A Framework to Handle Multimodal Multiobjective Optimization in Decomposition-Based Evolutionary Algorithms
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...
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| Vydané v: | IEEE transactions on evolutionary computation Ročník 24; číslo 4; s. 720 - 734 |
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| Jazyk: | English |
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New York
IEEE
01.08.2020
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| ISSN: | 1089-778X, 1941-0026 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Tanabe, Ryoji Ishibuchi, Hisao |
| Author_xml | – sequence: 1 givenname: Ryoji orcidid: 0000-0003-4049-0393 surname: Tanabe fullname: Tanabe, Ryoji email: rt.ryoji.tanabe@gmail.com organization: Department of Computer Science and Engineering, Shenzhen Key Laboratory of Computational Intelligence, University Key Laboratory of Evolving Intelligent Systems of Guangdong Province, Southern University of Science and Technology, Shenzhen, China – sequence: 2 givenname: Hisao orcidid: 0000-0001-9186-6472 surname: Ishibuchi fullname: Ishibuchi, Hisao email: hisao@sustech.edu.cn organization: Department of Computer Science and Engineering, Shenzhen Key Laboratory of Computational Intelligence, University Key Laboratory of Evolving Intelligent Systems of Guangdong Province, Southern University of Science and Technology, Shenzhen, China |
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| SubjectTerms | Benchmark testing Decision making Decomposition Decomposition-based evolutionary algorithms Equivalence Evolutionary algorithms Evolutionary computation Genetic algorithms Indexes multimodal multiobjective optimization Multiple objective analysis Optimization Pareto optimization Pareto optimum Performance enhancement reference vector-based evolutionary algorithms Solution space solution space diversity Spatial diversity |
| Title | A Framework to Handle Multimodal Multiobjective Optimization in Decomposition-Based Evolutionary Algorithms |
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