A Multi-Modal Multi-Objective Evolutionary Algorithm Considering Boundary Information

It is difficult for traditional multi-objective evolutionary algorithms (MOEAs) to find equivalent and approximate equivalent solutions for multi-modal multi-objective optimization problems (MMOPs). This results in decision-makers having no available alternatives if changes in the external environment render the original solution un-executable. Although some multi-modal multi-objective evolutionary algorithms (MMOEAs) have been designed to solve this problem, their search capabilities are weak. This paper designs a new MMOEA named BIMOEA. It uses improved local convergence fitness for environment selection, in which the distances between an individual and its neighbors are used to average the number of times that this individual is dominated. This improvement can reduce the occurrence probability of the same fitness and enhances the algorithm's ability to screen individuals. In addition, a new crowding distance calculation method is designed to promote population diversity in decision space. It not only calculates the crowding distances between individuals but also calculates the crowding distances between individuals and the boundary of the decision space, which promotes a more even distribution of the population in the decision space and improves the population's ability to explore unknown regions. The experiments on 17 benchmark problems show that BIMOEA can effectively improve search capabilities and provide decision-makers with more comprehensive solutions.