A Hierarchical Clustering Based Evolutionary Algorithm for Multimodal Multiobjective Optimization

Multi-modal multi-objective optimization tasks (MMOPs) involve locating several distinct yet equivalent Pareto solution sets (PSs) within the decision space, all of which correspond to an identical Pareto front (PF) in the objective space. However, existing multi-modal multi-objective evolutionary algorithms (MMEAs) often suffer from imbalanced solution distributions or fail to preserve high-quality local PSs due to dominance pressure and inadequate diversity maintenance. To address these issues, we propose HRSCD, a novel MMEA that integrates hierarchical ranking with a specialized crowding distance mechanism. The crowding distance is enhanced by Affinity Propagation (AP) clustering within each non-dominated front, enabling more accurate and adaptive diversity estimation. Meanwhile, hierarchical ranking incorporates a tunable parameter to selectively archive individuals that are non-dominated with respect to the global PF, thereby preserving both convergence and local solution diversity. Experimental evaluations on 22 benchmark instances demonstrate that HRSCD significantly outperforms six state-of-the-art MMEAs in terms of multi-modal performance metrics. The results confirm its effectiveness in maintaining well-distributed, high-quality equivalent PSs, making it a competitive approach for solving complex MMOPs.