Goal-directed multimodal multi-objective evolutionary algorithm converging on population derivation

Abstract

Recently, multimodal multi-objective problems (MMOPs) have become a popular research field in multi-objective optimization problems. The key to solving MMOPs lies in finding multiple equivalent Pareto sets (PSs) corresponding to the Pareto front (PF). Therefore, while balancing the convergence and diversity of the algorithm, it is crucial to enhance its search ability in the decision space. Current research mainly focuses on identifying solutions with exploratory potential, retaining their advantages during evolution, thereby increasing the chances of finding more equivalent PSs. However, these potential solutions and the resulting high-quality solutions are often scarce and require multiple iterations to effectively explore their space. Based on this, this paper proposes a goal-directed multimodal multi-objective evolutionary algorithm converging on population derivation, which includes three stages: population derivation, diversity maintenance, and convergence. In the population derivation stage, the algorithm identifies individuals with exploratory potential and derives more individuals in their subspaces to facilitate more efficient exploration of these subspaces. The diversity maintenance stage balances the population's distribution in both the decision and objective spaces, while the convergence stage accelerates the population's approach to the true PF. These three stages work synergistically under their respective objectives to optimize the distribution of solution sets in both the objective and decision spaces and to obtain the complete set of equivalent Pareto solutions. Experimental results show that this algorithm outperforms several mainstream algorithms on multiple MMOP test sets.