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• This study's key contributions are: • A Multimodal Multi-objective Evolutionary Algorithm based on Bi-dynamic Niche Strategy and Adaptive Weight Decomposition (MOEA/D-BDN) is proposed. • A decomposition-based approach and a historically excellent individual archiving strategy is designed. • A dual-space integrated ecological locality distance-based method is proposed. • a bi-dynamic habitat distance (BND) to calculate combined congestion in these spaces for the Pareto-optimal solution set. • An adaptive weight adjustment strategy is employed. Recently, multimodal multi-objective problems (MMOPs) have emerged as a prominent research focus in the field of multi-objective optimization. The key challenge in solving MMOPs is to identify multiple equivalent Pareto-optimal solution sets corresponding to discontinuous or complex Pareto fronts. To address this challenge, this paper proposes a novel multimodal multi-objective evolutionary algorithm (MOEA/D-BDN), which integrates a bi-dynamic niche strategy with an adaptive weight decomposition mechanism. Within the decomposition framework, the algorithm introduces an archiving mechanism to preserve historically outstanding individuals, thereby maintaining population diversity and convergence. Furthermore, a bi-dynamic niche distance (BDN) metric is employed to evaluate the overall density in both objective and decision spaces, enabling more effective updating and removal of solutions from the archive. To improve the uniformity of the Pareto front approximation, an adaptive weight adjustment strategy is used to dynamically guide the search direction. Experimental results on several benchmark MMOPs show that MOEA/D-BDN significantly outperforms state-of-the-art multimodal multi-objective evolutionary algorithms in terms of convergence, diversity, and distribution quality, demonstrating its effectiveness and competitiveness in handling complex MMOPs.
Zhang et al. (Wed,) studied this question.