Journal
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
Volume 51, Issue 9, Pages 5414-5426Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSMC.2019.2954491
Keywords
Linear programming; Pareto optimization; Evolutionary computation; Cybernetics; Automation; Decision feedback equalizers; Constrained multiobjective evolutionary algorithms (CMOEAs); constrained multiobjective optimization problems (CMOPs); constraint-handling technique; indicator
Funding
- Innovation-Driven Plan in Central South University [2018CX010]
- National Natural Science Foundation of China [61673397, 61976225]
- Beijing Advanced Innovation Center for Intelligent Robots and Systems [2018IRS06]
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This study combines indicator-based multiobjective evolutionary algorithms with constraint-handling techniques to develop a framework for constrained multiobjective optimization. Nine indicator-based CMOEAs were developed and experimentally evaluated on 19 widely used test functions. The results show the importance of both indicator-based MOEAs and constraint-handling techniques in the performance of indicator-based CMOEAs, providing valuable insights for future research.
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.
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