A Similar-Niching-Based Differential Evolution for Constrained Multimodal Multiobjective Optimization

Abstract

In constrained multimodal multiobjective optimization problems (CMMOPs), the existence of discrete and confined feasible regions bring great challenges to current multiobjective optimization evolutionary algorithms (MOEAs). To address these challenges, this article proposes a constrained multimodal multiobjective differential evolution algorithm, which incorporates a similar-niching-based reproduction operator and a novel environmental selection mechanism. The proposed algorithm initiates by segregating the population into distinct niches, thereby promoting independent evolution within each niche. This segmentation enhances the exploration of multiple discrete feasible regions, thus improving the capacity to find diverse Pareto optimal solutions. Moreover, the algorithm selects the most similar niche to collaboratively generate solutions, further enhancing its ability to generate effective feasible solutions. To improve the diversity within the population, the proposed environmental selection mechanism gives preference to solutions that enhance the distribution of the next-generation population. By considering the diversity in both two spaces, the population retains more pareto optimal solutions. Based on the Friedman test results of the comparison experiment with other representative algorithms and the champion algorithm of the CEC2023 CMMOPs competition, the proposed algorithm attained the top ranking, thereby reinforcing its demonstrated superiority. Meanwhile, the proposed algorithm is used to solve the constrained multimodal multiobjective location selection problem and results show its superiority.