A dual-population coevolutionary algorithm for balancing convergence and diversity in the decision space in multimodal multi-objective optimization

Abstract

Many multimodal multi-objective evolutionary algorithms (MMEAs) are effective in solving multimodal multi-objective problems (MMOPs), which have multiple equivalent Pareto optimal sets (PSs) mapping to the same Pareto optimal front (PF). Due to the existence of the global convergence-first mechanism, these MMEAs will remove the solutions that can improve the diversity of the decision space but have poor convergence and even lead to the loss of PS when encountering MMOPs with an imbalance between convergence and diversity in the decision space (MMOP-ICD) or an MMOP with a local PS (MMOPL). We propose a new dual-population coevolutionary algorithm to address these issues. The auxiliary population helps the main population locate areas where equivalent PSs may exist, and the main population focuses on balancing convergence and diversity in the decision space. When updating the auxiliary population, a strength local convergence quality (SLCQ) is used to explore the distribution of the equivalent PSs. When updating the main population, the new niche-based truncation strategy first deletes the solutions that contribute less to convergence. Then, a distance-based subset selection method balances the diversity between the decision and objective spaces. The comparison results show the overall performance of the proposed algorithm is significantly better than other state-of-the-art algorithms.