{"title":"Multiobjective Evolutionary Algorithms Are Still Good: Maximizing Monotone Approximately Submodular Minus Modular Functions","authors":"Chao Qian","doi":"10.1162/evco_a_00288","DOIUrl":"10.1162/evco_a_00288","url":null,"abstract":"As evolutionary algorithms (EAs) are general-purpose optimization algorithms, recent theoretical studies have tried to analyze their performance for solving general problem classes, with the goal of providing a general theoretical explanation of the behavior of EAs. Particularly, a simple multiobjective EA, that is, GSEMO, has been shown to be able to achieve good polynomial-time approximation guarantees for submodular optimization, where the objective function is only required to satisfy some properties and its explicit formulation is not needed. Submodular optimization has wide applications in diverse areas, and previous studies have considered the cases where the objective functions are monotone submodular, monotone non-submodular, or non-monotone submodular. To complement this line of research, this article studies the problem class of maximizing monotone approximately submodular minus modular functions (i.e., g-c) with a size constraint, where g is a so-called non-negative monotone approximately submodular function and c is a so-called non-negative modular function, resulting in the objective function (g-c) being non-monotone non-submodular in general. Different from previous analyses, we prove that by optimizing the original objective function (g-c) and the size simultaneously, the GSEMO fails to achieve a good polynomial-time approximation guarantee. However, we also prove that by optimizing a distorted objective function and the size simultaneously, the GSEMO can still achieve the best-known polynomial-time approximation guarantee. Empirical studies on the applications of Bayesian experimental design and directed vertex cover show the excellent performance of the GSEMO.","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 4","pages":"463-490"},"PeriodicalIF":6.8,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39089247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Anil Yaman, Giovanni Iacca, Decebal Constantin Mocanu, Matt Coler, George Fletcher, Mykola Pechenizkiy
{"title":"Evolving Plasticity for Autonomous Learning under Changing Environmental Conditions.","authors":"Anil Yaman, Giovanni Iacca, Decebal Constantin Mocanu, Matt Coler, George Fletcher, Mykola Pechenizkiy","doi":"10.1162/evco_a_00286","DOIUrl":"https://doi.org/10.1162/evco_a_00286","url":null,"abstract":"<p><p>A fundamental aspect of learning in biological neural networks is the plasticity property which allows them to modify their configurations during their lifetime. Hebbian learning is a biologically plausible mechanism for modeling the plasticity property in artificial neural networks (ANNs), based on the local interactions of neurons. However, the emergence of a coherent global learning behavior from local Hebbian plasticity rules is not very well understood. The goal of this work is to discover interpretable local Hebbian learning rules that can provide autonomous global learning. To achieve this, we use a discrete representation to encode the learning rules in a finite search space. These rules are then used to perform synaptic changes, based on the local interactions of the neurons. We employ genetic algorithms to optimize these rules to allow learning on two separate tasks (a foraging and a prey-predator scenario) in online lifetime learning settings. The resulting evolved rules converged into a set of well-defined interpretable types, that are thoroughly discussed. Notably, the performance of these rules, while adapting the ANNs during the learning tasks, is comparable to that of offline learning methods such as hill climbing.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 3","pages":"391-414"},"PeriodicalIF":6.8,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9172052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Iterated Local Search and Other Algorithms for Buffered Two-Machine Permutation Flow Shops with Constant Processing Times on One Machine.","authors":"Hoang Thanh Le, Philine Geser, Martin Middendorf","doi":"10.1162/evco_a_00287","DOIUrl":"https://doi.org/10.1162/evco_a_00287","url":null,"abstract":"<p><p>The two-machine permutation flow shop scheduling problem with buffer is studied for the special case that all processing times on one of the two machines are equal to a constant c. This case is interesting because it occurs in various applications, for example, when one machine is a packing machine or when materials have to be transported. Different types of buffers and buffer usage are considered. It is shown that all considered buffer flow shop problems remain NP-hard for the makespan criterion even with the restriction to equal processing times on one machine. However, the special case where the constant c is larger or smaller than all processing times on the other machine is shown to be polynomially solvable by presenting an algorithm (2BF-OPT) that calculates optimal schedules in O(nlogn) steps. Two heuristics for solving the NP-hard flow shop problems are proposed: (i) a modification of the commonly used NEH heuristic (mNEH) and (ii) an Iterated Local Search heuristic (2BF-ILS) that uses the mNEH heuristic for computing its initial solution. It is shown experimentally that the proposed 2BF-ILS heuristic obtains better results than two state-of-the-art algorithms for buffered flow shop problems from the literature and an Ant Colony Optimization algorithm. In addition, it is shown experimentally that 2BF-ILS obtains the same solution quality as the standard NEH heuristic, however, with a smaller number of function evaluations.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 3","pages":"415-439"},"PeriodicalIF":6.8,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9172054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Lower Bounds for Non-Elitist Evolutionary Algorithms via Negative Multiplicative Drift.","authors":"Benjamin Doerr","doi":"10.1162/evco_a_00283","DOIUrl":"https://doi.org/10.1162/evco_a_00283","url":null,"abstract":"<p><p>A decent number of lower bounds for non-elitist population-based evolutionary algorithms has been shown by now. Most of them are technically demanding due to the (hard to avoid) use of negative drift theorems-general results which translate an expected movement away from the target into a high hitting time. We propose a simple negative drift theorem for multiplicative drift scenarios and show that it can simplify existing analyses. We discuss in more detail Lehre's (2010) negative drift in populations method, one of the most general tools to prove lower bounds on the runtime of non-elitist mutation-based evolutionary algorithms for discrete search spaces. Together with other arguments, we obtain an alternative and simpler proof of this result, which also strengthens and simplifies this method. In particular, now only three of the five technical conditions of the previous result have to be verified. The lower bounds we obtain are explicit instead of only asymptotic. This allows us to compute concrete lower bounds for concrete algorithms, but also enables us to show that super-polynomial runtimes appear already when the reproduction rate is only a (1-ω(n-1/2)) factor below the threshold. For the special case of algorithms using standard bit mutation with a random mutation rate (called uniform mixing in the language of hyper-heuristics), we prove the result stated by Dang and Lehre (2016b) and extend it to mutation rates other than Θ(1/n), which includes the heavy-tailed mutation operator proposed by Doerr et al. (2017). We finally use our method and a novel domination argument to show an exponential lower bound for the runtime of the mutation-only simple genetic algorithm on OneMax for arbitrary population size.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 2","pages":"305-329"},"PeriodicalIF":6.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38616984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Offline Learning with a Selection Hyper-Heuristic: An Application to Water Distribution Network Optimisation.","authors":"William B Yates, Edward C Keedwell","doi":"10.1162/evco_a_00277","DOIUrl":"https://doi.org/10.1162/evco_a_00277","url":null,"abstract":"<p><p>A sequence-based selection hyper-heuristic with online learning is used to optimise 12 water distribution networks of varying sizes. The hyper-heuristic results are compared with those produced by five multiobjective evolutionary algorithms. The comparison demonstrates that the hyper-heuristic is a computationally efficient alternative to a multiobjective evolutionary algorithm. An offline learning algorithm is used to enhance the optimisation performance of the hyper-heuristic. The optimisation results of the offline trained hyper-heuristic are analysed statistically, and a new offline learning methodology is proposed. The new methodology is evaluated, and shown to produce an improvement in performance on each of the 12 networks. Finally, it is demonstrated that offline learning can be usefully transferred from small, computationally inexpensive problems, to larger computationally expensive ones, and that the improvement in optimisation performance is statistically significant, with 99% confidence.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 2","pages":"187-210"},"PeriodicalIF":6.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00277","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38069843","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
M Virgolin, T Alderliesten, C Witteveen, P A N Bosman
{"title":"Improving Model-Based Genetic Programming for Symbolic Regression of Small Expressions.","authors":"M Virgolin, T Alderliesten, C Witteveen, P A N Bosman","doi":"10.1162/evco_a_00278","DOIUrl":"https://doi.org/10.1162/evco_a_00278","url":null,"abstract":"<p><p>The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a model-based EA framework that has been shown to perform well in several domains, including Genetic Programming (GP). Differently from traditional EAs where variation acts blindly, GOMEA learns a model of interdependencies within the genotype, that is, the linkage, to estimate what patterns to propagate. In this article, we study the role of Linkage Learning (LL) performed by GOMEA in Symbolic Regression (SR). We show that the non-uniformity in the distribution of the genotype in GP populations negatively biases LL, and propose a method to correct for this. We also propose approaches to improve LL when ephemeral random constants are used. Furthermore, we adapt a scheme of interleaving runs to alleviate the burden of tuning the population size, a crucial parameter for LL, to SR. We run experiments on 10 real-world datasets, enforcing a strict limitation on solution size, to enable interpretability. We find that the new LL method outperforms the standard one, and that GOMEA outperforms both traditional and semantic GP. We also find that the small solutions evolved by GOMEA are competitive with tuned decision trees, making GOMEA a promising new approach to SR.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 2","pages":"211-237"},"PeriodicalIF":6.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00278","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38075060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Probabilistic Contextual and Structural Dependencies Learning in Grammar-Based Genetic Programming.","authors":"Pak-Kan Wong, Man-Leung Wong, Kwong-Sak Leung","doi":"10.1162/evco_a_00280","DOIUrl":"https://doi.org/10.1162/evco_a_00280","url":null,"abstract":"<p><p>Genetic Programming is a method to automatically create computer programs based on the principles of evolution. The problem of deceptiveness caused by complex dependencies among components of programs is challenging. It is important because it can misguide Genetic Programming to create suboptimal programs. Besides, a minor modification in the programs may lead to a notable change in the program behaviours and affect the final outputs. This article presents Grammar-Based Genetic Programming with Bayesian Classifiers (GBGPBC) in which the probabilistic dependencies among components of programs are captured using a set of Bayesian network classifiers. Our system was evaluated using a set of benchmark problems (the deceptive maximum problems, the royal tree problems, and the bipolar asymmetric royal tree problems). It was shown to be often more robust and more efficient in searching the best programs than other related Genetic Programming approaches in terms of the total number of fitness evaluation. We studied what factors affect the performance of GBGPBC and discovered that robust variants of GBGPBC were consistently weakly correlated with some complexity measures. Furthermore, our approach has been applied to learn a ranking program on a set of customers in direct marketing. Our suggested solutions help companies to earn significantly more when compared with other solutions produced by several well-known machine learning algorithms, such as neural networks, logistic regression, and Bayesian networks.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 2","pages":"239-268"},"PeriodicalIF":6.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38483671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Decomposition-Based Evolutionary Algorithm with Correlative Selection Mechanism for Many-Objective Optimization.","authors":"Ruochen Liu, Ruinan Wang, Renyu Bian, Jing Liu, Licheng Jiao","doi":"10.1162/evco_a_00279","DOIUrl":"https://doi.org/10.1162/evco_a_00279","url":null,"abstract":"<p><p>Decomposition-based evolutionary algorithms have been quite successful in dealing with multiobjective optimization problems. Recently, more and more researchers attempt to apply the decomposition approach to solve many-objective optimization problems. A many-objective evolutionary algorithm based on decomposition with correlative selection mechanism (MOEA/D-CSM) is also proposed to solve many-objective optimization problems in this article. Since MOEA/D-SCM is based on a decomposition approach which adopts penalty boundary intersection (PBI), a set of reference points must be generated in advance. Thus, a new concept related to the set of reference points is introduced first, namely, the correlation between an individual and a reference point. Thereafter, a new selection mechanism based on the correlation is designed and called correlative selection mechanism. The correlative selection mechanism finds its correlative individuals for each reference point as soon as possible so that the diversity among population members is maintained. However, when a reference point has two or more correlative individuals, the worse correlative individuals may be removed from a population so that the solutions can be ensured to move toward the Pareto-optimal front. In a comprehensive experimental study, we apply MOEA/D-CSM to a number of many-objective test problems with 3 to 15 objectives and make a comparison with three state-of-the-art many-objective evolutionary algorithms, namely, NSGA-III, MOEA/D, and RVEA. Experimental results show that the proposed MOEA/D-CSM can produce competitive results on most of the problems considered in this study.</p>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 2","pages":"269-304"},"PeriodicalIF":6.8,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38483670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Systematic Literature Review of the Successors of “NeuroEvolution of Augmenting Topologies”","authors":"Evgenia Papavasileiou;Jan Cornelis;Bart Jansen","doi":"10.1162/evco_a_00282","DOIUrl":"10.1162/evco_a_00282","url":null,"abstract":"<para>NeuroEvolution (NE) refers to a family of methods for optimizing Artificial Neural Networks (ANNs) using Evolutionary Computation (EC) algorithms. NeuroEvolution of Augmenting Topologies (NEAT) is considered one of the most influential algorithms in the field. Eighteen years after its invention, a plethora of methods have been proposed that extend NEAT in different aspects. In this article, we present a systematic literature review (SLR) to list and categorize the methods succeeding NEAT. Our review protocol identified 232 papers by merging the findings of two major electronic databases. Applying criteria that determine the paper's relevance and assess its quality, resulted in 61 methods that are presented in this article. Our review article proposes a new categorization scheme of NEAT's successors into three clusters. NEAT-based methods are categorized based on 1) whether they consider issues specific to the search space or the fitness landscape, 2) whether they combine principles from NE and another domain, or 3) the particular properties of the evolved ANNs. The clustering supports researchers 1) understanding the current state of the art that will enable them, 2) exploring new research directions or 3) benchmarking their proposed method to the state of the art, if they are interested in comparing, and 4) positioning themselves in the domain or 5) selecting a method that is most appropriate for their problem.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 1","pages":"1-73"},"PeriodicalIF":6.8,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38569425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effect of Objective Normalization and Penalty Parameter on Penalty Boundary Intersection Decomposition-Based Evolutionary Many-Objective Optimization Algorithms","authors":"Lei Chen;Kalyanmoy Deb;Hai-Lin Liu;Qingfu Zhang","doi":"10.1162/evco_a_00276","DOIUrl":"10.1162/evco_a_00276","url":null,"abstract":"<para>An objective normalization strategy is essential in any evolutionary multiobjective or many-objective optimization (EMO or EMaO) algorithm, due to the distance calculations between objective vectors required to compute diversity and convergence of population members. For the decomposition-based EMO/EMaO algorithms involving the Penalty Boundary Intersection (PBI) metric, normalization is an important matter due to the computation of two distance metrics. In this article, we make a theoretical analysis of the effect of instabilities in the normalization process on the performance of PBI-based MOEA/D and a proposed PBI-based NSGA-III procedure. Although the effect is well recognized in the literature, few theoretical studies have been done so far to understand its true nature and the choice of a suitable penalty parameter value for an arbitrary problem. The developed theoretical results have been corroborated with extensive experimental results on three to 15-objective convex and non-convex instances of DTLZ and WFG problems. The article, makes important theoretical conclusions on PBI-based decomposition algorithms derived from the study.</para>","PeriodicalId":50470,"journal":{"name":"Evolutionary Computation","volume":"29 1","pages":"157-186"},"PeriodicalIF":6.8,"publicationDate":"2021-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1162/evco_a_00276","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38069842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}