Two-Stage Clustering and Independent Competing-Based Evolutionary Algorithm for Multimodal Multiobjective Optimization

The multimodal multi-objective optimization problem (MMOP) involves multiple distinct components of the Pareto set (PS), which correspond to the same Pareto front (PF). Most existing multimodal multi-objective evolutionary algorithms (MMOEAs) face challenges in achieving both accuracy and timeliness in solving MMOPs. In this article, a two-stage clustering and independent competing based evolutionary algorithm (TSCICEA) is proposed for solving MMOPs. Firstly, in the early stage of population evolution, the K-means technique is used to coarsely cluster the population into multiple independent subpopulations, which aims to rapidly ascertain the approximate distribution structure of modalities and preliminarily locate their spatial positions. In the later stage, the DBSCAN technique is utilized to conduct fine clustering of the population, which aims to re-cluster misclustered individuals in the coarse clustering into new subpopulations, thus achieving a precise distinction between different modalities. Subsequently, to accurately identify the corresponding modality for each subpopulation, an independent competing strategy is proposed. This strategy can automatically assign different identification approaches for each modality based on their differences, and it simultaneously manages different modalities through parallel execution, thus significantly enhancing both the accuracy and timeliness of modality identification. To evaluate the effectiveness of TSCICEA, we compare it against state-of-the-art algorithms on benchmark test problems with 2–15 objectives and 4–15 variables. Experimental results demonstrate that TSCICEA achieves superior performance in terms of the IEDRX, IMST, and HV indicators