Multimodal multi-objective evolutionary algorithm for multiple path planning

•The differences between discrete and continuous MOPs are analyzed.•A special environmental selection strategy is proposed to maintain the diversity.•A diversity-based fitness indicator is proposed.•A novel multimodal multi-objective evolutionary algorithm is proposed. The multi-objective path planning problem has received much attention recently. Traditional solving methods try to find a single optimal path without considering the multiformity of the paths. In this study, we first analyze the situation that several different paths may have the same objective values, termed as multi-modal minimum path problems. To address these problems, we propose a novel solution-encoding method, which decreases the size of decision-space greatly. Then, to maintain the population diversity in the decision space, we propose an environmental selection strategy, in which the duplicate solutions are deleted first and then a second-selection method is adopted. Finally, an effective multi-objective evolutionary algorithm based on the special environmental selection is proposed, termed MMEA-SES. Through the experiments, the proposed method is proved effective and efficient compared to other state-of-the-art algorithms for multimodal multi-objective path planning.