Dynamic niching particle swarm optimization with an external archive-guided mechanism for multimodal multi-objective optimization

Abstract

Multimodal multi-objective optimization problems (MMOPs) contain multiple equivalent Pareto optimal sets (PSs) corresponding to the same Pareto front (PF). However, simultaneously locating well-distributed and well-converged multiple equivalent global PSs and PF remains challenging. Therefore, this paper proposes dynamic niching particle swarm optimization (PSO) with an external archive-guided (AG) mechanism, termed DNPSO-AG, for solving MMOPs. In DNPSO-AG, a clustering-based dynamic niching technique is integrated with PSO to divide the population into multiple niches. In addition, a leader updating method controls the updating of the leaders. Furthermore, a novel external archive-guided mechanism guides the evolution of multiple niches and enhances the distribution of solutions, which comprises two strategies: the adaptive division of the external archive strategy, which adaptively divides the external archive into multiple sub-archives, and the distance-based sub-archive and niche matching strategy, which assigns sub-archives to multiple niches for maintenance. The experimental results demonstrate that the proposed DNPSO-AG outperforms seven other state-of-the-art competitors on the CEC 2019 MMOP test suite in terms of the inverted generational distance (IGD) and IGD in the decision space (IGDX) metrics, with improvements of 21.3% and 9.1% over the best-performing competitor, respectively.