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A Framework to Handle Multimodal Multiobjective Optimization in decomposition-based evolutionary algorithms

IEEE TRANSACTIONS ON evolutionary COMPUTATION 2020年第4期24卷 720-734页

作者： Tanabe, Ryoji Ishibuchi, Hisao Southern Univ Sci & Technol Shenzhen Key Lab Computat Intelligence Univ Key Lab Evolving Intelligent Syst Guangdong Dept Comp Sci & Engn Shenzhen 518055 Peoples R China

Multimodal multiobjective optimization is to locate (almost) equivalent Pareto optimal solutions as many as possible. While decomposition-based evolutionary algorithms have good performance for multiobjective optimization, they are likely to perform poorly for multimodal multiobjective optimization due to the lack of mechanisms to maintain the solution space diversity. To address this issue, this article proposes a framework to improve the performance of decomposition-based evolutionary algorithms for multimodal multiobjective optimization. Our framework is based on three operations: 1) assignment;2) deletion;and 3) addition operations. One or more individuals can be assigned to the same subproblem to handle multiple equivalent solutions. In each iteration, a child is assigned to a subproblem based on its objective vector, i.e., its location in the objective space. The child is compared with its neighbors in the solution space assigned to the same subproblem. The performance of improved versions of six decomposition-based evolutionary algorithms by our framework is evaluated on various test problems regarding the number of objectives, decision variables, and equivalent Pareto optimal solution sets. Results show that the improved versions perform clearly better than their original algorithms.

关键词： Pareto optimization Indexes evolutionary computation Spatial diversity Decision making Benchmark testing decomposition-based evolutionary algorithms multimodal multiobjective optimization reference vector-based evolutionary algorithms solution space diversity

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Use of Two Penalty Values in Multiobjective evolutionary Algorithm based on decomposition

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IEEE TRANSACTIONS ON CYBERNETICS 2023年第11期53卷 7174-7186页

作者： Pang, Lie Meng Ishibuchi, Hisao Shang, Ke Southern Univ Sci & Technol Res Inst Trustworthy Autonomous Syst Shenzhen 518055 Peoples R China Southern Univ Sci & Technol Dept Comp Sci & Engn Guangdong Prov Key Lab Brain Inspired Intelligent Shenzhen 518055 Peoples R China

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) with the penalty-based boundary intersection (PBI) function (denoted as MOEA/D-PBI) has been frequently used in many studies in the literature. One essential issue in MOEA/D-PBI is its penalty parameter value specification. However, it is not easy to specify the penalty parameter value appropriately. This is because MOEA/D-PBI shows different search behavior when the penalty parameter values are different. The PBI function with a small penalty parameter value is good for convergence. However, the PBI function with a large value of penalty parameter is needed to preserve the diversity and uniformity of solutions. Although some methods for adapting the penalty parameter value for each weight vector have been proposed, they usually lead to slow convergence. In this article, we propose the idea of using two different values of penalty parameter simultaneously in MOEA/D-PBI. Although the idea is simple, the proposed algorithm is able to utilize both the convergence ability of a small penalty parameter value and the diversification ability of a large penalty parameter value of the PBI function. Experimental results demonstrate that the proposed algorithm works well on a wide range of test problems.

关键词： Convergence Statistics Sociology Optimization evolutionary computation Minimization Cybernetics decomposition-based evolutionary algorithms multiobjective evolutionary algorithm based on decomposition (MOEA D) multiobjective optimization penalty parameter values penalty-based boundary intersection (PBI)

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A clustering-assisted adaptive evolutionary algorithm based on decomposition for multimodal multiobjective optimization

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SWARM AND evolutionary COMPUTATION 2024年 91卷

作者： Hu, Tenghui Wang, Xianpeng Tang, Lixin Zhang, Qingfu Northeastern Univ Natl Frontiers Sci Ctr Ind Intelligence & Syst Opt Shenyang 110819 Peoples R China Northeastern Univ Key Lab Data Analyt & Optimizat Smart Ind Minist Educ Shenyang 110819 Peoples R China Liaoning Engn Lab Data Analyt & Optimizat Smart In Shenyang 110819 Peoples R China Liaoning Key Lab Mfg Syst & Logist Optimizat Shenyang 110819 Peoples R China City Univ Hong Kong Hong Kong Peoples R China

A multimodal multiobjective optimization problem can have multiple equivalent Pareto Sets (PSs). Since the number of PSs may vary in different problems, if the population is restricted to a fixed size, the number of solutions found for each PS will inevitably fluctuate widely, which is undesirable for decision makers. To address the issue, this paper proposes a clustering-assisted adaptive evolutionary algorithm based on decomposition (CA-MMEA/D), whose search process can be roughly divided into two stages. In the first stage, an initial exploration of decision space is carried out, and then solutions with good convergence are used for clustering to estimate the number and location of multiple PSs. In the second stage, new search strategies are developed on the basis of clustering, which can take advantage of unimodal search methods. Experimental studies show that the proposed algorithm outperforms some state-of-the-art algorithms, and CA-MMEA/D can keep the number of solutions found for each PS at a relatively stable level for different problems, thus making it easier for decision makers to choose the desired solutions. The research in this paper provides new ideas for the design of decomposition-based multimodal multiobjective algorithms.

关键词： Multimodal multiobjective optimization Clustering decomposition-based evolutionary algorithms

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Performance of decomposition-based Many-Objective algorithms Strongly Depends on Pareto Front Shapes

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IEEE TRANSACTIONS ON evolutionary COMPUTATION 2017年第2期21卷 169-190页

作者： Ishibuchi, Hisao Setoguchi, Yu Masuda, Hiroyuki Nojima, Yusuke Osaka Prefecture Univ Dept Comp Sci & Intelligent Syst Sakai Osaka 5998531 Japan

Recently, a number of high performance many-objective evolutionary algorithms with systematically generated weight vectors have been proposed in the literature. Those algorithms often show surprisingly good performance on widely used DTLZ and WFG test problems. The performance of those algorithms has continued to be improved. The aim of this paper is to show our concern that such a performance improvement race may lead to the overspecialization of developed algorithms for the frequently used many-objective test problems. In this paper, we first explain the DTLZ and WFG test problems. Next, we explain many-objective evolutionary algorithms characterized by the use of systematically generated weight vectors. Then we discuss the relation between the features of the test problems and the search mechanisms of weight vector-based algorithms such as multiobjective evolutionary algorithm based on decomposition (MOEA/D), nondominated sorting genetic algorithm III (NSGA-III), MOEA/dominance and decomposition (MOEA/DD), and.-dominance based evolutionary algorithm (theta-DEA). Through computational experiments, we demonstrate that a slight change in the problem formulations of DTLZ and WFG deteriorates the performance of those algorithms. After explaining the reason for the performance deterioration, we discuss the necessity of more general test problems and more flexible algorithms.

关键词： decomposition-based evolutionary algorithms many-objective evolutionary algorithms many-objective optimization many-objective test problems

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Review and analysis of three components of the differential evolution mutation operator in MOEA/D-DE

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SOFT COMPUTING 2019年第23期23卷 12843-12857页

A decomposition-based multi-objective evolutionary algorithm with a differential evolution variation operator (MOEA/D-DE) shows high performance on challenging multi-objective problems (MOPs). The DE mutation consists of three key components: a mutation strategy, an index selection method for parent individuals, and a bound-handling method. However, the configuration of the DE mutation operator that should be used for MOEA/D-DE has not been thoroughly investigated in the literature. This configuration choice confuses researchers and users of MOEA/D-DE. To address this issue, we present a review of the existing configurations of the DE mutation operator in MOEA/D-DE and systematically examine the influence of each component on the performance of MOEA/D-DE. Our review reveals that the configuration of the DE mutation operator differs depending on the source code of MOEA/D-DE. In our analysis, a total of 30 configurations (three index selection methods, two mutation strategies, and five bound-handling methods) are investigated on 16 MOPs with up to five objectives. Results show that each component significantly affects the performance of MOEA/D-DE. We also present the most suitable configuration of the DE mutation operator, which maximizes the effectiveness of MOEA/D-DE.

关键词： Multi-objective optimization decomposition-based evolutionary algorithms Differential evolution operators Implementation of algorithms

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On the Importance of Isolated Solutions in Constrained decomposition-based Many-objective Optimization 17

On the Importance of Isolated Solutions in Constrained Decom...

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Genetic and evolutionary Computation Conference (GECCO)

作者： Elarbi, Maha Bechikh, Slim Ben Said, Lamjed Univ Tunis SMART lab CS Dept Tunis Tunisia

ISBN: (纸本)9781450349208

During the few past years, decomposition has shown a high performance in solving Multi-objective Optimization Problems (MOPs) involving more than three objectives, called as Many-objective Optimization Problems (MaOPs). The performance of most of the existing decomposition-based algorithms has been assessed on the widely used DTLZ and WFG unconstrained test problems. However, the number of works that have been devoted to tackle the problematic of constrained many-objective optimization is relatively very small when compared to the number of works handling the unconstrained case. Recently, there has been some interest to exploit infeasible isolated solutions when solving Constrained MaOPs (CMaOPs). Motivated by this observation, we firstly propose an IS-update procedure (Isolated Solution-based update procedure) that has the ability to: (1) handle CMaOPs characterized by various types of difficulties and (2) favor the selection of not only infeasible solutions associated to isolated sub-regions but also infeasible solutions with smaller Constraint Violation (CV) values. The IS-update procedure is subsequently embedded within the Multi-Objective evolutionary Algorithm-based on decomposition (MOEA/D). The new obtained algorithm, named ISC-MOEA/D (Isolated Solution-based Constrained MOEA/D), has been shown to provide competitive and better results when compared against three recent works on the CDTLZ benchmark problems.

关键词： Constrained many-objective optimization decomposition-based evolutionary algorithms constraint handling isolated solutions

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D²MOPSO: MOPSO based on decomposition and Dominance with Archiving Using Crowding Distance in Objective and Solution Spaces

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evolutionary COMPUTATION 2014年第1期22卷 47-77页

作者： Al Moubayed, N. Petrovski, A. McCall, J. Robert Gordon Univ Aberdeen AB25 1HG Scotland

This paper improves a recently developed multi-objective particle swarm optimizer that incorporates dominance with decomposition used in the context of multi-objective optimization. decomposition simplifies a multi-objective problem (MOP) by transforming it to a set of aggregation problems, whereas dominance plays a major role in building the leaders' archive. introduces a new archiving technique that facilitates attaining better diversity and coverage in both objective and solution spaces. The improved method is evaluated on standard benchmarks including both constrained and unconstrained test problems, by comparing it with three state of the art multi-objective evolutionary algorithms: MOEA/D, OMOPSO, and dMOPSO. The comparison and analysis of the experimental results, supported by statistical tests, indicate that the proposed algorithm is highly competitive, efficient, and applicable to a wide range of multi-objective optimization problems.

关键词： Multi-objective particle swarm optimization decomposition-based evolutionary algorithms dominance archiving technique OMOPSO MOEA D

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