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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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 51; no. 9; pp. 4553 - 4566
Main Authors: Liang, Zhengping, Luo, Tingting, Hu, Kaifeng, Ma, Xiaoliang, Zhu, Zexuan
Format: Journal Article
Language:English
Published: United States IEEE 01.09.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">I ϵ⁺ indicator
boundary protection
Computational complexity
Convergence
coverage
diversity
Diversity reception
evolutionary algorithm
Evolutionary algorithms
Evolutionary computation
Genetic algorithms
many-objective evolutionary algorithm (MaOEA)
multiobjective evolutionary algorithm (MOEA)
Multiple objective analysis
Optimization
Sociology
Statistics
Strategy
ISSN:2168-2267, 2168-2275, 2168-2275
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Summary: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.
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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2019.2960302