A Multimodal Multiobjective Particle Swarm Optimization Algorithm Based on Special Crowding Distance and a Modality-Aware Strategy.

Existing multiobjective evolutionary algorithms (MOEAs) struggle to simultaneously achieve high-precision approximation of the Pareto front (PF) and effectively identify all Pareto subsets in the decision space. To address this issue, this article proposes a multimodal multiobjective particle swarm optimization (MOPSO) algorithm based on special crowding distance (SCD) and a modality-aware strategy (MMOPSO_SCDMA). The algorithm designs an SCD that simultaneously quantifies the distribution density of individuals in both the decision space and the objective space, employing a dynamic threshold selection strategy to balance diversity across the two spaces. An adaptive-parameter DBSCAN algorithm periodically clusters the external archive (EA) to construct a global leader set (GLS), while in nonclustering phases a reference point method generates a local leader set (LLS), thereby achieving a dynamic balance between coarse-grained exploration and fine-grained exploitation. In addition, a boundary-distance-sensitive mutation operator is introduced, which dynamically adjusts the perturbation intensity according to the particle position, effectively mitigating premature convergence. The experimental results on 20 test functions from the MMF and MMMOP benchmarks demonstrate that MMOPSO_SCDMA significantly outperforms 11 existing state-of-the-art algorithms across multiple performance metrics.