Indicator-Based Constrained Multiobjective Evolutionary Algorithms

• Published in: IEEE transactions on systems, man, and cybernetics. Systems man, and cybernetics. Systems, 2021-09, Vol.51 (9), p.5414-5426
• Main Authors: Liu, Zhi-Zhong, Wang, Yong, Wang, Bing-Chuan
• Format: Article
• Language: English
• Subjects: Automation; Constrained multiobjective evolutionary algorithms (CMOEAs); constrained multiobjective optimization problems (CMOPs); constraint-handling technique; Constraints; Cybernetics; Decision feedback equalizers; Evolutionary algorithms; Evolutionary computation; Genetic algorithms; Handling; indicator; Linear programming; Multiple objective analysis; Optimization; Pareto optimization
• ISSN: 2168-2216; 2168-2232
• DOI: 10.1109/TSMC.2019.2954491

Solving constrained multiobjective optimization problems (CMOPs) is a challenging task since it is necessary to optimize several conflicting objective functions and handle various constraints simultaneously. A promising way to solve CMOPs is to integrate multiobjective evolutionary algorithms (MOEAs) with constraint-handling techniques, and the resultant algorithms are called constrained MOEAs (CMOEAs). At present, many attempts have been made to combine dominance-based and decomposition-based MOEAs with diverse constraint-handling techniques together. However, for another main branch of MOEAs, i.e., indicator-based MOEAs, almost no effort has been devoted to extending them for solving CMOPs. In this article, we make the first study on the possibility and rationality of combining indicator-based MOEAs with constraint-handling techniques together. Afterward, we develop an indicator-based CMOEA framework which can combine indicator-based MOEAs with constraint-handling techniques conveniently. Based on the proposed framework, nine indicator-based CMOEAs are developed. Systemic experiments have been conducted on 19 widely used constrained multiobjective optimization test functions to identify the characteristics of these nine indicator-based CMOEAs. The experimental results suggest that both indicator-based MOEAs and constraint-handing techniques play very important roles in the performance of indicator-based CMOEAs. Some practical suggestions are also given about how to select appropriate indicator-based CMOEAs. Besides, we select a superior approach from these nine indicator-based CMOEAs and compare its performance with five state-of-the-art CMOEAs. The comparison results suggest that the selected indicator-based CMOEA can obtain quite competitive performance. It is thus believed that this article would encourage researchers to pay more attention to indicator-based CMOEAs in the future.