An Indicator-Based Many-Objective Evolutionary Algorithm With Boundary Protection

Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based sel...

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Vydané v:	IEEE transactions on cybernetics Ročník 51; číslo 9; s. 4553 - 4566
Hlavní autori:	Liang, Zhengping, Luo, Tingting, Hu, Kaifeng, Ma, Xiaoliang, Zhu, Zexuan
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States IEEE 01.09.2021 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
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ISSN:	2168-2267, 2168-2275, 2168-2275
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Abstract	Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the <inline-formula> <tex-math notation="LaTeX">{I}_{{\epsilon }^{+}} </tex-math></inline-formula> indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest <inline-formula> <tex-math notation="LaTeX">{I}_{{\epsilon }^{+}} </tex-math></inline-formula> value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e., <inline-formula> <tex-math notation="LaTeX">{I}_{{{ {SDE}}}^{+}} </tex-math></inline-formula>, SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms.
AbstractList	Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the <inline-formula> <tex-math notation="LaTeX">{I}_{{\epsilon }^{+}} </tex-math></inline-formula> indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest <inline-formula> <tex-math notation="LaTeX">{I}_{{\epsilon }^{+}} </tex-math></inline-formula> value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e., <inline-formula> <tex-math notation="LaTeX">{I}_{{{ {SDE}}}^{+}} </tex-math></inline-formula>, SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms. Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the Iε+ indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest Iε+ value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e., ISDE+, SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms. Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the [Formula Omitted] indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest [Formula Omitted] value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e., [Formula Omitted], SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms. Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the Iϵ+ indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest Iϵ+ value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e., I SDE+ , SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms.Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the Iϵ+ indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest Iϵ+ value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e., I SDE+ , SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms.
Author	Zhu, Zexuan Luo, Tingting Liang, Zhengping Hu, Kaifeng Ma, Xiaoliang
Author_xml	– sequence: 1 givenname: Zhengping orcidid: 0000-0001-6210-8373 surname: Liang fullname: Liang, Zhengping email: liangzp@szu.edu.cn organization: College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China – sequence: 2 givenname: Tingting surname: Luo fullname: Luo, Tingting email: luotingting2017@email.szu.edu.cn organization: College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China – sequence: 3 givenname: Kaifeng orcidid: 0000-0002-6762-5035 surname: Hu fullname: Hu, Kaifeng email: kaifengh@qq.com organization: College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China – sequence: 4 givenname: Xiaoliang surname: Ma fullname: Ma, Xiaoliang email: maxiaoliang@szu.edu.cn organization: College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China – sequence: 5 givenname: Zexuan orcidid: 0000-0001-8479-6904 surname: Zhu fullname: Zhu, Zexuan email: zhuzx@szu.edu.cn organization: College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, China
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Snippet	Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number...
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Title	An Indicator-Based Many-Objective Evolutionary Algorithm With Boundary Protection
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