Multimodal multi-objective optimization: Comparative study of the state-of-the-art

Multimodal multi-objective problems (MMOPs) commonly arise in the real world where distant solutions in decision space correspond to very similar objective values. To obtain more Pareto optimal solutions for MMOPs, many multimodal multi-objective evolutionary algorithms (MMEAs) have been proposed. For now, few studies have encompassed most of the representative MMEAs and made a comparative comparison. In this study, we first review the related works during the last two decades. Then, we choose 15 state-of-the-art algorithms that utilize different diversity-maintaining techniques and compared their performance on different types of the existing test suites. Experimental results indicate the strengths and weaknesses of different techniques on different types of MMOPs, thus providing guidance on how to select/design MMEAs in specific scenarios.