Enhancing Diversity and Convergence in MMOPs with a Gaussian Similarity-Based Evolutionary Algorithm

Abstract

Multi-modal multi-objective optimization problems (MMOPs) are challenging due to multiple solutions sharing similar objective values. Existing algorithms for solving MMOPs typically evaluate the crowding in the decision space and objective space independently, leading to an imbalance in diversity between the two spaces. We introduce a mechanism that balances diversity in both the decision and objective spaces, aiming to enhance diversity while maintaining convergence in both spaces. We propose a multi-modal multi-objective evolutionary algorithm (MMEA) that selects qualified solutions based on Gaussian similarity. Gaussian similarity assesses the closeness of solution pairs and serves as the diversity fitness criterion for the algorithm. We conducted experiments on 28 benchmark problems and compared MMEA-GS with five state-of-the-art approaches. The results demonstrate that MMEA-GS effectively addresses most MMOPs, achieving higher diversity and convergence.