two popular algorithms to identify factors which impact their effectiveness.

With the increasing demand of deploying convolutional neural networks (CNNs) on resource-constrained devices, designing high-performance and lightweight architectures has become a main challenge for neural architecture search (NAS). This paper develops an evolutionary multi-objective optimization framework to explore CNNs with different compactness in a flexible way. A multi-scale convolutional module is developed to enhance the feature learning capability. To further improve the architecture search efficiency, a low-cost metric based on neural tangent kernel is leveraged to estimate the trainability of CNNs instead of performing an expensive training process. Experiments are carried out on CIFAR-10 and CIFAR-100, to verify the effectiveness of the proposed method. Compared with the state-of-the-art algorithms, the proposed method discovers architectures with a smaller number of parameters and competitive classification performance using only up to 0.2 GPU days, showing a better trade-off between accuracy and model complexity.

The deep learning revolution has greatly been accelerated by the 'hardware lottery': Recent advances in modern hardware accelerators, compilers and the availability of open-source software paved the way for large-scale batch gradient optimization. Evolutionary optimization, on the other hand, has mainly relied on CPU-parallelism, e.g. using Dask scheduling and distributed multi-host infrastructure. Here we argue that also modern evolutionary computation can significantly benefit from the massive computational throughput provided by GPUs and TPUs. In order to better harness these resources and to enable the next generation of black-box optimization algorithms, we release evosax : A JAX-based library of evolution strategies which allows researchers to leverage powerful function transformations such as just-in-time compilation, automatic vectorization and hardware parallelization.¹ evosax implements 30 evolutionary optimization algorithms including finite-difference-based, estimation-of-distribution evolution strategies and various genetic algorithms. Every single algorithm can directly be executed on hardware accelerators and automatically vectorized or parallelized across devices using a single line of code. It is designed in a modular fashion and allows for flexible usage via a simple ask-evaluate-tell API. We thereby hope to facilitate a new wave of scalable evolutionary optimization algorithms.

There is a recent surge in interest for imitation learning, with large human video-game and robotic manipulation datasets being used to train agents on very complex tasks. While deep neuroevolution has recently been shown to match the performance of gradient-based techniques on various reinforcement learning problems, the application of deep neuroevolution techniques to imitation learning remains relatively unexplored. In this work, we propose to explore whether deep neuroevolution can be used for behaviour imitation on popular simulation environments. We introduce a simple co-evolutionary adversarial generation framework, and evaluate its capabilities by evolving standard deep recurrent networks to imitate state-of-the-art pre-trained agents on 8 OpenAI Gym state-based control tasks. Across all tasks, we find the final elite actor agents capable of achieving scores as high as those obtained by the pre-trained agents, all the while closely following their score trajectories. Our results suggest that neuroevolution could be a valuable addition to deep learning techniques to produce accurate emulation of behavioural agents. We believe that the generality and simplicity of our approach opens avenues for imitating increasingly complex behaviours in increasingly complex settings, e.g. human behaviour in real-world settings. We provide our source code, model checkpoints and results at github.com/MaximilienLC/gane/.

In recent years, machine learning has become increasingly important in daily life. One of the most popular machine learning models used in many applications is an Artificial Neural Network (ANN). While in applications such as automatic speech recognition there is sufficient knowledge about the expected behavior for each input to use supervised learning, other applications like robot control define only an overall target so that the expected output for a given input can be ambiguous, making supervised learning inapplicable. Therefore, Topology and Weight Evolving ANN (TWEANN) has been developed in the past to evolve ANN topologies and connection weights. However, challenges of TWEANN are the design of genetic recombination and the exploration of huge search spaces for suitable solutions induced in particular by large-scale problems which can lead to impractical runtimes.

To address the aforementioned issues, this paper proposes a novel evolutionary framework to evolve ensemble learners as specialized ANNs in a divide-and-conquer manner. Specifically, genetic recombination is heavily orchestrated for ANN combinations to effectively find suitable solutions in the search space restricted by ensemble methods. Experiments on various benchmark problems for solving control tasks show that the proposed framework clearly outperforms existing TWEANN algorithms.

We tackle the problem of open-ended learning by introducing a method that simultaneously evolves agents while also evolving increasingly challenging environments. Unlike previous open-ended approaches that optimize agents using a fixed neural network topology, we hypothesize that generalization can be improved by allowing agents' controllers to become more complex as they encounter more difficult environments. Our method, Augmentative Topology EPOET (ATEP), extends the Enhanced Paired Open-Ended Trailblazer (EPOET) algorithm by allowing agents to evolve their own neural network structures over time, adding complexity and capacity as necessary. Our empirical results demonstrate that ATEP produces general agents capable of solving more environments than fixed-topology baselines. We also investigate mechanisms for transferring agents between environments and find that a species-based approach further improves the performance and generalization of agents.

Crossover between neural networks is considered disruptive due to the strong functional dependency between connection weights. We propose a modularity-based linkage model at the weight level to preserve functionally dependent communities (building blocks) in neural networks during mixing. A proximity matrix is built by estimating the dependency between weights, then a community detection algorithm maximizing modularity is run on the graph described by such matrix. The resulting communities/groups of parameters are considered to be mutually independent and used as crossover masks in an optimal mixing EA. A variant is tested with an operator that neutralizes the permutation problem of neural networks to a degree. Experiments were performed on 8 and 10-bit parity problems as the intrinsic hierarchical nature of the dependencies in these problems are challenging to learn. The results show that our algorithm finds better, more functionally dependent linkage which leads to more successful crossover and better performance.

In this paper, we address the question of how to evolve neural networks for semi-supervised problems. We introduce neuroevolutionary approaches that exploit unlabeled instances by using neuron coverage metrics computed on the neural network architecture encoded by each candidate solution. In our neuroevolutionary approach, we define fitness functions that combine classification accuracy computed on labeled examples and neuron coverage metrics evaluated using unlabeled examples. Our results show that the use of neuron coverage metrics helps neuroevolution to become less sensitive to the scarcity of labeled data, and can lead in some cases to a more robust generalization of the learned classifiers.

Memristive Reservoir Computing (MRC) is a promising computing architecture for time series tasks, but lacks explainability, leading to unreliable predictions. To address this issue, we propose an evolutionary framework to explain the time series predictions of MRC systems. Our proposed approach attributes the feature importance of the time series via an evolutionary approach to explain the predictions. Our experiments show that our approach successfully identified the most influential factors, demonstrating the effectiveness of our design and its superiority in terms of explanation compared to state-of-the-art methods.

This paper proposes a neural architecture search space using ResNet as a framework, with search objectives including parameters for convolution, pooling, fully connected layers, and connectivity of the residual network. In addition to recognition accuracy, this paper uses the loss value on the validation set as a secondary objective for optimization. The experimental results demonstrate that the search space of this paper together with the optimisation approach can find competitive network architectures on the MNIST, Fashion-MNIST and CIFAR100 datasets.

This paper presents a neural architecture search method based on Transformer architecture, searching cross multihead attention computation ways for different number of encoder and decoder combinations. In order to search for neural network structures with better translation results, we considered perplexity as an auxiliary evaluation metric for the algorithm in addition to BLEU scores and iteratively improved each individual neural network within the population by a multi-objective genetic algorithm. Experimental results show that the neural network structures searched by the algorithm outperform all the baseline models, and that the introduction of the auxiliary evaluation metric can find better models than considering only the BLEU score as an evaluation metric.

Neuroevolution is a promising area of research that combines evolutionary algorithms and neural networks. A popular subclass of neuroevolutionary methods, called evolution strategies, rely on dense noise perturbations to mutate networks, which can be sample inefficient and challenging for large models with millions of parameters. We introduce an approach to alleviating this problem by decomposing dense mutations into low-dimensional subspaces. Restricting mutations in this way can significantly reduce variance as networks can handle stronger perturbations while maintaining performance. This approach is uniquely effective for the task of fine tuning pre-trained models, which is an increasingly valuable area of research as networks continue to scale in size and open source models become more widely available. We conduct an exploration of sparse mutation decompositions on the difficult ImageNet dataset, where we see small generalization improvements with only a single evolutionary generation across a wide variety of deep neural network architectures.

A prevalent limitation of optimizing over a single objective is that it can be misguided, becoming trapped in local optimum. This can be rectified by Quality-Diversity (QD) algorithms, where a population of high-quality and diverse solutions to a problem is preferred. Most conventional QD approaches, for example, MAP-Elites, explicitly manage a behavioral archive where solutions are broken down into predefined niches. In this work, we show that a diverse population of solutions can be found without the limitation of needing an archive or defining the range of behaviors in advance. Instead, we break down solutions into independently evolving species and use unsupervised skill discovery to learn diverse, high-performing solutions. We show that this can be done through gradient-based mutations that take on an information theoretic perspective of jointly maximizing mutual information and performance. We propose Diverse Quality Species (DQS) as an alternative to archive-based QD algorithms. We evaluate it over several simulated robotic environments and show that it can learn a diverse set of solutions from varying species. Furthermore, our results show that DQS is more sample-efficient and performant when compared to other QD algorithms. Relevant code and hyper-parameters are available at: https://github.com/rwickman/NEAT_RL

Recent work in deep learning has shown that neural networks can be pruned before training to achieve similar or even better results than training the full network. However, existing pruning methods are limited and do not necessarily yield optimal solutions. In this work, we show that perturbing the network by re-initializing the pruned weights and re-pruning can improve performance. We propose to iteratively re-initialize and re-prune using a hill climbing (1 + 1) evolution strategy. We examine the cause of these improvements and show that this method can consistently improve the subnetwork without increasing its size, pointing to a potential new application of evolutionary computing in deep learning.

The process of automatically extracting informative high-level features from skin cancer images is enhanced by integrating well-developed feature descriptors into learning algorithms. This paper develops a new genetic programming-based feature learning approach to automatically select and combine six well-developed descriptors to extract high-level features for skin cancer image classification. The new approach can automatically learn various global features for image classification. The experimental results show that the new approach achieves significantly better classification performance than the baseline approach and six commonly used feature descriptors on two real-world skin image datasets.

Buses are important for public transportation and beneficial for the environment. However, diesel buses are significant polluters emitting greenhouse gases and particulates. Consequently, with the advent of electric vehicles there has been a drive to transition to electric buses. Key to this transition is to optimise electric bus fleets to reduce distance travelled whilst maintaining service levels. This is complex due to the added constraint of the limited range of electric buses. This paper considers the use of a Sequence-based Selection Hyper Heuristic (SSHH) method to solve this problem. Moreover, an adaptive SSHH (A-SSHH) technique is introduced which significantly improves upon SSHH. Indeed, bus fleet non-service distances and sizes are reduced by as much as 10% using A-SSHH over SSHH. Comparing with an optimised diesel bus fleet electric buses reduce carbon dioxide emissions by over 60% and importantly for fleet operators, energy costs are similarly reduced.

This paper introduces a novel method of selecting the most significant filters in deep neural networks. We performed model simplification via pruning with Genetic Algorithm (GA) for trained deep networks. Pure GA has a weakness of local tuning and slow convergence, so it is not easy to produce good results for problems with large problem space such as ours. We present new ideas that overcome some of GA's weaknesses. These include efficient local optimization, as well as reducing the time of evaluation which occupies most of the running time. Additional time was saved by restricting the filters to preserve using the GLCM (Gray-Level Co-occurrence Matrix) to determine the usefulness of the filters. Ultimately, the saved time was used to perform more iterations, providing the opportunity to further optimize the network. The experimental result showed more than 95% of reduction in forward convolution computation with negligible performance degradation.

Evolutionary algorithms have been successfully applied to attack Physically Unclonable Functions (PUFs). CMA-ES is recognized as the most powerful option for a type of attack called the reliability attack. In this paper, we take a step back and systematically evaluate several metaheuristics for the challenge-response pair-based attack on strong PUFs. Our results confirm that CMA-ES has the best performance, but we note several other algorithms with similar performance while having smaller computational costs.

The recent COVID-19 pandemic highlighted a need for tools to help policy-makers make informed decisions on what policies to implement in order to reduce the impact of the pandemic. Several tools have previously been developed to model how non-pharmaceutical interventions (NPIs), such as social distancing, affect the rate of growth of a disease within a population. Much of the focus of the modelling effort have been on projections of health factors, relating them to the NPIs, with only few works addressing the health-economy trade-off. However, there is a particular gap in illustrations of real data-driven solutions in this area. In this paper, we proposed a purely data-driven framework where we modelled health and economic impacts with Bayesian and Recurrent Neural Network (RNN) models respectively, and used NSGA-II to identify policy stringencies over a three-week period. We demonstrate that this framework can produce a range of solutions trading off between health and economy projections based on real data, that may be used by policymakers to reach an informed decision.

The global COVID-19 pandemic has demonstrated the urgent need for diagnostic tools that can be both readily applied and dynamically calibrated by non-specialists, in terms of a sensitivity/specificity tradeoff that complies with relevant healthcare policies and procedures. This article describes the design and deployment of a novel machine learning algorithm, Structural Machine Learning (SML), that combines memetic grammar-guided program synthesis with self-supervised learning in order to learn effectively from small data sets while remaining relatively resistant to overfitting. SML is used to construct a signal processing pipeline for audio time-series, which then serves as the diagnostic mechanism for a wide-spectrum, infrasound-to-ultrasound e-stethoscope. In blind trials supervised by a third party, SML is shown to be superior to Deep Learning approaches in terms of the area under the ROC curve, while allowing for transparent interpretation of the decision-making process.

We present a collaboration between decision trees and an evolutionary algorithm inspired by Smart "Predict then Optimize" framework. In this work, we analyze the requirements for designing an evolutionary algorithm to solve complex combinatorial problem which can change over the time. We study the effect of changing the parameters of the objective function and how we can adapt the evolutionary algorithm to efficiently tackle new conditions of the problem. To predict the parameters of the objective function we use a decision tree. We evaluate our collaborative schema using instances for the shortest path problem and compare it with recently published work that uses complete techniques, obtaining encouraging results.

Cardiopulmonary resuscitation (CPR) is critical to the prevention of death from cardiac arrest. Smartwatches can help first responders perform CPR correctly by collecting real-time acceleration data to determine compression rate and depth. We present an approach for a smartwatch application that uses motion data from the inertial sensors and an evolutionary algorithm ((μ + λ)-ES) to compute compression depth and frequency and provide corrective feedback. The application was optimized for out-of-hospital CPR and evaluated in a pilot study using a CPR training manikin as a reference system and an existing smartphone app for comparison.

Property price prediction is not only of great importance for home-buyers but also vital for economic studies. The common approach in price prediction is analysing historical market prices and relevant economic data by a predictive model, such as ARIMA model, linear regression, and artificial neural networks. Regardless of the model, a successful prediction using this approach relies on an abundant amount of data, e.g. more than one million property transactions over the last few decades. However, such a large data set might not be readily available, and also expensive to obtain. Hence we propose evolutionary generative Generative Adversarial Networks (GAN), to learn the distribution of these transaction data and generate samples to enrich the data set. This generated data set can help achieve better prediction. In our experiments, we compare not only the performance of several GAN varieties including evolutionary GAN (E-GAN) and knowledge distillation evolutionary GAN (KDE-GAN), but also the differences in prediction results before and after using GAN enriched data set. Our study shows that evolutionary GAN can improve prediction performance without requiring a large amount of data. In addition, evolution does provide extra benefits to the GAN process and enhances its value not only in methodological advancement but also in commercial potential.

Complex adversarial operations typically involve the allocation of finite resources to meet a set of objectives over a number of phases. This poses a challenge for AI-based strategy discovery. A strategy for one phase cannot be developed in isolation as the resources available in any one phase are dependent on the outcome of previous phases. Our proposed solution is to combine an evolutionary algorithm search with human-guided evaluation. The approach uses simulation-based fitness evaluation, where a human operator can view the fittest solution after every set number of generations. The operator can 'lock in' strategies for particular phases, and 'suggest' alternative strategies to guide further evolution. Key to our approach is a representation encoding that allows relative proportions of resources to be represented where actual levels may not be known a priori. We evaluate our solution on a three-phase scenario of a real-time strategy game and compare the effectiveness of strategies that were purely human-devised, purely evolved, and those resulting from the human-evolution collaboration. The collaborative approach shows promising results in being able to find an optimum solution earlier.

In creative design, where aesthetics play a crucial role in determining the quality of outcomes, there are often multiple worthwhile possibilities, rather than a single "best" design. This challenge is compounded in the use of computational generative systems, where the sheer number of potential outcomes can be overwhelming. This paper introduces a method that combines evolutionary optimisation with AI-based image classification to perform quality-diversity search, allowing for the creative exploration of complex design spaces. The process begins by randomly sampling the genotype space, followed by mapping the generated phenotypes to a reduced representation of the solution space, as well as evaluating them based on their visual characteristics. This results in an elite group of diverse outcomes that span the solution space. The elite is then progressively updated via sampling and simple mutation. We tested our method on a generative system that produces abstract drawings. The results demonstrate that the system can effectively evolve populations of phenotypes with high aesthetic value and greater visual diversity compared to traditional optimisation-focused evolutionary approaches.

We used evolutionary computation to approximate the nuclear binding energy B of stable nuclei with atomic mass number A = Z + N. Our symbolic regression approximation outperformed the Liquid Drop Model (LDM) for lighter nuclides, and is less complex. We also used evolutionary computation to obtain upper and lower bounds for the binding energy of 3535 experimentally found nuclei, the large majority of which are unstable. Our bounds can be well-approximated by an analytic continued fraction dependent only on A, which we found via a memetic algorithm. Our data-driven fitting with analytic continued fractions suggest the possibility of other nuclides between the obtained lower bound and known nuclides, up to A = 338 a value close to where the bounds meet.

Integrating renewable generation into the existing electricity grid to reduce Greenhouse Gas (GHG) emissions involves several challenges. These include, e.g., volatile generation and demand, and can be overcome by increasing flexibility in the grid. One possibility to provide this flexibility is the optimized scheduling of Distributed Energy Resources (DERs). Such a scheduling task requires a powerful optimization algorithm, such as Evolutionary Algorithms (EAs). However, EAs can produce poor solution quality w.r.t. solution time when solving complex and large scale scheduling tasks of DERs. Hence, in our work, a concept for improving the EA optimization process for scheduling DERs is presented and evaluated. In this concept, Machine Learning (ML) algorithms learn from already found solutions to predict the optimization quality in advance. By this, the computational effort of the EA is directed to particularly difficult areas of the search space. This is achieved by dynamic interpretation and consequent interval length assignment of the solutions proposed by the EA. We evaluate our approach by comparing two experiments and show that our novel concept leads to a significant increase of the evaluated fitness by up to 9.4%.

We introduce a novel black box optimization method, which we term Polynomial-Model-Based Optimization (PMBO). The main idea of this algorithm originates from Bayesian Optimization (BO) [16], however, instead of inferring a stochastic process, a polynomial surrogate of the objective function is fitted and exploited in the regions where the objective is expected to minimize. We compare PMBO with state-of-the-art optimization algorithms for common test functions and a real-world optimization problem. The results demonstrate PMBO to be capable of inferring the inherent structure of the objective function, resulting in its efficiency. This suggests that PMBO might be the pivotal choice for the optimization of highly structured real-world problems.

This paper presents an interactive genetic algorithm (IGA) approach for video digest suggestion. The goal of the approach is to personalize video digest, which is personalized summary of video, by using a method with less fatigue. This approach utilizes the process called Preferred Diversity-based Interactive Genetic Algorithm (PD-IGA), which incorporates the preference shot method to swiftly consider user preferences in the optimization process. The use of diversity preserving sampling is also included to prevent early convergence. In order to validate the performance of the PD-IGA process in the proposed approach, a simulation experiment using human model was performed on video data of varying lengths. The results of these experiments showed that the proposed method generates higher quality video digests compared to traditional IGA algorithms. The personalized video digest system using this approach was able to produce high-quality video digest according to the user's personalized purpose.

Efficient charging of electric vehicles (EVs) on highways is important for ensuring e-mobility because of the comparably limited range of EVs and the potentially very long charging times during longer trips. For reducing the carbon footprint of EVs, matching demand with availability of renewable energy matters, i.e., the latter should be used when available. Hence, we opt for dynamic 'anytime' optimization of the allocation of EVs to charging sites preferably at time slots where renewable energy is predicted to be available, while taking into account charging properties of batteries as well. This paper outlines a genetic algorithm approach for this optimization task, which takes these objectives into account as well as charging station availability and the number of yet unscheduled EVs. Our algorithm integrates with Eclipse SUMO (Simulation of Urban MObility) for simulating the real-world environment. The proposed algorithm operates on a real highway network (the one in Austria) and offers efficient and sustainable solutions for reducing the environmental impact of EVs.

Robot swarms have already demonstrated their ability to accomplish complex missions collectively while solely relying on individual behaviours. The inherent resilience and scalability properties of such systems make them highly attractive for space applications, and thus sees a growing interest, including from the NASA and ESA. In this article we propose the Orbital Formation Algorithm (OFA) to address formations of autonomous spacecraft with the aim of surveying asteroids. The objective is to spread evenly the swarm members around the orbiting body to maximise its coverage, while minimising propellant consumption. We introduce a set of parameters for the swarm formation problem and optimise them using a genetic algorithm to obtain general optimal solutions for each case study, comprising swarms of 2, 3, 5, and 10 satellites. Moreover, we propose an alternative method to obtain optimal parameters individually for each satellite using a light-weight simulated annealing algorithm to be run onboard. Results from simulations show that the OFA performs well on the 400 scenarios analysed and that the onboard optimisation approach is more accurate than the general solutions, although it uses computing resources from each satellite.

Robustness is a desired quality in many real-world engineered systems. The p-median problem is an optimization process in which a set of facilities must be found to minimize the average distance between each individual in a given population and the nearest facility. By introducing perturbations drawn from a specified distribution during evolution, we simulate the effect of natural disasters or other catastrophes on the placement of facilities. We use a non-dominated multi-objective procedure to select facilities with high fitness and robustness. We show that facilities evolved in this way are similarly fit and more robust than optimal solutions evolved without perturbation. Importantly, evolved facility layouts are much less susceptible to large catastrophic failures that are of the greatest concern in the placement of public infrastructure.

Green cloud computing, an emerging computing paradigm in IT industry, is about providing efficient utilization of cloud's resources with minimal impact on the environment. The virtual machine placement has a considerable impact on a data center's energy and resource utilisation. The assignment of Virtual Machines (VMs) to Physical Machines (PMs) is an NP-hard problem to be solved using approximate algorithms at a reasonable computing time. In this paper, an energy-aware based algorithm is proposed for virtual machine placement. Our aim is to reduce the energy consumption and CO2 emission under a set of constraints. The performance and the efficiency of the proposed approach is tested on a cloud computing simulation toolkit.

This paper presents the integration of machine learning and image analysis techniques into a material science experimental workflow. The aim is to optimise the properties of an Aluminium Scandium Nitride thin film through the manipulation of experimental input parameters. This is formulated as an optimisation problem, were the search space consists in the set of experimental input parameters used during the film's synthesis. The solution's fitness is obtained through the analysis of Scanning-Electron-Microscopy images and corresponds to the surface defect density over a film. An optimum solution to this problem is defined as the set of input parameters that consistently produces a film with no measurable surface defects. The search space is a black box with possibly more than one optimum and the limited amount of experiments that can be undertaken make efficient exploration challenging. It is shown that classification can be used to reduce the problem's search space by identifying areas of infeasibility. Using nested cross-validation, tree-based classifiers emerge as the most accurate, and importantly, interpretable algorithms for this task. Subsequently, Particle Swarm Optimisation is used to find optimal solutions to the surface defect minimisation problem. Preliminary experimental results show a significant decrease in defect density average achieved.

This paper proposes a novel meta-learning approach to optimize a robust portfolio ensemble. The method uses a deep generative model to generate diverse and high-quality sub-portfolios combined to form the ensemble portfolio. The generative model consists of a convolutional layer, a stateful LSTM module, and a dense network. During training, the model takes a randomly sampled batch of Gaussian noise and outputs a population of solutions, which are then evaluated using the objective function of the problem. The weights of the model are updated using a gradient-based optimizer. The convolutional layer transforms the noise into a desired distribution in latent space, while the LSTM module adds dependence between generations. The dense network decodes the population of solutions. The proposed method balances maximizing the performance of the sub-portfolios with minimizing their maximum correlation, resulting in a robust ensemble portfolio against systematic shocks. The approach was effective in experiments where stochastic rewards were present. Moreover, the results (Fig. 1) demonstrated that the ensemble portfolio obtained by taking the average of the generated sub-portfolio weights was robust and generalized well. The proposed method can be applied to problems where diversity is desired among co-optimized solutions for a robust ensemble. The source-codes and the dataset are in the supplementary material.

Search-Based Software Testing (SBST) has drawn a lot of interests as a powerful approach for automated test data generation. One major limitation of search-based methods is that they may get stuck in local optima and become inefficient if the fitness function does not provide any direction toward a test target, particularly when dealing with hard branch targets (e.g., nested predicates). Recent research has focused on enhancing the fitness function by taking branch hardness into account in order to direct the evolutionary process. However, either the characteristics of constraints (e.g., their involved variables' domain) are not taken into account or the difficulty level of a branch is separately studied. In this paper, we aim to address the test data generation with a focus on hard branches by proposing a novel fitness function based on nested constraints (i.e., including the target constraint and those that impact its coverage) and the domain sizes of their variables. The empirical study promises efficiency and effectiveness for the new fitness function. Our proposed approach outperforms its counterparts significantly, particularly for the branches that are difficult to be covered.

The processing of quantum information is defined by quantum circuits. For applications on current quantum devices, these are usually parameterized, i.e., they contain operations with variable parameters. The design of such quantum circuits and aggregated higher-level quantum operators is a challenging task which requires significant knowledge in quantum information theory, provided a polynomial-sized solution can be found analytically at all. Moreover, finding an accurate solution with low computational cost represents a significant trade-off, particularly for the current generation of quantum computers. To tackle these challenges, we propose a multi-objective genetic programming approach---hybridized with a numerical parameter optimizer---to automate the synthesis of parameterized quantum operators. To demonstrate the benefits of the proposed approach, it is applied to a quantum circuit of a hybrid quantum-classical algorithm, and then compared to an analytical solution as well as a non-hybrid version. The results show that, compared to the non-hybrid version, our method produces more diverse solutions and more accurate quantum operators which even reach the quality of the analytical baseline.

Using MAGPIE (Machine Automated General Performance Improvement via Evolution of software) we show genetic improvement GI can reduce the cache load of existing computer programs. Cache miss reduction is tested on two industrial open source C programs (Google's Open Location Code OLC and Uber's Hexagonal Hierarchical Spatial Index H3) and two C++ 2D photograph image processing tasks, counting pixels and OpenCV's SEEDS segmentation algorithm. Magpie's patches functionally generalise. In one case they reduce data misses on the highest performance L1 cache by 47%.

Experienced programmers use editing scripts to effectively modify selected lines and columns in a file or a set of files according to a desired editing transformation. For many non-programmers, it is, however, out of their skill sets to develop such scripts. We propose a software tool that significantly simplifies this task. The user is asked to create a snippet of the file before and after the desired edits (input and output example). The proposed tool uses these examples to evolve an editing script which is then executed on all lines of the input files to perform the expected transformation. We developed a simple programming language for file edits and a genetic programming-based system capable of evolving scripts in this language. For typical source files in which some data has to be deleted, added, or modified, the proposed system can evolve a valid script performing desired transformations in order of seconds or minutes.

The component-based view for metaheuristic research promotes the identification of structural components of metaheuristics and metaheuristic-algorithms for analysis. In this study, we propose a method for measuring similarity between metaheuristic-algorithms. The method is based on a modified version of a signal flow representation of metaheuristic-algorithms that is aligned with the component-based view. The method takes any two metaheuristic-algorithms and decomposes them into their heuristic components whilst taking note of the order of execution of the heuristics. Features of the heuristics are then extracted, and finally a feature-based similarity calculation, that also considers the position of the heuristics, is performed to obtain an overall similarity score between the two metaheuristic-algorithms. The method incorporates more structural information in the similarity calculation than previous component-wise similarity measures and can be extended to cover a comprehensive set of metaheuristic components.

A main focus in the theory of Particle Swarm Optimization (PSO) was the convergence of the particles where various frameworks and assumptions have been adopted which lead to a variety of outcomes differing in their relevance as a predictor of the performance of the algorithm. We discuss here the interesting phenomenon that the study of the stochastic dynamics of the particles provides a limit case, while the average dynamics yields a different limit. We can specify differences between the best particle and other particles in the swarm which has an effect on the performance of the algorithm and was not considered in previous approaches. In addition to benchmark results, also the swarm entropy confirms this formulation of the stability properties of PSO. This framework enables us to describe the time scales of excursions of particles away from the best location found so far, which indicates the diversity of locations in the search space discovered so far by the particles.

This paper proposes a general method for the visualization fitness landscapes. The method transforms the original fitness landscape to a 3D visualized network from the perspective of the optimization algorithms. This method can visualize the fitness landscapes of continuous problems of different dimensions, combinatorial problems and even the mixed integer problems. Experiments show that the proposed method can maintain most of the critical properties of problems, such as modality, ruggedness and neutrality.

Co-evolutionary algorithms have found several applications in game-theoretic applications and optimisation problems with an adversary, particularly where the strategy space is discrete and exponentially large, and where classical game-theoretic methods fail. However, the application of co-evolutionary algorithms is difficult because they often display pathological behaviour, such as cyclic behaviour and evolutionary forgetting. These challenges have prevented the broad application of co-evolutionary algorithms.

We derive, via rigorous mathematical methods, bounds on the expected time of a simple co-evolutionary algorithm until it discovers a Maximin-solution on the discrete Bilinear problem. Despite the intransitive nature of the problem leading to a cyclic behaviour of the algorithm, we prove that the algorithm obtains the Maximin-solution in expected O(n^1.5) time. However, the algorithm quickly forgets the Maximin-solution and moves away from it. Along the way, we present new mathematical tools to compute the expected time for co-evolutionary algorithms to obtain a Maximin-solution. We are confident that these tools can help further advance runtime analysis in both co-evolutionary and evolutionary algorithms.

While it is mathematically proven that the (μ + 1) GA optimizes Jump_k efficiently for low crossover probabilities, theory research still struggles with the analysis of crossover-based optimization for high crossover probabilities on this key test function. Research in this area has improved our understanding of crossover in general, in particular regarding the emergence of diversity, the crucial ingredient for successful optimization with genetic algorithms.

In this paper we study the optimizing process after the (μ + 1) GAhas reached the plateau of Jump_k. We are interested in (a) the stationary distribution of the algorithm on the plateau (when ignoring the optimum) and (b) the dynamics of the stationary distribution. We experimentally show that the (μ+1) GA achieves 10% complementary pairs if μ = 10 · k, unless n is very small. Regarding the dynamics, we show samples of how bit positions gain and lose individuals with a 0 at that position.

Lexicase selection is a state of the art parent selection technique for problems that can be broken down into multiple selection criteria. Prior work has found cases where lexicase selection fails to find a Pareto-optimal solution due to the presence of multiple objectives that contradict each other. In other cases, however, lexicase selection has performed well despite the presence of such objectives. Here, we develop theory identifying circumstances under which lexicase selection will or will not fail to find a Pareto-optimal solution. Ultimately, we find that lexicase selection can perform well under many circumstances involving contradictory objectives, but that there are limits to the parameter spaces where high performance is possible. Additionally, we show empirical evidence that epsilon-lexicase selection is much more strongly impacted by contradictory objectives. Our results inform parameter value decisions under lexicase selection and decisions about which problems to use lexicase selection for.

Bayesian Optimization(BO) is a popular sample-efficient computational strategy to solve expensive black-box optimization problems. BO framework mainly consists of two parts: surrogate model and acquisition function. In practice, BO is usually built on a non-parametric probabilistic model called Gaussian Process(GP). Based on GP, various acquisition functions are defined by modulating different trade-offs in order to make suggestions for GP to make sample decisions. A great number of acquisition functions have been proposed over the years. More often than not, different implementations of BO vary in terms of the choice of acquisition functions, hence they lead to the difference in performance. However, there has yet to be a guideline for choosing an acquisition function in existing literature nor a thorough performance benchmark. In this paper, we aim to conduct a comprehensive empirical study on popular batched acquisition functions. We'll show the relative performance of these functions across a plethora of test problems to reveal consistent better performer giving certain conditions. The results will provide strong empirical evidence to some common beliefs about acquisition functions. And thus, we could draw a pragmatic guideline of choosing acquisition function for BO process.

New meta-heuristics are often neglected in terms of the methods used to describe them. Uninspired descriptions are given of the speed to the global minima and the number of local minima found, but little to describe the search characteristics that make it possible to do so. The lack of search behaviour descriptors results in a loss. Without discussing the tools used to make meta-heuristics efficient, we are unable to apply those same tools elsewhere. By using such descriptors, older meta-heuristics can be improved using new ideas, and new meta-heuristics can be continually iterated on. Without such a cycle, all meta-heuristics are destined to be shelved.

In order to address these concerns, the process of creating methods to describe meta-heuristic search behaviour is illustrated. Categories of interest within search behaviour are discussed. The categories named iterate on exploration and exploitation, such as the social dynamics and movement styles of an algorithm. The process of defining search characteristics is illustrated through four examples. These four characteristics are designed to reflect known traits of search behaviour, and are tested using well-known meta-heuristics. Guidance is given on how to collect data, and visualisation techniques are discussed.

Evaluating the fitness of individuals in the initial population of an evolutionary algorithm (EA) is usually straightforward and poses few theoretical problems. In asynchronous steady-state EAs (ASSEAs), however, the choice of initialization strategy can significantly alter the algorithm's long-term behavior. ASSEAs have long been recognized as an important alternative to parallel and distributed evolution, because unlike the more commonly used generational model, they avoid leaving processing resources idle while waiting for a generation boundary. In our work on ASSEAs, we have observed that colleagues' intuitions tend to differ about what a basic asynchronous initialization strategy should look like---but the implications of this choice have not been studied before. This paper analyzes the results of three competing initialization strategies that have appeared in prior literature---the immediate, until-finished, and extra strategies---and concludes that the immediate strategy in particular, which relies on maintaining a queue of jobs waiting to be evaluated, incurs a slow evolutionary feedback loop and should be used with caution. Queuing is a necessary part of scaling ASSEAs up to be resilient to node failures in large HPC environments, however---so this work suggests that further research is needed to understand how asynchronous initialization can be used most effectively for expensive optimization.

Existing research lacks studies on how state-of-the-art evolutionary multi-objective algorithms behave when dealing with problems that involve mixed-variable types. To address this gap, we examine how the popular SMS-EMOA performs on a class of problems that involve both continuous and discrete variables. More particularly, we study the algorithmic behavior on a family of mixed-integer (MI) bi-objective optimization problems of partially discretized convex quadratic models. We are considering search by means of a MI Evolution Strategy (ES), and aim to investigate the evolutionary mechanisms as they operate subject to scenarios of box-constrained decision variables. We also account for a white-box approach to solve the models, and qualitatively mention the relative performance of SMS-EMOA with respect to it. We discuss the ES operation within the SMS-EMOA on the current MI case-study, with a particular focus on the step-size adaptation and the success-rate of offspring generation over time. It is evident that progress is made in the initial stage of the optimization, whereas the process tends to stagnate later on. Moreover, for problems whose decision variables are loosely bounded, the step-sizes exhibit effective self-adaptation. We conclude by summarizing the challenges and opportunities when treating MI problems by ES-driven heuristics.

The Borg MOEA [8] is an optimization algorithm, designed to handle real-world problems of a multi objective and multimodal nature. In this report, we examine the effectiveness of Borg for solving optimization problems with only two objectives. To this end, we benchmark the performance of the algorithm on the bbob-biobj test suite via the COCO platform, comparing it to current state-of-the-art algorithms.

The study uses standard values for all the parameters but one, as retrieved from http://borgmoea.org/. The only parameter that varies between different problem instances is the ε parameter, a crucial scale tuning parameter. To adapt this parameter, we devised and applied a heuristic.

We find that the algorithm performs respectably, although it does not surpass the current state-of-the-art algorithms for any of the problem instances examined, and particularly loses performance on problems with a high-dimensional search space. Additionally, we observed that our heuristic for tuning the ε-parameter results in significant performance improvements compared to using a fixed value for ε.

This paper benchmarks the canonical version of Whale Optimization Algorithm (WOA) with two recent adaptations: "Enhanced WOA (E-WOA)" and "modified Symbiotic organism search - Differential Evolution - WOA (m-SDWOA)" with the desire to research the improvement potential of the WOA. We also used Black-Box Differential Evolution with normalization of the scaling factor (BBDE-N), included in the data set of the bbob test suite, as a baseline to compare the performance. The results show that E-WOA and m-SDWOA improve significantly efficiency and the percentage of problems hit by WOA.

In this paper we introduce modified versions of CMA-ES with the objective to help to prove convergence of CMA-ES. In order to ensure that the modifications do not alter the performances of the algorithm too much, we benchmark variants of the algorithm derived from them on problems of the bbob test suite. We observe that the main performances losses are observed on ill-conditioned problems, which is probably due to the absence of cumulation in the adaptation of the covariance matrix. However, the versions of CMA-ES presented in this paper have globally similar performances to the original CMA-ES.

Collaborative optimization (CO) is an architecture within the multi-disciplinary design optimization (MDO) paradigm that partitions a constrained optimization problem into system and subsystem problems, with couplings between them. Multi-objective CO has multiple objectives at the system level and inequality constraints at the subsystem level. Whilst CO is an established technique, there are currently no scalable, constrained benchmark problems for multi-objective CO. In this study, we extend recent methods for generating scalable MDO benchmarks to propose a new benchmark test suite for multi-objective CO that is scalable in disciplines and variables, called 'CO-ZDT'. We show that overly-constraining the number of generations in each iteration of the system-level optimizer leads to poor consistency constraint satisfaction. Increasing the number of subsystems in each of the problems leads to increasing system-level constraint violation. In problems with two subsystems, we find that convergence to the global Pareto front is very sensitive to the complexity of the landscape of the original non-decomposed problem. As the number of subsystems increases, convergence issues are encountered even for the simpler problem landscapes.

In recent years, there has been significant progress in the development of new DIRECT-type algorithms for black-box optimization problems. In this paper, we evaluate three well-performing DIRECT-type methods from a recent extensive numerical study on the BBOB noiseless testbed in dimensions 2, 3, 5, 10, and 20. We discuss the strengths and weaknesses of these algorithms on different classes of functions and provide a comparison with the original DIRECT method, as well as with three other well-established methods: RL-SHADE, L-BFGS-B, and SLSQP.

We compare the performances of one implementation of CMA-ES (pycma version 3.3.0) for optimizing functions with both continuous and integer variables. The implementation incorporates a lower bound on the variance along the integer coordinates to keep the optimization from stalling. This benchmark will serve as a baseline for further works on pycma. Results show substantial improvement since the last benchmarked version of pycma. Also this implementation is competitive with other mixed integer algorithms.

We consider optimisation in the context of the need to apply an optimiser to a continual stream of instances from one or more domains, and consider how such a system might 'keep learning': by drawing on past experience to improve performance and learning how to both predict and react to instance and/or domain drift.

Designing machine learning models involves determining not only the network architecture, but also non-architectural elements such as training hyperparameters. Further confounding this problem, different architectures and datasets will perform more optimally with different hyperparameters. This problem is exacerbated for neuroevolution (NE) and neural architecture search (NAS) algorithms, which can generate and train architectures with a wide variety of architectures in order to find optimal architectures. In such algorithms, if hyperparameters are fixed, then suboptimal architectures can be found as they will be biased towards the fixed parameters. This paper evaluates the use of the simplex hyperparameter optimization (SHO) method, which allows co-evolution of hyperparameters over the course of a NE algorithm, allowing the NE algorithm to simultaneously optimize both network architectures and hyperparameters. SHO has been previously shown to be able to optimize hyperparameters for convolutional neural networks using traditional stochastic gradient descent with Nesterov momentum, and this work extends on this to evaluate SHO for evolving recurrent neural networks with additional modern weight optimizers such as RMSProp and Adam. Results show that incorporating SHO into the neuroevolution process not only enables finding better performing architectures but also faster convergence to optimal architectures across all datasets and optimization methods tested.

In the field of Explainable AI, population-based search metaheuristics are of growing interest as they become more widely used in critical applications. The ability to relate key information regarding algorithm behaviour and drivers of solution quality to an end-user is vital. This paper investigates a novel method of explanatory feature extraction based on analysis of the search trajectory and compares the results to those of sensitivity analysis using "Weighted Ranked Biased Overlap". We apply these techniques to search trajectories generated by a genetic algorithm as it solves a staff rostering problem. We show that there is a significant overlap between these two explainability methods when identifying subsets of rostered workers whose allocations are responsible for large portions of fitness change in an optimization run. Both methods identify similar patterns in sensitivity, but our method also draws out additional information. As the search progresses, the techniques reveal how individual workers increase or decrease in the influence on the overall rostering solution's quality. Our method also helps identify workers with a lower impact on overall solution fitness and at what stage in the search these individuals can be considered highly flexible in their roster assignment.

A very common and powerful step in the design process of a new learning algorithm or extensions and improvements of existing algorithms is the benchmarking of models produced by said algorithm. We propose a paradigm shift in the benchmarking of explainable if-then-rule-based models like the ones generated by Learning Classifier Systems or Fuzzy Rule-based Systems. The principled method we suggest is based on synthetic data sets being sampled from randomly generated but known processes that have the same overall structure as the models that are being benchmarked (i. e. each process consists of a set of components each of which corresponds to one if-then rule) which is up-to-date not available among the many synthetic data generators. This approach has several benefits over other benchmarks and we expect that it will lead to fresh insights into how algorithms producing such explainable models work and can be improved. We demonstrate its usage by benchmarking the effects of different rule representations in the XCSF classifier system.

We consider and discuss the ways in which search landscapes might contribute to the future of explainable artificial intelligence (XAI), and vice versa. Landscapes are typically used to gain insight into algorithm search dynamics on optimisation problems; as such, it could be said that they explain algorithms and that they are a natural bridge between XAI and evolutionary computation. Despite this, there is very little existing literature which utilises landscapes for XAI, or which applies XAI techniques to landscape analysis. This position paper reviews the existing works, discusses possible future avenues, and advocates for increased research effort in this area.

The complexity of the transmission network expansion planning (TNEP) problem has been increasing due to the new constraints given by renewable generation uncertainty, new market rules and players, and the continuous demand growth with the introduction of electric vehicles and energy storage systems. The problem consists of finding the optimal number and location of new transmission lines to support the demand, which can be extremely hard to optimize. As such, in this paper, we focus on metaheuristic optimization to solve a TENP problem proposed in testbed 2 of the 2023 competition on evolutionary computation in the energy domain. The 87-bus north-northeast Brazilian transmission system is considered for the case study, and different DE metaheuristics are used for the optimization process. Results show that the HyDE algorithm presents the overall best performance when compared to other DE strategies. HyDE is able to achieve the overall lowest costs with a reduction of around 67% compared to L-SHADE.

This paper proposes a novel multi-objective decision making benchmark problem. The problem addresses the need in the multi-objective decision making realm for an easy to construct, scalable benchmark problem in the vain of the DTLZ, ZTD, and WFG problems. The problem is inspired by a real-world decision making problem that pilots face in the cockpit. The new problem is an amalgamation of two well-established problems within the literature, the DTLZ and multiplexer problems. The problem additionally makes use of the main concepts and ideas from Robust Decision Making and Multi-scenario Multi-objective Robust Decision Making, especially as these problems enable decision making problems to be somewhat converted into an optimization task. The problem is showcased here and is solved initially using a modified multi-objective optimization variant of a Learning Classifier System, which shows superior results when compared to a random agent.

The problem of recommending a group itinerary is considered to be NP-hard and can be defined as an optimization problem. The goal is to recommend the best series of points of interest (POIs) to a group of people who are visiting a destination based on their preferences and past experiences. This paper proposes an evolutionary approach based on cultural algorithms to address this problem. Our objective is to maximize the group's satisfaction by recommending an itinerary comprised of the optimal series of visiting POIs, considering the interests of all members, total travel time, and visit duration while minimizing the travel costs within their assigned budget. The proposed algorithm uses historical and normative knowledge to create a belief space used later to guide the search direction and decision-making. The belief space is a knowledge repository that tracks the evolution of decisions during the search process. We evaluated the performance of the proposed algorithm on a set of real-world datasets and compared that with state-of-the-art approaches. We also conducted non-parametric tests to analyze the results. Compared with other algorithms, the proposed approach is capable of recommending efficient and satisfactory itineraries to groups with diverse interests.

Multiobjective optimization problems have multiple conflicting objective functions to be optimized simultaneously. They have many Pareto optimal solutions representing different trade-offs, and a decision-maker needs to find the most preferred one. Although most multiobjective evolutionary algorithms approximate the Pareto optimal set, their variants incorporate preference information to focus on a subset of solutions that interest the decision-maker. Interactive methods allow decision-makers to provide preference information iteratively during the solution process, enabling them to learn about available solutions and their preferences' feasibility. Nevertheless, most interactive evolutionary methods do not sufficiently support the decision-maker in finding the most preferred solution and may be cognitively too demanding.

We propose a framework for designing and implementing interactive evolutionary methods. It contains algorithmic components based on similarities in the structure of existing preference-based evolutionary algorithms and decision-makers' needs during interaction. The components can be combined in different ways to create new interactive methods or to instantiate the existing ones. We show an example of the implementation of the proposed framework composed of three elements: a graphical user interface, a database, and a set of algorithmic components. The resulting software can be utilized to develop new methods and increase their usability in real-world applications.

Many libraries of open-source implementations of multiobjective optimization problems (MOPs) and evolutionary algorithms (MOEAs) have been developed in recent years. These libraries enable researchers to solve their MOPs using diverse MOEAs. Some libraries also implement interactive MOEAs, which enable decision-makers (experts in the domain of the MOP) to provide their preferences and guide the optimization process toward their region of interest. These libraries also provide access to visualization methods and benchmarking tools. However, they do not currently implement a database to store and utilize the data generated while running MOEAs.

We propose the creation of SIVA DB, a database designed to be easily incorporated into existing libraries as a modular addition. SIVA DB provides a standard way to archive an MOEA's population and the metadata associated with each population member. Such metadata can include, e.g., the parameters and state of the MOEA and the preferences the decision-maker gives (in the case of interactive MOEAs). The database can store data from multiple runs of any number of MOEAs, and even data from different MOPs. SIVA DB provides easy access to the contained data to analyze the optimization process or create efficient MOEAs. We demonstrate the latter in this paper with experiments.

A Sequence-based Selection Hyper-Heuristic (SSHH) utilises a hidden Markov model (HMM) to generate sequences of low-level heuristics to apply to a given problem. The HMM represents learnt probabilistic relationships in transitioning from one heuristic to the next for generating good sequences. However, a single HMM will only represent one learnt behaviour pattern which may not be ideal. Furthermore, using a single HMM to generate sequences is sequential in manner but most processors are parallel in nature. Consequently, this paper proposes that the effectiveness and speed of SSHH can be improved by using multiple SSHH, an ensemble. These will be able to operate in parallel exploiting multi-core processor resources facilitating faster optimisation. Two methods of parallel ensemble SSHH are investigated, sharing the best found solution amongst SSHH instantiations or combining HMM information between SSHH models. The effectiveness of the methods are assessed using a real-world electric bus scheduling optimisation problem. Sharing best found solutions between ensembles of SSHH models that have differing sequence behaviours significantly improved upon sequential SSHH results with much lower run-times.

This paper introduces our auto-ML system, MLStar, which uses genetic programming to create scikit-learn and Keras-based Python programs to perform supervised learning. MLStar leverages our own genetic programming system (GPStar4) and provides a greater search space compared to traditional genetic programming frameworks.

Key elements that enable MLStar's performance include representing individuals as Directed Acyclic Graphs (DAGs), a rich type system to shape the kinds of graphs generated, novel genetic operators which work on the DAG structure, and advanced hyperparameter tuning via the Optuna hyperparameter optimization framework. MLStar also offers multiobjective fitnesses and a variety of complex population types.

We show that MLStar performs favorably to several other auto-ML frameworks on benchmark tests. We also demonstrate that MLStar is capable of competitive solutions even when running with computationally expensive features disabled.

With a recently defined AutoGCOP framework, the design of local search algorithms can be defined as the composition of the basic elementary algorithmic components. These compositions into the best algorithms thus retain useful knowledge of effective algorithm design. This paper investigates effective algorithmic compositions with sequential rule mining techniques to discover valuable knowledge in algorithm design. With the collected effective algorithmic compositions, sequential rules of basic algorithmic components are extracted and further analysed to automatically compose basic algorithmic components within the general AutoGCOP framework to develop new effective meta-heuristics. The sequential rules present superior performance in composing the basic algorithmic components for solving the benchmark vehicle routing problems with time window constraints, demonstrating its effectiveness in designing new algorithms automatically.

The parameter adaptation is one of the main problems in many evolutionary algorithms, including differential evolution. Instead of manual development of new methods, a hyper-heuristic approach can be used, where an algorithm is applied to search for parameter adaptation scheme. In this study the symbolic regression genetic programming is applied to design parameter adaptation method for differential evolution algorithm with two populations L-NTADE. Due to algorithmic scheme different from popular L-SHADE, the L-NTADE may require specific adaptation mechanisms. Each solution in genetic programming consists of three trees, which generate scaling factor values based on current resource, success rate and current values in the memory cells, containing scaling factor and crossover rate. The training is performed on a set of 30 benchmark functions from CEC 2017 competition on numerical optimization, and at every generation of genetic programming new problem dimension, computational resource, optima location and rotation matrices are generated for every test function. The testing is performed on two benchmarks, CEC 2017 and CEC/GECCO 2022. The results comparison shows that the automatically designed parameter adaptation heuristics are capable of outperforming the success-history adaptation in many cases, including high-dimensional problems and problems with different computational resource.

Automatic algorithm configuration procedures aim at supporting the design and application of optimization algorithms by providing specialized tools to automatically adjust their parameters to use the available computational resources effectively. The irace configurator is a state-of-the-art method implementing an iterated racing procedure that, in its current implementation, allows parallel executions of the target algorithm. Parallel evaluation is crucial for the efficient use of computational resources, reducing the wall-clock time that the configuration process needs to find a good configuration. In this work, we propose an alternative to irace that performs a single race instead of iterative races. The continuously racing configurator (crace) evaluates, removes and generates new configurations asynchronously, granting a high level of flexibility regarding the configuration process when compared to the previous iterative scheme. In this paper, we provide a general description of the crace configuration procedure and perform initial exploratory experiments on five configuration scenarios. These experiments focus on evaluating the effect of the minimum number of configurations required to be involved in the race and the number of parallel evaluations. The first results are encouraging, showing that crace can be a competitive procedure on the scenarios evaluated.

Defeating dangerous families of malware like polymorphic and metamorphic malware have become well studied due to their increased attacks on computer systems and network. Traditional Machine Learning (ML) models have been used in detecting this malware, however they are often not resistant to future attacks. In this paper, an Evolutionary based Generative Adversarial Network (GAN) inspired approach is proposed as a step towards defeating metamorphic malware. This method uses an Evolutionary Algorithm as a generator to create malware that are designed to fool a detector, a deep learning model into classifying them as benign. We employ a personal information stealing malware family (Dougalek) as a testbed, selected based on its malicious payload and evaluate the samples generated based on their adversarial accuracy, measured based on the number of Antivirus (AV) engines they are able to fool and their ability to fool a set of ML detectors (k-Nearest Neighbors algorithm, Support Vector Machine, Decision Trees, and Multi-Layer Perceptron). The results show that the adversarial samples are on average able to fool 63% of the AV engines and the ML detectors are susceptible to the new mutants achieving an accuracy between 60%-77%.

Artificial Neural Networks are vulnerable to adversarial examples, malicious inputs that aim to subvert neural networks' outputs. Generative Adversarial Networks (GANs) are generative models capable of generating data that follows the training data distribution. We explore the hypothesis of using the latent space of the trained GAN to find adversarial examples. We test the adversarial examples on external classifiers trained on the same training data. Thus, we propose a framework for Generating adversariaL exAmpleS through latent Space Exploration (GLASSE). A Genetic Algorithm evolves latent vectors as individuals and uses a trained GAN to generate examples to maximise a target activation value of the discriminator network. After the evolutionary process, an external classifier trained on the same dataset evaluates whether it is adversarial. The results indicate that we can optimise the objective and find adversarial examples. We tested the generated examples with models from the adversarial learning literature, showing that 82% on average of the generated examples resulted in successful attacks. We show a t-SNE analysis of the examples, showcasing that generated adversarial examples are blended in the cluster of each belonging class and visually similar to the training dataset examples, showcasing the viability of the proposed approach.

This article presents an explicit multiobjective evolutionary approach for synthetic human face image generation, exploring the latent space of generative adversarial networks. The approach considers the similarity to a target image and the race attribute. The evolutionary search explores the real-coded latent space of Style-GAN3 and applies DeepFace for similarity and race evaluation. Realistic images are generated, properly exploring the search space and the Pareto front of the problem. The generated images pose a challenge to the automatic detection system in DeepFace. Results are applicable to enhance the security of face recognition systems.

Recently, different neuroevolutionary approaches have been proposed to enhance the architecture and hyperparameters of generative neural models. Many of these approaches have to train the candidate architectures before their evaluation. The gradient descent algorithm used to do so is often overlooked in the evolutionary procedure, despite being a critical aspect of the training. In this paper, we investigate the role played by the gradient-based optimizer chosen to train a generative adversarial network when its architecture has been obtained using neuroevolution. We focus on 2D Gaussian mixture approximation problem and evaluate the effect of a set of representative gradient-based techniques on the quality of the performance of the GANs. Our results show that the particular choice of the gradient optimizer can be as relevant as the appropriate selection of the architecture.

Hierarchic Memetic Strategy (HMS) is a stochastic global optimizer designed to tackle highly multimodal problems. It consists of parallel running optimization methods organized in a tree hierarchy. Depending on the task, different algorithms can be utilized on each of the levels. In this paper, we incorporate into HMS's structure a mechanism for choosing its configuration based on information gathered by a set of Exploratory Landscape Analysis (ELA) methods and hyperparametric optimization. We compared the performance of such configured HMS with a portfolio of proven state-of-the-art algorithms on the suite of black-box optimization functions. The results of this work show the efficacy of HMS and provide a set of default parameters evaluated for algorithms users. The use of ELA methods to select the configuration of a composite algorithm extends their standard use as part of an algorithm selector and provides insight into the relationship between exploration and exploitation for different types of fitness functions.

Particle Swarm Optimization (PSO) has received increasing attention from researchers due to its fast convergence ability. This paper proposes a new improvement in Multi-objective Particle Swarm Optimization based on Pareto dominance. This research aims to develop an efficient exploration and exploitation algorithm with faster convergence using a limited iterative process. Researchers have already proved that popular EA algorithms can converge faster as well as provide efficient exploration. However, there are some shortcomings in establishing success in smaller iterative outcomes after maintaining both population diversity as well as best optimal solutions. Therefore, our proposed approach incorporates the hybrid evolutionary computation process with PSO to address multi-objective problems. The results indicate that the proposed method is highly competitive and is able to approximate the Pareto Front where other algorithms struggle.

This research paper aims to explore the possibilities of parameterization of state-of-the-art adaptive mechanisms incorporated in the self-organizing migrating algorithm (SOMA). This algorithm has gained renewed interest from the research community while the algorithm's internal dynamics, mechanisms, and dependencies of the functionality on parameter settings have not been thoroughly examined using a data-driven approach. Our extensive test workflow has yielded valuable insights into the performance of the SOMA and its sensitivity to parameter settings that affect the migration of individuals. Important findings were also obtained regarding the appropriate parameter settings required for more complex techniques such as clustering, organization, and population restart. The research also highlighted the influence of different modern adaptation techniques and the suitability of combining different modern adaptation mechanisms, leading to the modular design of different configurations. The simulation experiments conducted provided new insights that could be useful for further research, especially with the rapid development in automatic configurators of meta-heuristic algorithms, modular concepts of algorithms, and their performance prediction.

In this paper, we investigate the potential of using Large Language Models (LLMs) such as GPT-4 to generate novel hybrid swarm intelligence optimization algorithms. We use the LLM to identify and decompose six well-performing swarm algorithms for continuous optimization: Particle Swarm Optimization (PSO), Cuckoo Search (CS), Artificial Bee Colony (ABC), Grey Wolf Optimizer (GWO), Self-Organizing Migrating Algorithm (SOMA), and Whale Optimization Algorithm (WOA). We leverage GPT-4 to propose a hybrid algorithm that combines the strengths of these techniques for two distinct use-case scenarios. Our focus is on the process itself and various challenges that emerge during the use of GPT-4 to fulfill a series of set tasks. Furthermore, we discuss the potential impact of LLM-generated algorithms in the metaheuristics domain and explore future research directions.

This paper presents an experimental study that compares four adaptive variants of the self-organizing migrating algorithm (SOMA). Each variant uses three different constraint handling methods for the optimization of a time delay system model. The paper emphasizes the importance of metaheuristic algorithms in control engineering for time-delayed systems to develop more effective and efficient control strategies and precise model identifications.

The study includes a detailed description of the selected variants of the SOMA and the adaptive mechanisms used. A complex workflow of experiments is described, and the results and discussion are presented. The experimental results highlight the effectiveness of the SOMA variants with specific constraint handling methods for time delay system optimization.

Overall, this study contributes to the understanding of the challenges and advantages of using metaheuristic algorithms in control engineering for time delay systems. The results provide valuable insights into the performance of the SOMA variants and can help guide the selection of appropriate constraint handling methods and the adaptive mechanisms of metaheuristics.

This study presents an application that offers an interactive representation of the learning cycle of a learning classifier system (LCS), a rule-based machine learning technique. The research approach utilized a combination of human-computer interaction requirements, design heuristics, and user-centred engineering to scaffold the development of a graphical user interface for an LCS. The evaluation of the application by LCS experts and a novice yielded encouraging results, demonstrating its ability to convey the LCS mechanics to the users. In addition, the experts validated the correctness of the learning cycle. The study's contribution is two-fold: it presents an innovative approach to making the user understand the underlying mechanics of LCS and validates the effectiveness of the developed application. Furthermore, this work sets the stage for future research towards design revision and to further develop the application to accommodate different LCS models and custom data.

Rule Compaction of populations of Learning Classifier Systems (LCS) has always been a topic of interest to get more insights into the discovered underlying patterns from the data or to remove useless classifiers from the populations. However, these techniques have neither been used nor adapted to Anticipatory Learning Classifier Systems (ALCS). ALCS differ from other LCS in that they build models of their environments from which decision policies to solve their learning tasks are learned. We thus propose CRACS (Compaction of Rules in Anticipatory Classifier Systems), a compaction algorithm for ALCS that aims to reduce the size of their environmental models without impairing these models or the ability of these systems to solve their tasks. CRACS relies on filters applied to classifiers and subsumption principles. The capabilities of our compaction algorithm have been studied with three different ALCS on a thorough benchmark of 23 mazes of various levels of environmental uncertainty. The results show that CRACS reduces the size of populations of classifiers while the learned models of environments and the ability of ALCS to solve their tasks are preserved.

In 'time-to-event' problems, such as survival analysis in biomedical research, investigators seek to identify the factors that impact/predict not only whether an event occurred (e.g. death), but also when. Further, in the domain of kidney transplantation, there has been recent interest in determining whether higher resolution features, i.e. amino-acid mismatches (AA-MMs) between donors and recipients, can improve risk stratification for transplant failure and identify subsets of AA-MM positions for evaluating risk in future transplants. Motivated by these problems, the FIBERS algorithm was previously developed, which applies a genetic algorithm to learn a population of feature bins (i.e. OR-rules) for predicting right-censored time-to-event survival outcomes. Here, instances are categorized as high-risk if an AA-MM is present for any AA-MM position specified in a given rule, and low-risk if not. In the present study we focus further on the FIBERS algorithm; (1) implementing it as an accessible scikit-learn compatible machine learning package, and (2) applying a variety of simulated right-censored survival datasets to validate scikit-FIBERS efficacy and examine the limitations of its performance to guide ongoing development. We present preliminary results demonstrating the efficacy of scikit-FIBERS, and the limitations of both the algorithm and survival data simulator to guide future work.

Scheduling problems are one of the most important combinatorial optimization problems. Solving them is often a tedious and lengthy task. We introduce PyScheduling, a scheduling framework designed to help users model and solve scheduling problems. The framework considers more than 130 scheduling problems and allows solving them with a few lines of code. The framework incorporates several machine environments, constraints and objective functions. Moreover, the framework provides the user with a number of features that help visualize, analyze and use the proposed solutions. Thanks to its architecture, the framework is easily extensible, allowing researchers and advanced practitioners to adapt it to their use cases by adding machine environments, constraints, objective functions, solution approaches or any other desired feature with minimal effort. PyScheduling is therefore designed for several categories of users including researchers, students and practitioners. PyScheduling is open source and available on https://github.com/scheduling-cc/pyscheduling.

Exploiting knowledge about the structure of a problem can greatly benefit the efficiency and scalability of an Evolutionary Algorithm (EA). Model-Based EAs (MBEAs) are capable of doing this by explicitly modeling the problem structure. The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is among the state-of-the-art of MBEAs due to its use of a linkage model and the optimal mixing variation operator. Especially in a Gray-Box Optimization (GBO) setting that allows for partial evaluations, i.e., the relatively efficient evaluation of a partial modification of a solution, GOMEA is known to excel. Such GBO settings are known to exist in various real-world applications to which GOMEA has successfully been applied. In this work, we introduce the GOMEA library, making existing GOMEA code in C++ accessible through Python, which serves as a centralized way of maintaining and distributing code of GOMEA for various optimization domains. Moreover, it allows for the straightforward definition of BBO as well as GBO fitness functions within Python, which are called from the C++ optimization code for each required (partial) evaluation. We describe the structure of the GOMEA library and how it can be used, and we show its performance in both GBO and Black-Box Optimization (BBO).

In many applications of evolutionary algorithms the computational cost of applying operators and storing populations is comparable to the cost of fitness evaluation. Furthermore, by knowing what exactly has changed in an individual by an operator, it is possible to recompute fitness value much more efficiently than from scratch. The associated time and memory improvements have been available for simple evolutionary algorithms, few specific genetic algorithms and in the context of gray-box optimization, but not for all algorithms, and the main reason is that it is difficult to achieve in algorithms using large arbitrarily structured populations.

This paper makes a first step towards improving this situation. We show that storing the population as a minimum spanning tree, where vertices correspond to individuals but only contain meta-information about them, and edges store structural differences, or patches, between the individuals, is a viable alternative to the straightforward implementation. Our experiments suggest that significant, even asymptotic, improvements --- including execution of crossover operators! --- can be achieved in terms of both memory usage and computational costs.

This work presents the Maelstrom framework for strong-typed tree GP. Maelstrom is a Python library designed to facilitate rapid prototyping and exploration of weak-typed tree GP, strong-typed tree GP, island model, and coevolution with flexibility that enables support for accelerator frameworks such as JAX. The architecture and features of Maelstrom are discussed alongside several example applications employing Gym environments and an accelerated version of predator-prey.

We introduce moptipy, a toolbox for implementing, experimenting with, and applying optimization algorithms. It features mechanisms for executing fully reproducible experiments. Our seeding procedure for random number generators makes our experiments deterministic. Our system creates self-documenting log files that store the algorithm setup, the system configuration, the random seed, the final solutions, and the progress of the optimization algorithm over time. The parallelization and distribution of experiments works on most operating systems and requires no additional synchronization, inter-process-communication, or libraries. moptipy supports both single- and multi-objective optimization with arbitrary search spaces. Time measurements and computational budgets can be based both on wall clock time and objective function evaluations. moptipy is also an educational platform with comprehensive documentation and an accompanying free electronic book introducing the basic concepts of metaheuristics, discussing the implemented algorithms, and showing their performance on basis of actual experimental results.

We present MAHF, a Rust framework for the modular construction and subsequent evaluation of evolutionary algorithms, but also any other metaheuristic framework, including non-population-based and constructive approaches. We achieve high modularity and flexibility by splitting algorithms into components with a uniform interface and allowing communication through a shared blackboard. Nevertheless, MAHF is aimed at being easy to use and adapt to the specific purposes of different practitioners. To this end, this paper focuses on providing a general description of the design of MAHF before illustrating its application with a variety of different use cases, ranging from simple extension of the set of implemented components and the subsequent construction of algorithms not present within the framework to hybridization approaches, which are often difficult to realize in specialized software frameworks. By providing these comprehensive examples, we aim to encourage others to utilize MAHF for their needs, evaluate its effectiveness, and improve upon its application.

GPStar4 is a flexible workbench for experimenting with population algorithms. It is a framework that defines a genetic cycle, with inflection points for implementing an algorithm's specific behaviors; it also provides a variety of implementations for these inflection points. A user of the system can select from the provided implementations and customize the places where alternative behavior is desired, or even create their own implementations. Components interact through a context mechanism that enables both mutable and immutable information sharing, type checking, computed defaults and event listeners.

Interesting predefined components included in GPStar4 are implementations for classical tree-based expression structures; acyclic multigraphs with named ports, type systems for flat, hierarchical and attribute types, recursively defined populations using both subpopulation and build-from-parts semantics, and numeric and multi-objective fitnesses. Key enabling technologies for this flexibility include context mechanisms, choosers, and a variety of caches.

GPStar4 can be run as an API library for other applications, as a command-line application, or as a stand-alone application with its own GUI.

Our study aims to compare the effects of direct mutation and graph-based mutation on representations of music domain. We focus on short tunes from the Irish folk tradition, represented as integer sequences, and use a graph-based representation based on Pathway Assembly (a directed acyclic graph) and the Sequitur algorithm. We define multiple mutation operators to work directly on the sequences or on the graphs, hypothesizing that graph-based mutations will tend to preserve the pattern used per tune, while direct mutation of sequences will tend to destroy patterns, resulting in new generated tunes that are more complex. We perform experiments on a corpus of tunes and apply the mutation operators many times consecutively to analyze their effects.

The automatic construction of an image filter is a difficult task for which many recent machine-learning methods have been proposed. Cartesian Genetic Programming (CGP) has been effectively used in image-processing tasks by evolving programs with a function set specialized for computer vision. Although standard CGP is able to construct understandable image filter programs, we hypothesize that explicitly using a mechanism to control the size of the generated filter programs would help reduce the size of the final solution while keeping comparable efficacy on a given task. It is indeed central to keep the graph size as contained as possible as it improves our ability to understand them and explain their inner functioning. In this work, we use the Lexicase selection as the mechanism to control the size of the programs during the evolutionary process, by allowing CGP to evolve solutions based on performance and on the size of such solutions. We extend Kartezio, a Cartesian Genetic Programming for computer vision tasks, to generate our programs. We found in our preliminary experiment that CGP with Lexicase selection is able to achieve similar performance to the standard CGP while keeping the size of the solutions smaller.

Formula 1 is a highly competitive and ever-evolving sport, with teams constantly searching for ways to gain an edge over the competition. In order to meet this challenge, we propose a custom Genetic Algorithm that can simulate a race strategy given data from free practices and compute an optimal strategy for a specific circuit. The algorithm takes into account a variety of factors that can affect race performance, including weather conditions as well as tire choice, pit-stops, fuel weight, and tire wear. By simulating and computing multiple race strategies, the algorithm provides valuable insights and can help make informed strategic decisions, in order to optimize the performance on the track. The algorithm has been evaluated on both a video-game simulation and with real data on tire consumption provided by the tire manufacturer Pirelli. With the help of the race strategy engineers from Pirelli, we have been able to prove the real applicability of the proposed algorithm.

While offering a cost-competitive option and system support benefits. However, its intermittent nature and the stochastic grid environment pose operational and technical challenges, increasing complexity for a secure and reliable grid operation and planning. In this regard, the need for harvesting potential energy from an intermittent source without compromising the actual grid infrastructure and operation is crucial. Thus, this work proposes a novel probabilistic framework for PV hosting capacity assessment and enhancement considering the voltage and current probabilistic restrictions as well as PV inverter power factor control. This work uses the Particle Swarm Optimization (PSO) algorithm that embeds the probabilistic approach based on Monte Carlo simulation (MCS). A sensitivity analysis of the PSO parameters was performed to achieve the best possible results. Tests in the IEEE 33-bus radial distribution system with four PV units with power factor control yield a more realistic PV hosting capacity.

Same-day delivery problems (SDDPs) deal with efficient near-term satisfaction of dynamic and stochastic customer demand. During the day, a sequence of decisions has to be performed related to delivery route construction and driver dispatching. Formulated as Markov decision process, the goal is to find a policy that maximizes the expected reward over a specified class of instances. In the literature, scalar reward functions have dominated so far, by either considering only one objective or several objectives transformed into one using a weighted sum or lexicographic order. In this work, we consider a vector-valued reward with two dimensions, tardiness and costs, for a real-world inspired SDDP with tight soft deadlines within hours. The goal is to evolve non-dominated sets of policies for typical days with a certain stochastic load pattern and geographical order distribution in advance and let the decision maker select which one to deploy. We achieve this utilizing classical multi-objective genetic algorithms, NSGA-II and SPEA2, and by parallelization of the computationally intensive policy evaluations. Based on the experimental results, we observe that accepting a small amount of additional tardiness initially leads to a substantial return in terms of reduced mean delivery times per order.

Fluidized beds are widely used in various industrial applications that require efficient mixing, heat and mass transfer between gas and solid particles. This paper explores the relationship between input parameters of inlet gas velocity into the fluidized bed, by varying the amplitude and the frequency of the velocity, and the objective outputs, such as the total number of bubbles per unit time and the average bubble size in a fluidized bed, using CFD-DEM simulations. The goal of the paper is to define a multi-objective optimization problem and provide an insight into the landscape in the search space. Since the CFD-DEM simulation of a fluidized bed requires a significant computational effort, this landscape analysis is aimed to give an overview and a ground truth for further research in this area.

Real-world optimization problems often require time-consuming fitness evaluations because of simulations or complex numerical calculations. A hybrid rocket engine (HRE) design problem is a time-consuming real-world application. HRE is a rocket engine that stores either the oxidizer or fuel in solid form and the other in liquid form. A surrogate model can reduce the number of expensive objective/constraint function calculations for such expensive optimization problems by searching for promising solutions. This study applies a new surrogate-assisted constraint-handling evolutionary algorithm, CHDE+ELDR, to solve the HRE design problem with fewer evaluations. CHDE+ELDR combines CHDE, a constraint-handling differential evolution, and ELDR, a pairwise ranking surrogate model. We conduct an experiment on the HRE design problem with limited evaluations and compare CHDE+ELDR with CHDE without a surrogate model. The experimental results show that CHDE+ELDR can consistently obtain high-quality HRE designs with fewer evaluations than simple CHDE.

This paper verified the effects of a supervised multi-objective optimization algorithm (SMOA) efficiently upconverting the Pareto front representation by utilizing known solutions on a real-world multi-objective building facility control optimization problem. Also, several sampling methods for evaluating promising candidate solutions in SMOA were proposed and compared. Evolutionary variations, such as crossover and mutation involving randomness, are not preferred in practical scenarios, particularly when the objective functions are computationally expensive. In order to suppress obtaining inferior solutions, SMOA constructs the Pareto front and Pareto set estimation models using known solutions, samples promising candidate solutions, and evaluates them. It was reported that SMOA could efficiently generate well-distributed solutions that upconvert the Pareto front representation compared to evolutionary variations with limited solution evaluations in artificial test problems. This paper focuses on the real-world building facility control problem with 15 known solutions, and results show that SMOA can efficiently improve the Pareto front representation compared to evolutionary variations. Also, results show that crowding distance-based one-time sampling considering the distribution of the known solutions achieved the best Pareto front approximation performance in the sampling methods compared in this paper.

This paper proposes an evolutionary algorithm integrating genetic programming and a decomposition-based multi-objective algorithm to address a crude oil refinery scheduling problem. Four objectives are modelled, two related to maintaining the crude oil processing level, and the other two aim to keep the refinery operations as smooth as possible. The proposed method, Constrained-Decomposition of Quantum-Inspired Grammar-based Linear Genetic Programming (C-DQIGLGP), uses Quantum-Inspired Grammar-based Linear Genetic Programming (QIGLGP), replacing its hierarchical approach for the objectives with a multi-objective decomposition-based one. To achieve this goal, QIGLGP was profoundly modified regarding sorting individuals, updating the population, and applying the evolutionary operator. Individuals whose objective values related to processing level are under a predefined limit are better ranked. We compare the results of C-DQIGLGP for five scenarios from a real refinery to those obtained by QIGLGP and Constrained Non-dominated Sort QIGLGP (C-NSQIGLGP), from literature, demonstrating the better performance of C-DQIGLGP for all cases.

End users can benefit from automatic program synthesis in a variety of applications, many of which require the user to specify the program they would like to generate. Recent advances in genetic programming allow it to generate general purpose programs similar to those humans write, but require specifications in the form of extensive, labeled training data, a barrier to using it for user-driven synthesis. Here we describe the prototype of a human-driven genetic programming system that can be used to synthesize programs from scratch. In order to address the issue of extensive training data, we draw inspiration from counterexample-driven genetic programming, allowing the user to initially provide only a few training cases and asking the user to verify the correctness of potential solutions on automatically generated potential counterexample cases. We present anecdotal experiments showing that our prototype can solve a variety of easy program synthesis problems entirely based on user input.

We present a comprehensive survey on the topic of sound and music composition using interactive evolutionary computation (IEC). After explaining the fundamentals of IEC and computer music, we investigate the research subject from various aspects, including the presentation of sound and music in computer programming, IEC optimization algorithm studies, fitness function design, and interface design and evaluation methods in IEC. These subjects drive the theoretical study in this field. There are a variety of studies addressing IEC application-oriented studies, and we summarize the findings related to auditory and acoustic design with IEC. Knowledge discovery of auditory perception with IEC and IEC for auditory aid are two unique research subjects using IEC. Finally, we discuss potential research directions and subjects, including IEC for physiological and psychological research of auditory and the extension of IEC into the acoustic design of long-time music genres. IEC is not only a technique for optimization in auditory and acoustic design with human factors but also an implementation tool to achieve intelligent composition systems and creative art design with human-in-the-loop. It is a powerful tool to implement an artificial intelligence system with more considerations of human factors.

We consider the case of interactive multi-objective Bayesian optimization where decision maker (DM) preferences can be elicited by asking the DM to select the more preferred among pairs of observations. Assuming that there is a cost to evaluating a solution as well as to eliciting preferences, and given a total budget, we propose an acquisition function that, in each iteration, decides whether to evaluate another solution or to query the DM. Thus, the approach automatically chooses how often and when to interact with the DM. It furthermore decides which pair of observations is likely to be most informative when shown to the DM. We show empirically that the proposed criterion is not only able to pick suitable pairs of observations, but also automatically results in a sensible balance between optimization and querying the DM.

In this paper, we present a grammatical evolution-based framework to produce new scalarizing functions, which are known to have a significant impact on the performance of both decomposition-based multi-objective evolutionary algorithms (MOEAs) and indicator-based MOEAs which use R2. We perform two series of experiments using this framework. First, we produce many scalarizing functions using different benchmark problems to explore the behavior of the resulting functions according to the geometry of the problem adopted to generate them. Then, we perform a second round of experiments adopting two combinations of problems which yield better results in some test instances. We present the experimental validation of these new functions compared against the Achievement Scalarizing Function (ASF), which is known to provide a very good performance. For this comparative study, we adopt several benchmark problems and we are able to show that our proposal is able to generate new scalarizing functions that can outperform ASF in different problems.

The representation of individuals in Genetic Programming (GP) has a large impact on the evolutionary process. In this work, we investigate the evolutionary process of three Grammar-Guided GP (GGGP) methods, Context-Free Grammars GP (CFG-GP), Grammatical Evolution (GE) and Structured Grammatical Evolution (SGE), in the context of the complex, real-world problem of predicting the glucose level of people with diabetes two hours ahead of time. Our analysis differs from previous analyses by (1) comparing all three methods on a complex benchmark, (2) implementing the methods in the same framework, allowing a fairer comparison, and (3) analyzing the evolutionary process outside of performance. We conclude that representation choice is more impactful with a higher maximum depth, and that CFG-GP better explores the search space for deeper trees, achieving better results. Furthermore, we find that CFG-GP relies more on feature construction, whereas GE and SGE rely more on feature selection. Finally, we altered the GGGP methods in two ways: using ε-lexicase selection, which solved the overfitting problem of CFG-GP; and with a penalization of complex trees, to create more interpretable trees. Combining ε-lexicase selection with CFG-GP performed best.

Robust initialisation has shown to greatly improve the performance of genetic programming on a wide variety of tasks. Many of these have been adapted to work with grammatical evolution, with varying success. We are the first to examine the effectiveness of some of the most popular grammatical evolution initialisation techniques using structured grammatical evolution. Namely, we investigate sensible initialisation and probabilistic tree creation 2, as well as the standard initialisation procedure used in structured grammatical evolution, grow.

We examine their performance, as well as the diversity of solutions they create, on 7 well-known benchmarks. We observe that probabilistic tree creation 2 created the fittest initialisation populations on every benchmark considered. This did not result in overall better runs, however, and SGE runs with below average initialisation performance were seen to overcome their "bad start". The diversity of solutions, particularly fitness diversity, at the end of the run was lower for probabilistic tree creation 2 than for both sensible initialisation and grow.

Activation functions play a significant role in neural network design by enabling non-linearity. The choice of activation function was previously shown to influence the properties of the resulting loss landscape. Understanding the relationship between activation functions and loss landscape properties is important for neural architecture and training algorithm design. This study empirically investigates neural network loss landscapes associated with hyperbolic tangent, rectified linear unit, and exponential linear unit activation functions. Rectified linear unit is shown to yield the most convex loss landscape, and exponential linear unit is shown to yield the least flat loss landscape, and to exhibit superior generalisation performance. The presence of wide and narrow valleys in the loss landscape is established for all activation functions, and the narrow valleys are shown to correlate with saturated neurons and implicitly regularised network configurations.

Algorithms used to train neural networks (NNs) converge in valleylike parts of the loss landscape. The point of convergence is considered a flat minimum when the valley is wide, and a sharp minimum when the valley is narrow. It has been hypothesized that flat minima in wide valleys generalize better than sharp minima in narrow valleys, but this has not been shown to hold in general. Theoretical studies propose conflicting ideas about the relevance, shape, and definition of sharp and flat minima. This study proposes a method for sampling the neighborhood around local minima of NN error landscapes. Using this method, we define two metrics to quantify the sharpness of minima as well as a 2-dimensional visualization for approximating the structure of the basins of attraction. We then conduct experiments to verify or refute the correlation between the sharpness of a valley around a local minimum and the ability of the NN to generalize well at that minimum. Results provide no evidence to support this correlation.

In this paper, we consider the problem of finding perfectly balanced Boolean functions with high non-linearity values. Such functions have extensive applications in domains such as cryptography and error-correcting coding theory. We provide an approach for finding such functions by a local search method that exploits the structure of the underlying problem. Previous attempts in this vein typically focused on using the properties of the fitness landscape to guide the search. We opt for a different path in which we leverage the phenotype landscape (the mapping from genotypes to phenotypes) instead. In the context of the underlying problem, the phenotypes are represented by Walsh-Hadamard spectra of the candidate solutions (Boolean functions). We propose a novel selection criterion, under which the phenotypes are compared directly, and test whether its use increases the convergence speed (measured by the number of required spectra calculations) when compared to a competitive fitness function used in the literature. The results reveal promising convergence speed improvements for Boolean functions of sizes N = 6 to N = 9.

Fitness landscape analysis (FLA) refers to a set of techniques to characterise optimisation problems. This paper presents an FLA of three types of genetic programming (GP) benchmarks: parity, symbolic regression, and artificial ant. We applied a modern graph-based FLA tool called Local Optima Networks and several classical FLA metrics (fitness distance correlation, neutrality, and ruggedness measures) to study the tree-based GP search spaces. Our analysis shows that the search spaces for all problems contain many local optima and are highly deceptive. The parity problems are highly rugged and neutral. Conversely, the problems of symbolic regression are less rugged and neutral. Finally, the artificial ant problem is highly rugged but less neutral. Our results indicate that a mutation in deep nodes makes finding the global optimum difficult.

Real-world optimization problems frequently have constraints that define feasible and infeasible combinations of decision variables. Evolutionary algorithms do not inherently work with constraints, so they must be modified to include a suitable constraint handling technique (CHT) before they can be used to solve such problems. A range of different approaches to handling constraints have been used effectively with evolutionary algorithms, such as penalty-based, repair, feasibility rules, and bi-objective approaches. In this study we investigate different CHTs with an evolutionary algorithm on the 0/1 knapsack problem. We present results to show that performance complementarity exists between different CHTs on the knapsack problem. Landscape analysis is then used to characterize the search space of a large number of knapsack instances, and decision tree induction is used to derive rules for selecting the most appropriate CHT and switching it adaptively based on landscape features. We finally implement a landscape-aware CHT approach and show that it out-performs the constituent CHT approaches.

Compressed monotonic local optima networks (CMLONs) provide a powerful means to visualise the global structure of the fitness landscapes of optimisation problems as network graphs. Historically, they have been developed for discrete optimisation problems, but they have more recently been extended to continuous problems. However, experience is limited because they have only been applied to a few analytical problems and even fewer real-world problems. This work aims to address that gap by providing a systematic and comprehensive catalogue of CMLONs for the well-known black box optimisation benchmark functions. These are a set of continuous analytical functions with diverse properties. CMLONs are calculated for each of the twenty-four benchmark functions in three, five, eight, twelve, and twenty dimensions. Network metrics are also calculated for each of the CMLONs and dimensionality reduction used to classify and compare the functions. It was found that the CMLONs have diverse representations that are related to both the functions' properties and their dimensionality. Network metrics were important for multimodal functions in higher dimensional problems, where the CMLONs were too dense to visualise meaningfully. These results provide an extensive catalogue of CMLONs for a variety of continuous functions and provide a useful reference for real-world optimisation problems.

Fitness landscape analysis often relies on visual tools to provide insight to a search space, allowing for reasoning before optimisation. Currently, the dominant approach for visualisation is the local optima network, where the local structure around a potential global optimum is visualised using a network with the nodes as local minima and the edges as transitions between those minima through an optimiser. In this paper, we present an approach based on extrema graphs, originally used for isosurface extraction in volume visualisation, where transitions are captured between both maxima and minima embedded in two dimensions through dimensionality reduction techniques (multidimensional scaling in our prototype). These diagrams enable evolutionary computation practitioners to understand the entire search space by incorporating global information describing the spatial relationships between extrema. We demonstrate the approach on a number of continuous benchmark problems from the literature and highlight that the resulting visualisations enable the observation of known problem features, leading to the conclusion that extrema graphs are a suitable tool for extracting global information about problem landscapes.

University course timetabling is a well-known problem in combinatorial optimization. When using evolutionary algorithms to solve it as a many-objective problem, measures aimed at encouraging population diversity are commonly applied in the objective value space. Difficulties can arise when the search encounters plateau regions, caused by multiple designs evaluating to a common objective vector. To address this, we propose an enhanced diversity procedure that includes genotype crowding as an additional integrated selection criterion behind dominance and phenotype diversity. We also introduce a standard form encoding to handle solution equivalence and reduce metric entropy. Four metrics and a baseline are tested across problems from the International Timetabling Competition 2007 Track 3 benchmark, using a solver based on NSGA-III. Hyper-volume is the primary performance measure. We find that genotype Hamming distance performs best. This goes against our intuition that the use of metrics closer approximating the Levenshtein distance would lead to superior performance.

We consider statistical randomness in the construction of local optima networks (LONs) and conduct a preliminary and exploratory study into this. LONs capture a fitness landscape into network format: the nodes are local optima, and edges are heuristic search transitions between them. Problem instances from the benchmark quadratic assignment problem library are used in the analysis. LONs are constructed using an iterated local search (ILS) and several different random seeds. Metrics are computed from the networks and visualised to assess the effect of randomness. Algorithm performance models for ILS runtime are built using metrics of LONs constructed using different seeds and the results compared. The results show that some LON metrics seem consistent across seeds, while others vary substantially. Additionally, the quality of algorithm performance models using LON metrics as predictors can differ depending on randomness. Finally, LON metrics associated with separate seeds can lead to different algorithm configuration recommendations for the same instance.

This paper presents an analysis of the trends and behavior of Fitness Landscape Analysis (FLA) and corresponding algorithm performance features for instances of the Quadratic Assignment Problem (QAP) and the instance space between them. Given two QAPLIB instances, a transformation generates 30 intermediary instances, i.e. problem versions for further experimentation. For each problem version, we track algorithm performance of robust tabu search (RTS) and variable neighborhood search (VNS), as well as FLA measures obtained by various types of walks. Thus, we are able to analyze how these performances and measures change during the transformation. We observe that RTS dominates VNS in earlier problem versions, while VNS outperforms RTS in later problem versions. Overall, the transformation leads to a smooth traversal of the instance space, and both algorithm performance and FLA measures correlate with problem versions.

Spiking Neural Networks (SNNs) have attracted recent interest due to their energy efficiency and biological plausibility. However, the performance of SNNs still lags behind traditional Artificial Neural Networks (ANNs), as there is no consensus on the best learning algorithm for SNNs. Best-performing SNNs are based on ANN to SNN conversion or learning with spike-based backpropagation through surrogate gradients. The focus of recent research has been on developing and testing different learning strategies, with hand-tailored architectures and parameter tuning. Neuroevolution (NE), has proven successful as a way to automatically design ANNs and tune parameters, but its applications to SNNs are still at an early stage. DENSER is a NE framework for the automatic design and parametrization of ANNs, based on the principles of Genetic Algorithms (GA) and Structured Grammatical Evolution (SGE). In this paper, we propose SPENSER, a NE framework for SNN generation based on DENSER, for image classification on the MNIST and Fashion-MNIST datasets. SPENSER generates competitive performing networks with a test accuracy of 99.42% and 91.65% respectively.

Even the most efficient approaches to neural architecture search can be very computationally expensive, which leaves little room for inefficiencies. Unfortunately, evolutionary approaches to neural architecture search (NAS) - neuroevolution - often suffer from these inefficiencies due in part to their massive, intractable search spaces. In the past several years, differentiable approaches to neural architecture search have garnered significant attention for their efficiency and performance. In this work, we suggest an approach to create a hybrid algorithm: a neuroevolutionary metaheuristic which employs a local differentiable stochastic neural architecture search during the fitness evaluation step. Our preliminary results demonstrate that this approach is successful in selecting recurrent neural network memory cells.

Transfer Learning (TL) has been widely used in machine learning where the neuronal layers in a learned source Artificial Neural Network (ANN) are transferred to a target ANN so as to speed up the latter's learning. TL most often requires that the source and target domains are similar. However, its use in dissimilar domains as also in ANNs that use neuroevolution strategies has hardly been investigated. In this paper, we present a mechanism, suited for neuroevolution, that can identify specific neurons that need to be transferred. These Hot neurons from the source ANN, when transferred to the target ANN, helps in hastening the learning at the target. Simulations conducted using robots, clearly indicate that the mechanism is well suited for both similar and dissimilar tasks or environments.

This paper proposes EvoPrunerPool - an Evolutionary Pruner using Pruner Pool for Compressing Convolutional Neural Networks. EvoPrunerPool formulates filter pruning as a search problem for identifying the right set of pruners from a pool of off-the-shelf filter pruners and applying them in appropriate sequence to incrementally sparsify a given Convolutional Neural Network. The efficacy of EvoPrunerPool has been demonstrated on LeNet model using MNIST data as well as on VGG-19 deep model using CIFAR-10 data and its performance has been benchmarked against state-of-the-art model compression approaches. Experiments demonstrate a very competitive and effective performance of the proposed Evolutionary Pruner. Since EvoPrunerPool employs the native representation of a popular machine learning framework and filter pruners from a well-known AutoML toolkit the proposed approach is both extensible and generic. Consequently, a typical practitioner can use EvoPrunerPool without any in-depth understanding of filter pruning in specific and model compression in general.

The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific phenomena, is one of the key techniques at the forefront of recent advances. PINNs are typically trained using stochastic gradient descent methods, akin to their deep learning counterparts. However, analysis in this paper shows that PINNs' unique loss formulations lead to a high degree of complexity and ruggedness that may not be conducive for gradient descent. Unlike in standard deep learning, PINN training requires globally optimum parameter values that satisfy physical laws as closely as possible. Spurious local optimum, indicative of erroneous physics, must be avoided. Hence, neuroevolution algorithms, with their superior global search capacity, may be a better choice for PINNs relative to gradient descent methods. Here, we propose a set of five benchmark problems, with open-source codes, spanning diverse physical phenomena for novel neuroevolution algorithm development. Using this, we compare two neuroevolution algorithms against the commonly used stochastic gradient descent, and our baseline results support the claim that neuroevolution can surpass gradient descent, ensuring better physics compliance in the predicted outputs.

When using Quality Diversity (QD) optimization to solve hard exploration or deceptive search problems, we assume that diversity is extrinsically valuable. This means that diversity is important to help us reach an objective, but is not an objective in itself. Often, in these domains, practitioners benchmark their QD algorithms against single objective optimization frameworks. In this paper, we argue that the correct comparison should be made to multi-objective optimization frameworks. This is because single objective optimization frameworks rely on the aggregation of sub-objectives, which could result in decreased information that is crucial for maintaining diverse populations automatically. In order to facilitate a fair comparison between quality diversity and multi-objective optimization, we present a method that utilizes dimensionality reduction to automatically determine a set of behavioral descriptors for an individual, as well as a set of objectives for an individual to solve. Using the former, one can generate solutions using standard quality diversity optimization techniques, and using the latter, one can generate solutions using standard multi-objective optimization techniques. This allows for a level comparison between these two classes of algorithms, without requiring domain and algorithm specific modifications to facilitate a comparison.

While standard approaches to optimisation focus on producing a single high-performing solution, Quality-Diversity (QD) algorithms allow large diverse collections of such solutions to be found. If QD has proven promising across a large variety of domains, it still struggles when faced with uncertain domains, where quantification of performance and diversity are non-deterministic. Previous work in Uncertain Quality-Diversity (UQD) has proposed methods and metrics designed for such uncertain domains. In this paper, we propose a first set of benchmark tasks to analyse and estimate the performance of UQD algorithms. We identify the key uncertainty properties to easily define UQD benchmark tasks: the uncertainty location, the type of distribution and its parameters. By varying the nature of those key UQD components, we introduce a set of 8 easy-to-implement and lightweight tasks, split into 3 main categories. All our tasks build on the Redundant Arm: a common QD environment that is lightweight and easily replicable. Each one of these tasks highlights one specific limitation that arises when considering UQD domains. With this first benchmark, we hope to facilitate later advances in UQD.

This work introduces a new lightweight and massively parallelizable implementation of a Quality-Diversity (QD) task: the libfastsim maze. This QD task involves finding a collection of neural network controllers navigating a robot to diverse positions in a maze. The proposed implementation, called Kheperax, can be used as a benchmark task for standard QD algorithms, but also for Model-based, Unsupervised and Uncertain QD algorithms. It can automatically run and parallelize parameter evaluations on hardware accelerators, such as Graphical Processing Units (GPUs). When evaluating large batches of parameters, Kheperax is at least 4 times faster than the original libfastsim implementation. The source code is available online¹.

Multi-objective optimisation problems involve finding solutions with varying trade-offs between multiple and often conflicting objectives. Ising machines are physical devices that aim to find the absolute or approximate ground states of an Ising model. To apply Ising machines to multi-objective problems, a weighted sum objective function is used to convert multi-objective into single-objective problems. However, deriving scalarisation weights that archives evenly distributed solutions across the Pareto front is not trivial. Previous work has shown that adaptive weights based on dichotomic search, and one based on averages of previously explored weights can explore the Pareto front quicker than uniformly generated weights. However, these adaptive methods have only been applied to bi-objective problems in the past. In this work, we extend the adaptive method based on averages in two ways: (i) we extend the adaptive method of deriving scalarisation weights for problems with two or more objectives, and (ii) we use an alternative measure of distance to improve performance. We compare the proposed method with existing ones and show that it leads to the best performance on multi-objective Unconstrained Binary Quadratic Programming (mUBQP) instances with 3 and 4 objectives and that it is competitive with the best one for instances with 2 objectives.

Despite quantum computing is revealing an increasingly promising technology that has the potential to introduce a significant speed-up in many areas of computation, the number of problems that it can represent and solve is currently rather limited. Therefore, one of the current challenges faced by the quantum computing community is to broaden the class of problems that can be tackled. Among these problems, scheduling problems are a class of particularly interesting and hard combinatorial problems; in this paper, we present a novel solution for representing and solving the Flexible Open Shop Scheduling Problem (FOSSP) to optimality by minimizing the makespan. We firstly present a compact formulation of this problem as a Quadratic unconstrained binary optimization (QUBO), which can be used to solve this problem with a quantum annealer. Then, we proceed to the Quantum Approximate Optimization Algorithm (QAOA) problem formulation, thus producing both the cost and mix Hamiltonians related to the problem. From the Hamiltonians, we provide the complete description of the quantum circuit that can be used to tackle the FOSSP within the QAOA framework. This second approach can be used to solve the optimization problem with a general-purpose quantum gate-based hardware.

Reinforcement learning algorithms including AlphaZero are powerful artificial intelligence (AI) algorithms, but are known to be resource intensive and unable to train within a reasonable budget. Speeding up learning would be valuable to further expand application areas for real world problems. In this paper, we investigate two quantum computing methods to enhance AlphaZero, with the goal of speeding up training. We evaluate the results by playing the board game Othello, an adversarial multi-agent turn based game similar to the game Go. First, parameterized quantum circuits (PQC) have been shown to train hybrid quantum-classical reinforcement learning agents in standard benchmark environments. With this inspiration, we replace the classical neural network with a PQC quantum neural network (QNN) in the AlphaZero architecture. Second, tensor-network quantum circuits have been used to extract important features for convolutional neural networks (CNNs) in image classification tasks. Using this as inspiration, we use a tree tensor network (TTN) to extract features from the Othello game board, generating a new set of feature vectors for a classical neural network to estimate the policy and value. Results show both novel methods converge to master the game and achieve the same level of play compared to the classical AlphaZero agent.

The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum algorithm described as ansatzes that represent both the problem and the mixer Hamiltonians. Both are parameterizable unitary transformations executed on a quantum machine/simulator and whose parameters are iteratively optimized using a classical device to optimize the problem's expectation value. To do so, in each QAOA iteration, most of the literature uses a quantum machine/simulator to measure the QAOA outcomes. However, this poses a severe bottleneck considering that quantum machines are hardly constrained (e.g. long queuing, limited qubits, etc.), likewise, quantum simulation also induces exponentially-increasing memory usage when dealing with large problems requiring more qubits. These limitations make today's QAOA implementation impractical since it is hard to obtain good solutions with a reasonably-acceptable time/resources. Considering these facts, this work presents a new approach with two main contributions, including (I) removing the need for accessing quantum devices or large-sized classical machines during the QAOA optimization phase, and (II) ensuring that when dealing with some k-bounded pseudo-Boolean problems, optimizing the exact problem's expectation value can be done in polynomial time using a classical computer.

We present experiments in solving constrained optimization and constraint satisfaction problems by means of Quantum Annealing in terms of QUBO (Quadratic Unconstrained Binary Optimization). We investigate different QUBO formulations for the encoding of integers into Booleans and for the encoding of the At-Most-One constraint, which is used in combinatorial problems requiring capacity constraints. We compare four different QUBO models and report experiments done on the D-Wave annealing computer and the "quantum-inspired" Fixstars Amplify Annealing Engine. For this, we consider a simple example taken from the domain of Constraint Satisfaction Problems (CSP), the N-queens problem, as its formulation involves multiple instances of the At-Most-One constraints.

The Differential Evolution (DE) algorithm is an efficient algorithm with strong search capability. This algorithm is easy to implement and used for solving large-scale optimization problems. However, DE also has drawbacks of insufficient diversity in the later search stage, while solving optimization problems, slow convergence speed, and a high search stagnation possibility. Quantum Entanglement inspired Differential Evolution algorithm (QE-DE) has been proposed in this paper to solve the drawbacks of DE. For solving high-dependency optimization problems, QE-DE integrates entangled states in its Qubits (or quantum bit). The optimization process is further accelerated by utilizing the quantum local search. The proposed QE-DE algorithm is evaluated on the IEEE Congress of Evolutionary Computing (CEC 2017) benchmark set for 10 and 30-dimensions. QE-DE is also compared with existing variants of DE and some other popular algorithms. QE-DE outperforms the performance comparison results.

We discuss a small study on how to compare the performance of various solving techniques for quadratic unconstrained binary optimization (QUBO). Since well-known metrics are seldomly applicable, we suggest comparing the relative performance, i.e., how much the quality of solution (compared to other solutions of the same solver) for a QUBO shifts between different solving techniques. We propose looking for big shifts systematically for an empirical complexity analysis.

Code is available at github.com/thomasgabor/gecco-relative.

Supply chain planning is a complex optimization problem that involves the coordination of multiple resources in order to reduce costs and maximize benefit. In this study, we propose a QUBO formulation for the scheduling of the transportation of materials to a factory with uncertain arrival times. The standard methods like network flow or MILP solvers escalate exponentially with the problem parameters, making computation times grow rapidly. Quantum annealing is a candidate for an optimization poccess that can solve this computationally intense problems, and thus it is important to be able to find compatible formulations. The model proposed makes use of the QUBO formulation to give optimal solutions to the scheduling with unceratinty. We will establish the problem from a stochastic optimization point of view, and then build a hamiltonian that encodes it, following the QUBO formulation. With the quick increase in qubit numbers of quantum computers, this model seems like a promising tool that will provide solutions to very relevant and computionally hard problems in the near future.

Grover search is currently one of the main approaches to obtain quantum speed-ups for combinatorial optimization problems. The combination of Quantum Minimum Finding (obtained from Grover search) with dynamic programming has proved particularly efficient to improve the worst-case complexity of several NP-hard optimization problems. Specifically, for these problems, the classical dynamic programming complexity (ignoring the polynomial factors) in O* (cⁿ) can be reduced by a bounded-error hybrid quantum-classical algorithm to O* (cⁿ_quant) for c_quant < c. In this paper, we extend the resulting hybrid dynamic programming algorithm to three examples of single-machine scheduling problems: minimizing the total weighted completion time with deadlines, minimizing the total weighted completion time with precedence constraints, and minimizing the total weighted tardiness. The extension relies on the inclusion of a pseudo-polynomial term in the state space of the dynamic programming as well as an additive term in the recurrence.

Quantum computing is a next-generation computing paradigm that offers potential advantages for addressing complex real-world applications, such as portfolio optimization (PO). Quantum-inspired optimization (QIO) algorithms simulate quantum mechanisms to achieve quantum advantages using classical computers. QIO algorithms can serve as a bridge to realizing preliminary quantum advantages by exploiting classical computation abilities. In a detailed analysis of PO, a domain-dependent optimization technique is proposed combined with an effective QIO, called the entanglement local search-assisted (ELSA) technique. ELSA introduces the novel concept of the entangled neighborhood for PO and assists QIO in accurately searching a potential area, thus significantly promoting the quality of the solution. The entanglement relationship can decrease the degree of freedom searched. The proposed ELSA-QIO technique is employed in a trend ratio-based intelligent system to search for a steady uptrend portfolio in the global G20 markets. This study discusses the expanded markets to demonstrate the superior ability of the proposed QIO method in a vast solution space. Experiments demonstrate that the proposed system outperforms state-of-the-art methods. This study investigates the world's largest markets in-depth and proposes a strategy for global financial management that expands the use of quantum computing.

Quadratic Unconstrained Binary Optimization (QUBO) has emerged as a vital unifying model for combinatorial optimization problems, and (meta-)heuristic approaches are commonly used to solve them due to their NP-hard nature. Scatter Search (SS), a population-based metaheuristic framework, is one such method that has shown promising results for QUBO problems. Generating new solutions from more promising ones is a crucial operation in SS. Path Relinking (PR) based SS has been previously used to solve challenging QUBO problems with high-quality solutions. This paper introduces two new variants of the SS algorithm. The first is the (Multi) Uniform Crossover (MUC) based SS while the second is the Univariate Marginal Distribution Algorithm (UMDA) based SS. MUC and UMDA are well-known operators in Genetic Algorithms and Estimation of Distribution Algorithms respectively. When compared to the existing PR based SS, this work shows that more promising results can be achieved when the newly proposed MUC and UMDA-based SS are applied to QUBO formulations of the Quadratic Knapsack Problem (QKP) instances.

We study the flow-shop scheduling problem under the makespan minimization. The Grover's algorithm is adapted and implemented to solve the problem. We introduce an encoding for the data and variables and propose a feasibility and optimization oracles. The first oracle checks the feasibility of the solution while the second oracle allows compute the objective function of the solution, when valid. The proposed algorithm is illustrated using an example of the two machine flow-shop.

Quantum computing provides powerful algorithmic tools that have been shown to outperform established classical solvers in specific optimization tasks. A core step in solving optimization problems with known quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) is the problem formulation. While quantum optimization has historically centered around Quadratic Unconstrained Optimization (QUBO) problems, recent studies show, that many combinatorial problems such as the TSP can be solved more efficiently in their native Polynomial Unconstrained Optimization (PUBO) forms. As many optimization problems in practice also contain continuous variables, our contribution investigates the performance of the QAOA in solving continuous optimization problems when using PUBO and QUBO formulations. Our extensive evaluation on suitable benchmark functions, shows that PUBO formulations generally yield better results, while requiring less qubits. As the multi-qubit interactions needed for the PUBO variant have to be decomposed using the hardware gates available, i.e., currently single- and two-qubit gates, the circuit depth of the PUBO approach outscales its QUBO alternative roughly linearly in the order of the objective function. However, incorporating the planned addition of native multi-qubit gates such as the global Mølmer-Sørenson gate, our experiments indicate that PUBO outperforms QUBO for higher order continuous optimization problems in general.

To solve 3sat instances on quantum annealers they need to be transformed to an instance of Quadratic Unconstrained Binary Optimization (QUBO). When there are multiple transformations available, the question arises whether different transformations lead to differences in the obtained solution quality. Thus, in this paper we conduct an empirical benchmark study, in which we compare four structurally different QUBO transformations for the 3sat problem with regards to the solution quality on D-Wave's Advantage_system4.1. We show that the choice of QUBO transformation can significantly impact the number of correct solutions the quantum annealer returns. Furthermore, we show that the size of a QUBO instance (i.e., the dimension of the QUBO matrix) is not a sufficient predictor for solution quality, as larger QUBO instances may produce better results than smaller QUBO instances for the same problem. We also empirically show that the number of different quadratic values of a QUBO instance, combined with their range, can significantly impact the solution quality.

In this work we introduce a new framework for multi-objective Bayesian optimisation where the multi-objective functions can only be accessed via choice judgements, such as "I pick options x₁, x₂, x₃ among this set of five options x₁, x₂, ..., x₅". The fact that the option x₄ is rejected means that there is at least one option among the selected ones x₁, x₂, x₃ that I strictly prefer over x₄ (but I do not have to specify which one). We assume that there is a latent vector function u for some dimension d which embeds the options into the real vector space of dimension d, so that the choice set can be represented through a Pareto set of non-dominated options. By placing a Gaussian process prior on u and by using a novel likelihood model for choice data, we derive a surrogate model for the latent vector function. We then propose two novel acquisition functions to solve the multi-objective Bayesian optimisation from choice data.

Data-driven evolutionary algorithms (DDEAs) using surrogate models have been successfully applied in solving expensive optimization problems. However, many real-world engineering optimization problems can only build surrogate models with limited offline data. Inspired by the K-Fold cross validation and the Bootstrap aggregating, an offline DDEA based on elite model strategy (DDEA-EMS) is developed in this work. In DDEA-EMS, the K-Fold generalized mean square error (KGMSE) is employed to select the surrogate model with best prediction accuracy. KGMSE can evaluate the prediction accuracy of surrogates with different hyper-parameters or types. The Bootstrap aggregating method is employed to further improve the robustness of the elite model selected by KGMSE. The DDEA-EMS is successfully applied to the expensive structural optimization of a soft pneumatic actuator.

JADE belongs to the top efficient versions of the Differential Evolution concept. We couple JADE with k Nearest Neighbors surrogate model approximating the fitness function. The model is global, i.e., it is identical for all points in the population. The procedure to control the surrogate model learning process is a version of a method that has been initially introduced for the CMA-ES algorithm. Tests of the algorithm on the CEC'2013 benchmark suite reveal the efficiency increase thanks to the surrogate model for a majority of problems contained in the test suite.

Design space exploration for engineering design involves identifying feasible designs that satisfy design specifications, often represented by feasibility constraints. To determine whether a design is feasible, an expensive simulation is required. Therefore, it is crucial to find and model the feasible region with as few simulations as possible.

Model-based Active learning (AL) is a data-efficient, iterative sampling framework that can be used for design space exploration to identify feasible regions with the least amount of budget spent. A common choice for the budget is the number of (sampling) iterations. This is a good choice when every simulation has an equal cost. However, simulation cost can vary depending on the design parameters and is often unknown. Thus, some regions in the design space are cheaper to evaluate than others.

In this work, we investigate if incorporating the unknown cost in the AL strategy leads to better sampling and, eventually, faster identification of the feasible region.

Evolutionary algorithms are a well-known optimisation technique. They can handle very different optimisation tasks and deal with distorted search spaces as well as non-differentiable optimisation functions. One crucial aspect in the design of evolutionary algorithms is the choice of encoding. Especially its interplay with the other components of the evolutionary algorithm is a relevant factor for the success of an evolutionary algorithm. While some encoding situations are relatively trivial, others pose a challenge. We focus on encoding repetitive processes, i.e. processes that consist of several variations of the same basic process (only with varied parameters). Our work proposes a possible technique that enables the validity of the encoded search space. We also provide adaptions to the standard operators of evolutionary algorithms to ensure they produce valid solutions. Furthermore, we show how this encoding technique is compatible with using a surrogate function for the fitness calculation and may reduce the necessary training data.

Surrogate-based optimization is a common practice in different application fields in engineering and sciences, mainly when the objective function is computationally expensive. The selection of the best modeling approach to design the surrogate impacts how the optimization will perform. This paper explores online surrogates trained during the optimization process and applied to filter non-promising solutions before considering the evaluation with the actual fitness function. The study analyses two online alternative approaches proposed by the literature to implement surrogates. On the one hand, we consider traditional regression-based approaches that construct the surrogate as a continuous approximation of the fitness function; based on experiments on the same benchmark, this paper takes XGBoost regressor as the representative surrogate for this approach. On the other, we include a pairwise model that predicts whether a candidate solution is better than a reference one as a binary classifier; for this type of surrogate, we take a Decision Tree classifier, which performed the best in the same baseline study.

The analysis of the two surrogates shows that the contribution of the surrogate varies during the different optimization phases. This paper demonstrates how combining complementary surrogates improves their behavior and the performance of the optimization as a whole.

The dramatic growth of deep learning over the past decade has increased the demand for effective hyperparameter optimization (HPO). At the moment, evolutionary algorithms such as the covariance matrix adaptation evolution strategy (CMA-ES) are recognized as one of the most promising approaches for HPO. However, it is often problematic for practitioners that HPO is a time-consuming task because of its computationally expensive objective even if evaluations were parallelized in each generation of an evolutionary algorithm. To address the problem, multi-fidelity optimization that exploits cheap-to-evaluate lower-fidelity alternatives instead of the true maximum-fidelity objective can be utilized for faster optimization. In this paper, we introduce a new fidelity-selecting strategy designed to solve HPO problems with an evolutionary algorithm. Then, we demonstrate that the CMA-ES with the proposed strategy accelerates the search by about 8.5%--15% compared with the vanilla CMA-ES while keeping the quality of the solutions obtained.

Multi-objective Bayesian optimization is a sequential optimization strategy in which an optimizer searches for optimal solutions by maximizing an acquisition function. Most existing acquisition functions assume that objectives are independent, but none of them incorporates the correlations among objectives through an explicit formula for exact computation. This paper proposes a novel acquisition function, namely, correlated probability of improvement (cPoI), for bi-objective optimization problems. The cPoI method builds on the probability of improvement and addresses the correlations between objectives by utilizing 3 distinct approaches to compute the posterior covariance matrix from a multi-task Gaussian process. This paper presents both an explicit formula for exact computation of cPoI and a Monte Carlo method for approximating it. We evaluate the performance of the proposed cPoI against 4 state-of-the-art multi-objective optimization algorithms on 8 artificial benchmarks and 1 real-world problem. Our experimental results demonstrate the effectiveness of cPoI in achieving superior optimization performance.

Bound constraints on the variables are the most basic constraints in an optimization problem formulation and, thus, among the most common. It is therefore essential to understand the impact of different boundary handling techniques on algorithm performance. Equally, it is important to understand the practical impact of using bound constraint handling in an algorithm on principally unbounded problems but where the user has a good indication of the domain of the (sought) optimum. Both questions will be investigated in this paper on the newly introduced box-constrained version sbox-cost of the well-known, unconstrained test suite bbob and for the example of the two boundary handling techniques, implemented in the CMA-ES python module pycma. The numerical experiments performed with the COCO platform show that there is (i) only a minor difference in performance between the two test suites and (ii) a slight performance reduction for the (default) BoundTransform boundary handling compared to the BoundPenalty version of CMA-ES.

In this paper we report the benchmarking results of four algorithms on the Strict Box-Constraint Optimization Studies (SBOX-COST) benchmarking suite which, as the name states, employs strict box constraints. These results are compared to the benchmarking results on the Black-box Optimization Benchmarking (BBOB) suite which serves as basis for the SBOX-COST suite, but is less restrivtive with respect to box constraints. SBOX-COST enforces its box constraints by returning an invalid value (∞) whenever a point outside of the bounds is evaluated. We use the following four algorithms from the Nevergrad Toolbox: Estimation of Multivariate Normal Algorithm (EMNA), Differential Evolution (DE), Constrained Optimization BY Linear Approximation (Cobyla) and Particle Swarm Optimization (PSO). All algorithms are employed without parameter tuning. Generally, all algorithms perform quite similiar on both suites but we notice a slight advantage for the algorithms that are allowed to evaluate the functions outside of the bounds. The effect of the advantage varies very much with function ID and in some cases, an algorithm's performance on a problem from the SBOX-COST suite is even better than on the corresponding problem from the BBOB suite.

Recently, Boundary Control Methods (BCMs) have become increasingly relevant in the field of metaheuristic algorithms. In this study, we investigate the relationship between the activation frequency of different BCMs and the problem's dimensionality. Additionally, we analyze each problem dimension independently. Our research primarily concentrates on the top three algorithms from the IEEE CEC 2020 competition: AGSK, IMODE, and j2020, utilizing the competition benchmark set to conduct experiments. Our findings provide valuable insights into the metaheuristic domain, underlining the significance of comprehending BCM activation patterns to improve algorithm design and benchmarking practices.

This study investigates the influence of several bound constraint handling methods (BCHMs) on the search process specific to Differential Evolution (DE), with a focus on identifying similarities between BCHMs and grouping patterns with respect to the number of cases when a BCHM is activated. The empirical analysis is conducted on the SBOX-COST benchmarking test suite, where bound constraints are enforced on the problem domain. This analysis provides some insights that might be useful in designing adaptive strategies for handling such constraints.

Box-constraints limit the domain of decision variables and are common in real-world optimization problems, for example, due to physical, natural or spatial limitations. Consequently, solutions violating a box-constraint may not be evaluable. This assumption is often ignored in the literature, e.g., existing benchmark suites, such as COCO/BBOB, allow the optimizer to evaluate infeasible solutions. This paper presents an initial study on the strict-box-constrained benchmarking suite (SBOX-COST), which is a variant of the well-known BBOB benchmark suite that enforces box-constraints by returning an invalid evaluation value for infeasible solutions. Specifically, we want to understand the performance difference between BBOB and SBOX-COST as a function of two initialization methods and six constraint-handling strategies all tested with modular CMA-ES. We find that, contrary to what may be expected, handling box-constraints by saturation is not always better than not handling them at all. However, across all BBOB functions, saturation is better than not handling, and the difference increases with the number of dimensions. Strictly enforcing box-constraints also has a clear negative effect on the performance of classical CMA-ES (with uniform random initialization and no constraint handling), especially as problem dimensionality increases.

In Evolutionary Robotics, techniques inspired by biological evolution are used to evolve robotic morphology and behaviors. Evolution Strategies is a popular algorithm in this field due to its capability to perform continuous optimization. In evolutionary robotics, the use of approaches as, for instance, niching techniques and environmental variation, has shown promising results in order to develop more effective adaptive behaviors or even improve the convergence time. The objective of this work is to analyze how a recent adaptation of Evolution Strategies developed by OpenAI, which we call OpenAI-ES, behaves when working alongside environmental variation and niching techniques. The results showed that this approach applied to the double pole balancing benchmark can improve performance by 9% for OpenAI-ES.

PyTorch has profoundly impacted the machine learning (ML) community by allowing researchers of all backgrounds to train models efficiently. While PyTorch is the de facto standard in ML, the evolutionary algorithms (EA) community instead relies on many different libraries, each with low adoption in practice. In an effort to provide a standardized library for EA, packages like LEAP and PyGAD have been developed. However, these libraries fall short in either scalability or usability. In particular, neither of these packages offers efficient support for neuroevolutionary tasks. We argue that the best way to develop a PyTorch-like library for EAs is to build on the already solid foundation of PyTorch itself. We present Gaggle, an efficient PyTorch-based EA library that better supports GPU-based tasks like neuroevolution while maintaining the efficiency of CPU-based problems. We evaluate Gaggle on various problems and find statistically significant improvements in runtime over prior work on problems like training neural networks. In addition to efficiency, Gaggle provides a simple single-line interface making it accessible to beginners and a more customizable research interface with detailed configuration files to better support the EA research community.

The optimization performed by compilers when generating executable programs is critical for software performance yet tuning this process to maximize efficiency is difficult due to the large number of possible modifications and the almost limitless number of potential input programs. To promote the application of artificial intelligence and machine learning to this challenge, Facebook Research released Compiler Gym[1], a reinforcement learning environment to allow the training of agents to perform compiler optimization control on real C/C++ programs. Whereas previously published approaches use techniques such as Proximal Policy Optimization or Deep Q Networks, this work utilizes neuroevolution and achieves competitive performance on the cBench-v1[2] program set while demonstrating the highly adaptive properties of the neuroevolution approach.

The issue of structure learning in large Bayesian networks has gained significant attention from the academic community in recent years due to its wide-ranging applications in various fields. Efficient algorithms for structure learning are crucial for enabling the practical use of Bayesian networks in real-world scenarios where the number of variables can be substantial. In previous approaches, addressing this problem has resulted in either prolonged convergence times or significant degradation of the problem. Although evolutionary algorithms have been effective in training Bayesian Networks (BNs), their application to large BNs has been impractical due to lengthy convergence times. In this paper, we introduce a modified evolutionary algorithm for training large BNs by dividing the network into smaller ones, coding and connecting them through evolutionary optimization. Our proposed approach significantly accelerates the training process, achieving a time acceleration of more than twenty times compared to existing solutions, while maintaining comparable or slightly degraded quality.

The crossover is considered as an essential component of the evolutionary algorithms. There exist different ways of how to use it, and in this paper we compare two approaches commonly used in pseudo-Boolean optimization, the classic approach of (μ + 1) GA using a uniform crossover which combines the best features of the parents, and the approach of the (1 + (λ, λ)) GA genetic algorithm, where crossover is used as a repair mechanism after a strong mutation. We study empirically how these two approaches perform on the rugged landscapes and conclude that the classic approach works better, but only when we use mechanisms which support the diversity in the population.

The School Bus Routing Problem (SBRP) is a well-known example of an optimization problem in which, given a variety of feasible solutions to the problem of transporting pupils to school, we seek out an optimal solution. With over 1.3 million students in England having special education needs and a growing demand for inclusion in the educational community, creating optimal and inclusive school bus routes is essential to promoting this inclusion. The standard SBRP is a highly constrained problem. When considering the needs of pupils with Special Educational Needs and Disabilities (SEND), the problem becomes even more complex and constrained. In this study, we describe an SBRP formulation capturing SEND specific requirements, catering for heterogeneous fleets, mixed riding, time windows and the use of travel assistants for pupils with special needs. We then present preliminary results investigating the performance of a meta-heuristic and an exact approach, in the context of a real-life case study. Our findings show that when the number of instances increases, exact solvers very rapidly become unworkable. This motivates the development of metaheuristic approaches to this problem. Our results encourage additional research into optimizing school bus routing algorithms to benefit from both precise and heuristic solvers.

Parameter tuning in evolutionary algorithms is a very important topic, as the correct choice of parameters greatly affects their performance. Fitness landscape analysis can help identify similar problems and allow for gathering problem structure insights for fitness-aware optimization algorithm parameter choice.

In this paper, we present an approach to an automatic dynamic parameter control method that uses exploratory landscape analysis and machine learning. Using a dataset of optimal parameter values we collected on different instances of W-model benchmark problem, we trained a machine learning model capable of suggesting parameter values for the (1 + (λ, λ)) genetic algorithm. The results of our experiments show that the machine learning model is able to capture important landscape features and recommend algorithm parameters based on this information. The comparison results with other tuning methods suggest this approach is more effective than static tuning or heuristics-based dynamic parameter control.

Denoising autoencoder genetic programming (DAE-GP) is an estimation of distribution genetic programming (EDA-GP) algorithm. It uses denoising autoencoder long short-term memory networks as probabilistic model to replace the standard mutation and recombination operators of genetic programming (GP). Recent work has shown several advantages regarding solution length and overall performance of DAE-GP when compared to GP. However, training a neural network at each generation is computationally expensive, where model training is the most time consuming process of DAE-GP. In this work, we propose pretraining to reduce the runtime of the DAE-GP. In pretraining, the neural network is trained preceding the evolutionary search. In experiments on 8 real-world symbolic regression tasks we find that DAE-GP with pretraining has a reduced overall runtime of an order of magnitude while generating individuals with similar or better fitness.

The design of Boolean functions which exhibit high-quality cryptography properties is a crucial aspect when implementing secure stream ciphers. To this end, several methods have been proposed to search for secure Boolean functions, and, among those, evolutionary algorithms play a prominent role. In this paper, Genetic Programming (GP) is applied for the evolution of Boolean functions in order to maximize one essential property for strong cryptography functions, namely non-linearity. Differently from other approaches, the evolution happens in the space of Walsh Transforms, instead of using a direct representation of the Boolean functions. Specifically, we evolve coefficients of the Walsh Transform to obtain a generic Walsh spectrum, from which it is possible, through spectral inversion, to obtain a pseudo-Boolean function that, consequently, can be mapped to (one of) the nearest Boolean one. Since that function might not be unique, we propose a strategy in which balancedness, another important cryptography property, is preserved as much as possible. To show that the evolutionary search is actually effective in this task, we evolved Boolean functions from 6 to 16 variables. The results show that not only GP is effective in evolving Boolean functions with high non-linearity, but also that balanced functions are discovered.

Bayesian Optimization (BO) is a class of black-box, surrogate-based heuristics that can efficiently optimize problems that are expensive to evaluate and therefore allow only small evaluation budgets. Regardless of the size of the budget, high dimensionality also poses a challenge to BO, whose performance reportedly often suffers when the dimension exceeds 15 variables. Many new algorithms have been proposed to address this problem. However, it is not well understood which one is the best for which optimization scenario.

In this work, we compare five state-of-the-art high-dimensional BO algorithms, with vanilla BO and CMA-ES on the 24 BBOB functions of the COCO environment at two dimensionalities, 10 and 60 variables. Our results confirm the superiority of BO over CMA-ES for limited evaluation budgets and suggest that the most promising approach to improve BO at high dimensionality is the use of trust regions. However, we also observe significant performance differences for different function landscapes and budget exploitation phases, indicating improvement potential, e.g., through hybridization of algorithmic components.

Tackling large-scale and ill-conditioned problems is demanding even for the covariance matrix adaptation evolution strategy (CMA-ES), which is a state-of-the-art algorithm for black-box optimization. The coordinate selection is a technique that mitigates the ill-conditionality of large-scale problems by updating parameters in partially selected coordinate spaces. This technique can be applied to various CMA-ES variants and improves their performance especially for ill-conditioned problems. However, it often fails to improve the performance of well-conditioned problems, because it is difficult to choose appropriate coordinate spaces according to the ill-conditionality of problems. We introduce a dynamic partial update method for coordinate selection to solve the above problem. We use the second-order partial derivatives of an objective function to estimate the condition number and select coordinates so that the condition number of each pair does not exceed the given allowable value. In this method, the number of clusters becomes to be small for well-conditioned problems and large for ill-conditioned cases. In particular, the selection does not execute if the condition number of the full space is less than the allowable value. We observe significant improvements in well-conditioned problems and comparable performances in ill-conditioned cases in numerical experiments.

Generative Adversarial Networks (GANs) have gained popularity due to their ability to produce realistic examples from existing data without any supervision. However, they are dependent on their hyperparameters, the tuning of which is usually a manual task. Additionally, the computing resources required for such training are also extremely high. In this paper, ATLAS - a Cloud-based Co-evolutionary Framework for training such adversarial networks using Evolutionary Algorithms is proposed. ATLAS views the GAN components (generator and discriminator) as in a predator-prey relationship and involves co-evolution as a method to address the challenges of overfitting, exploding/vanishing gradients and tunes the hyperparameters of both the components of the GAN. The ATLAS framework is designed to be customizable, and resource flexible to allow for set-up and easy usage for training complex adversarial networks in both distributed and cloud environments. Experiments testing ATLAS capability for anomaly detection were performed and the results show that ATLAS can consistently evolve and produce high-performance GAN models.

When choosing between competing symbolic models for a data set, a human will naturally prefer the "simpler" expression or the one which more closely resembles equations previously seen in a similar context. This suggests a non-uniform prior on functions, which is, however, rarely considered within a symbolic regression (SR) framework. In this paper we develop methods to incorporate detailed prior information on both functions and their parameters into SR. Our prior on the structure of a function is based on a n-gram language model, which is sensitive to the arrangement of operators relative to one another in addition to the frequency of occurrence of each operator. We also develop a formalism based on the Fractional Bayes Factor to treat numerical parameter priors in such a way that models may be fairly compared though the Bayesian evidence, and explicitly compare Bayesian, Minimum Description Length and heuristic methods for model selection. We demonstrate the performance of our priors relative to literature standards on benchmarks and a real-world dataset from the field of cosmology.

Operon is a C⁺⁺ framework for symbolic regression with the ability to perform local search by optimizing model coefficients using the Levenberg-Marquardt algorithm. This enhancement has proven to be effective in a variety of regression tasks. Operon took part in the Interpretable Symbolic Regression for Data Science hosted at the 2022 Genetic and Evolutionary Computation Conference, where it ranked overall 4^th based on criteria of accuracy, simplicity as well as task-specific goals. Although accurate, the returned models were exceedingly complex and ranked poorly in terms of simplicity. In this paper, we investigate the application of the Minimum Description Length (MDL) principle for selecting models with a better compromise between accuracy and complexity from the final Pareto front returned by the algorithm. A new experiment on the synthetic track of the competition highlights the critical role played by model selection in algorithm performance. The MDL-enhanced approach obtains the best overall score and demonstrates excellent results on all synthetic tracks.

Symbolic Regression is a powerful data-driven technique that searches for mathematical expressions that explain the relationship between input variables and a target of interest. Due to its efficiency and flexibility, Genetic Programming can be seen as the standard search technique for Symbolic Regression. However, the conventional Genetic Programming algorithm requires storing all data in a central location, which is not always feasible due to growing concerns about data privacy and security. While privacy-preserving research has advanced recently and might offer a solution to this problem, their application to Symbolic Regression remains largely unexplored. Furthermore, the existing work only focuses on the horizontally partitioned setting, whereas the vertically partitioned setting, another popular scenario, has yet to be investigated. Herein, we propose an approach that employs a privacy-preserving technique called Secure Multiparty Computation to enable parties to jointly build Symbolic Regression models in the vertical scenario without revealing private data. Preliminary experimental results indicate that our proposed method delivers comparable performance to the centralized solution while safeguarding data privacy.

Evolutionary computation is a powerful optimization method that is well-suited for high-dimensional parameter spaces. In this work, we apply it to an integral task in optical physics, namely, to the problem of programming a deformable mirror to generate laser beams that are partially coherent in space. This involves precise tuning of (on the order of) tens of thousands of phase values in the interval [-π, π) such that they exhibit defined second-order statistical characteristics. We discuss the implementation of two primary methods, the evolution of phase values and of a correlating linear transformation, and provide results based on a Gaussian covariance function. We show that the first-order statistical properties are fixed by the method of choice, which we suggest may be overcome by a multi-objective evolutionary calculation involving symbolic transformations. This is a largely unexplored domain in which stochastic processes, such as genetic algorithms, are superior. Lastly, we discuss the inherently physical limitations that prevent certain types of phase statistics from being realized, even with the genetic algorithm approach.