Indicator-Based Constrained Multiobjective Evolutionary Algorithms
Indicator-Based Constrained Multiobjective Evolutionary Algorithms
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DOI：
10.1109/tsmc.2019.2954491
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
Zhi-Zhong Liu;Yong Wang;Bing-chuan Wang
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文献类型：
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作者：
Zhi-Zhong Liu;Yong Wang;Bing-chuan Wang
求解约束多目标优化问题是一项具有挑战性的任务，因为它需要同时优化多个相互冲突的目标函数并处理各种约束。将多目标进化算法（moea）与约束处理技术相结合是求解cmoops的一种很有前途的方法，这种算法被称为约束moea （cmoea）。目前，已经有许多尝试将基于支配和基于分解的moea与各种约束处理技术相结合。然而，对于moea的另一个主要分支，即基于指标的moea，几乎没有投入任何努力来扩展它们以解决CMOPs。本文首次探讨了基于指标的moea与约束处理技术相结合的可能性和合理性。然后，我们开发了一个基于指标的CMOEA框架，该框架可以方便地将基于指标的moea与约束处理技术结合起来。基于所提出的框架，开发了9个基于指标的cmoea。对19个广泛使用的约束多目标优化测试函数进行了系统实验，以识别这9种基于指标的cmoea的特征。实验结果表明，基于指标的决策模型和约束处理技术对基于指标的决策模型的性能起着非常重要的作用。本文还就如何选择合适的指标型cmoea提出了一些实用建议。此外，我们从这9种基于指标的cmoea中选择了一种较优的方法，并将其与5种最先进的cmoea进行了比较。对比结果表明，所选择的基于指标的CMOEA可以获得较好的绩效。因此，相信本文将鼓励研究者在未来更多地关注基于指标的cmoea。
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.