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A hierarchical clustering algorithm for addressing multi-modal multi-objective optimization problems

EXPERT SYSTEMS WITH APPLICATIONS 2025年 264卷

作者： Gu, Qinghua Niu, Yiwen Hui, Zegang Wang, Qian Xiong, Naixue Xian Univ Architecture & Technol Sch Resources Engn Xian 710055 Shaanxi Peoples R China Xian Univ Architecture & Technol Xian Key Lab Intelligent Ind Percept Calculat & De Xian 710055 Peoples R China Xian Univ Architecture & Technol Sch Management Xian 710055 Shaanxi Peoples R China James Madison Univ Integrated Sci & Technol Harrisonburg VA 22807 USA Ross State Univ Dept Comp Math & Phys Sci Alpine TX 79830 USA

Many evolutionary multi-modal multi-objective algorithms (MMEAs) have been proposed to solve multi-modal multi-objective optimization problems (MMOPs). Unfortunately, the environmental selection process causes many algorithms to place too much emphasis on solution variety in the decision space, which leads to solutions with low convergence quality. As a result, not only are all local Pareto fronts reversed, but objective values are also far lower than the global Pareto Fronts. To tackle these tasks, this paper proposes a hierarchical clustering-based MMOEA_DC_HR model that uses decision space clustering methods to group neighborhood solutions into several local clusters, preserving local Pareto Sets. And secondary clustering is performed in the objective space to select temporary populations from these local clusters to maintain the diversity of the objective space. Additionally, a hierarchical ranking method is introduced to update the convergence archive, aiding in maintaining the convergence of the algorithm and controlling the quality of the Pareto Front. The test results show that this novel algorithm exhibits competitive performance in solving selected benchmark problems when compared to other cutting-edge MMEAs.

关键词： multi-modal multi-objective optimization Evolutionary computation Hierarchical clustering Local convergence

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multi-modal multi-objective optimization: Problem Analysis and Case Studies

Multi-modal Multi-objective Optimization: Problem Analysis a...

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IEEE Symposium Series on Computational Intelligence (SSCI)

作者： Peng, Yiming Ishibuchi, Hisao Shang, Ke Southern Univ Sci & Technol SUSTech Dept Comp Sci & Engn Univ Key Lab Evolving Intelligent Syst Guangdong Shenzhen Key Lab Computat Intelligence Shenzhen Peoples R China

ISBN: (纸本)9781728124858

In many real-world applications, multi-objective optimization problems may have more than one Pareto sets. The goal of multi-modal multi-objective optimization is to find all Pareto sets in the decision space. As a relatively new research area, difficulties in solving multi-modal multi-objective optimization problems have not been carefully analyzed in the literature. In this paper, first we point out that standard evolutionary multi-objective algorithms show difficulties when solving multi-modal multi-objective optimization problems. Next, using the concept of genetic drift, we clearly explain the decrease of diversity in the decision space during the evolutionary process. Then, we report performance evaluation results of state-of-the-art evolutionary multi-modal multi-objective algorithms using scalable test problems.

关键词： multi-modal multi-objective optimization genetic drift evolutionary algorithms

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Analysis of inter and intra-front operations in multi-modal multi-objective optimization problems

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NATURAL COMPUTING 2023年第2期22卷 341-356页

作者： Javadi, Mahrokh Mostaghim, Sanaz Otto von Guericke Univ Fac Comp Sci Magdeburg Germany

Many real-world multi-objective optimization problems inherently have multiple multi-modal solutions and it is in fact very important to capture as many of these solutions as possible. Several crowding distance methods have been developed in the past few years to approximate the optimal solution in the search space. In this paper, we discuss some of the shortcomings of the crowding distance-based methods such as inaccurate estimates of the density of neighboring solutions in the search space. We propose a new classification for the selection operations of Pareto-based multi-modal multi-objective optimization algorithms. This classification is based on utilizing nearby solutions from other fronts to calculate the crowding values. Moreover, to address some of the drawbacks of existing crowding methods, we propose two algorithms whose selection mechanisms are based on each of the introduced types of selection operations. These algorithms are called NxEMMO and ES-EMMO. Our proposed algorithms are evaluated on 14 test problems of various complexity levels. According to our results, in most cases, the NxEMMO algorithm with the proposed selection mechanism produces more diverse solutions in the search space in comparison to other competitive algorithms.

关键词： Pareto dominance-based algorithms multi-modal multi-objective optimization Harmonic average distance Inter-front operations Intra-front operations Euclidiean distance

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A two-archive algorithm with decomposition and fitness allocation for multi-modal multi-objective optimization

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INFORMATION SCIENCES 2021年 574卷 413-430页

作者： Li, Zhipan Zou, Juan Yang, Shengxiang Zheng, Jinhua Xiangtan Univ Key Lab Intelligent Comp & Informat Proc Minist Educ Informat Engn Coll Xiangtan Hunan Peoples R China Univ Xiangtan Fac Informat Engn Xiangtan 411105 Peoples R China Hunan Prov Key Lab Intelligent Informat Proc & Ap Hengyang 421002 Peoples R China De Montfort Univ Sch Comp Sci & Informat Leicester LE1 9BH Leics England

This paper proposes a two-archive algorithm with decomposition and fitness allocation for multi-modal multi-objective optimization problems which have more than one Pareto-optimal solution set corresponding to the same objective vector. The general framework of the proposed method uses two archives, the convergence archive (CA) and the diversity archive (DA), which focus on the convergence and diversity of population, respectively. Both archives are based on a decomposition-based framework. In CA, the population update strategy adopts a fitness scheme, which is designed according to the change state of population during evolution, combining the convergence of the objective space with the diversity of the decision space. In DA, we use the crowding distance strategy to ensure the diversity of the decision space. Moreover, different neighborhood criteria are used to ensure the convergence and diversity of population for two archives. The algorithm is shown to not only locate and maintain a larger number of Pareto-optimal sets, but also to obtain good diversity and convergence in both the decision and objective spaces. In addi-tion, the proposed algorithm is empirically compared with five state-of-the-art evolution-ary algorithms on two series of test functions. Comparison results show that the proposed algorithm has better performance than the competing algorithms. (c) 2021 Elsevier Inc. All rights reserved.

关键词： multi-modal multi-objective optimization Two-archive Decomposition Fitness allocation Crowding distance strategy Neighborhood criteria

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A Decomposition-based Hybrid Evolutionary Algorithm for multi-modal multi-objective optimization

A Decomposition-based Hybrid Evolutionary Algorithm for Mult...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： Peng, Yiming Ishibuchi, Hisao Southern Univ Sci & Technol Dept Comp Sci & Engn Guangdong Prov Key Lab Brain Inspired Intelligent Shenzhen 518055 Peoples R China

ISBN: (纸本)9781665442077

multi-modal multi-objective optimization problems (MMOPs) have received increasing attention from the evolutionary multi-objective optimization community. To solve MMOPs, an optimizer is required to locate multiple sets of Pareto optimal solutions in the decision space. In this paper, a novel decomposition-based hybrid evolutionary algorithm is proposed for handling MMOPs efficiently. In the proposed algorithm, each reference vector is associated with a sub-population. In this manner, each reference vector is able to preserve multiple optima of the corresponding sub-problem in its own sub-population. In each generation, the following three procedures are used to update each sub-population. First, the sub-population evolves independently based on the deterministic crowding mechanism to maintain the diversity in the decision space. Second, the sub-population evolves in a collaborative manner with neighboring sub-populations. Subsequently, solutions that are converging to the same optimal solution are identified. All identified solutions except for the best one are re-initialized. This mechanism impels the solutions in each sub-population to converge to different optima in the decision space. Experimental results show that the proposed algorithm achieves superior performance in comparison with four state-of-the-art algorithms on various test problems.

关键词： multi-objective optimization multi-modal multi-objective optimization niching MOEA/D

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Dynamic multi-modal multi-objective optimization: A Preliminary Study 17th

Dynamic Multi-modal Multi-objective Optimization: A Prelimin...

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17th International Conference on Parallel Problem Solving from Nature (PPSN)

作者： Peng, Yiming Ishibuchi, Hisao Southern Univ Sci & Technol Dept Comp Sci & Engn Guangdong Prov Key Lab Brain Inspired Intelligent Shenzhen 518055 Peoples R China

ISBN: (纸本)9783031147210;9783031147203

Many real-world multi-modal multi-objective optimization problems are subject to continuously changing environments, which requires the optimizer to track multiple equivalent Pareto sets in the decision space. To the best of our knowledge, this type of optimization problems has not been studied in the literature. To fill the research gap in this area, we provide a preliminary study on dynamic multi-modal multi-objective optimization. We give a formal definition of dynamic multi-modal multi-objective optimization problems and point out some key challenges in solving them. To facilitate algorithm development, we suggest a systematic approach to construct benchmark problems. Furthermore, we provide a feature-rich test suite containing 10 novel dynamic multi-modal multi-objective test problems.

关键词： Evolutionary multi-objective optimization multi-modal multi-objective optimization Dynamic multi-objective optimization Benchmark problems

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A Decomposition-based Large-scale multi-modal multi-objective optimization Algorithm

A Decomposition-based Large-scale Multi-modal Multi-objectiv...

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IEEE Congress on Evolutionary Computation (CEC) as part of the IEEE World Congress on Computational Intelligence (IEEE WCCI)

作者： Peng, Yiming Ishibuchi, Hisao Southern Univ Sci & Technol Dept Comp Sci & Engn Guangdong Prov Key Lab Brain Inspired Intelligent Shenzhen 518055 Peoples R China

ISBN: (纸本)9781728169293

A multi-modal multi-objective optimization problem is a special kind of multi-objective optimization problem with multiple Pareto subsets. In this paper, we propose an efficient multi-modal multi-objective optimization algorithm based on the widely used MOEA/D algorithm. In our proposed algorithm, each weight vector has its own sub-population. With a clearing mechanism and a greedy removal strategy, our proposed algorithm can effectively preserve equivalent Pareto optimal solutions (i.e., different Pareto optimal solutions with same objective values). Experimental results show that our proposed algorithm can effectively preserve the diversity of solutions in the decision space when handling large-scale multi-modal multi-objective optimization problems.

关键词： Evolutionary multi-objective optimization multi-modal multi-objective optimization diversity maintenance MOEA/D

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A knowledge-guided regional division based evolutionary algorithm for multi-modal multi-objective optimization

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APPLIED SOFT COMPUTING 2024年 165卷

作者： Lei, Xuanyan Xia, Yizhang Deng, Qi Zou, Juan Xiangtan Univ Hunan Engn Res Ctr Intelligent Syst Optimizat & Se Xiangtan 411105 Hunan Peoples R China

The characteristic of multi-modal multi-objective optimization problems (MMOPs) is that multiple equivalent Pareto solution sets (PSs) in the decision space correspond to the same Pareto front (PF) in the objective space. The difficulty in solving the MMOPs lies in how to maintain the distribution in space. Many multi- modal multi-objective evolutionary algorithms (MMEAs) take convergence as the primary selection criterion, which makes it difficult for the algorithm to find all PSs in the decision space. In view of this situation, this paper proposes a partitioned knowledge-guided MMEA with multi-stage. The algorithm makes stage changes according to the proportion of evaluation consumed by the algorithm during the evolution, and adjusts the environment selection strategy as the stage changes. At the beginning of evolution, region division is carried out to prevent the solutions on each PS from interfering with each other and evolving independently. When the evaluation consumption reaches a certain proportion, it enters the middle stage. The information of the obtained solutions are used to guide the evolutionary direction of the population, and the deleted promising solutions are reclaimed. In the later stage, the steady state updating is performed to improve the distribution of population. The experimental results on four multi-modal multi-objective test suites with different features show that the proposed algorithm is more competitive than other seven excellent algorithms.

关键词： Evolutionary algorithm multi-modal multi-objective optimization Region division Solutions reclaim strategy

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Decomposition in decision and objective space for multi-modal multi-objective optimization

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SWARM AND EVOLUTIONARY COMPUTATION 2021年 62卷 100842-100842页

作者： Pal, Monalisa Bandyopadhyay, Sanghamitra Indian Stat Inst Machine Intelligence Unit 203 Barrackpore Trunk Rd Kolkata 700108 India

multi-modal multi-objective optimization problems (MMMOPs) have multiple subsets within the Pareto-optimal Set, each independently mapping to the same Pareto-Front. Prevalent multi-objective evolutionary algorithms are not purely designed to search for multiple solution subsets, whereas, algorithms designed for MMMOPs demon-strate degraded performance in the objective space. This motivates the design of better algorithms for addressing MMMOPs. The present work identifies the crowding illusion problem originating from using crowding distance globally over the entire decision space. Subsequently, an evolutionary framework, called graph Laplacian based optimization using Reference vector assisted Decomposition (LORD), is proposed, which uses decomposition in both objective and decision space for dealing with MMMOPs. Its filtering step is further extended to present LORD-II algorithm, which demonstrates its dynamics on multi-modal many-objective problems. The efficacies of the frameworks are established by comparing their performance on test instances from the CEC 2019 multi-modal multi-objective test suite and polygon problems with the state-of-the-art algorithms for MMMOPs and other multi-and many-objective evolutionary algorithms. The manuscript is concluded by mentioning the limitations of the proposed frameworks and future directions to design still better algorithms for MMMOPs. The source code is available at https://***/lord .

关键词： multi-modal multi-objective optimization Non-dominated sorting Crowding distance Reference vector based decomposition Graph Laplacian

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multi-modal multi-objective Evolutionary optimization for Problems with Solutions of Variable-Length

Multi-Modal Multi-Objective Evolutionary Optimization for Pr...

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IEEE Congress on Evolutionary Computation (IEEE CEC)

作者： Moshaiov, Amiram Breslav, Yosef Farhi, Eliran Tel Aviv Univ Sch Mech Engn Tel Aviv Israel

ISBN: (纸本)9781728183923

This paper focuses on solving a special kind of multi-modal multi-objective optimization problems (MMOPs) in which solutions are of variable length. First, problem definition and solution framework is suggested to allow using standard multi-modal multi-objective evolutionary algorithms (MMEAs) to solve the considered type of problems. Next, a real-life example of the considered type of problems is suggested concerning optimal antennas' layout-allocation design for a wireless communication network. Finally, a modification to NSGA-II is suggested and employed to solve such layout problems. When compared with other MMEAs, it is shown that the proposed algorithm provides not only better solution diversity in the decision-space, but also solutions with superior performance vectors. It is suggested here that this is attributed to the type of archive that is used here.

关键词： multi-concept optimization multi-modal multi-objective optimization wireless communication network location optimization variable number of dimensions variable length problem MMEAs

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