Block optimization and switchable hybrid clustering for multimodal multiobjective evolutionary optimization with shifted local Pareto front

Abstract

Existing multimodal multiobjective evolutionary algorithms (MMOEAs) often struggle with translated test functions and fail to effectively identify and maintain local Pareto fronts (PFs) due to the lack of niche-based strategies. To overcome these limitations, a novel two-stage MMOEA termed MMOEA-BH is proposed with block optimization and switchable hybrid clustering. Key innovations include a block optimization strategy utilizing adaptive region stretching and regression-based dimensional analysis, and a switchable hybrid clustering method combining affinity propagation, k-means, and density-based spatial clustering of applications with noise (DBSCAN). These innovations enable MMOEA-BH to effectively address translated test functions and maintain both global and local niches in decision and objective spaces. To address the lack of robust evaluation methods for MMOEAs when solving translated MMOPs, a new set of shifted multimodal multiobjective functions (SMMF) is introduced by translating the existing MMOPs. Experimental results, including comparisons with state-of-the-art algorithms, ablation studies on block optimization, and sensitivity analyses on key parameters, demonstrate that MMOEA-BH outperforms existing algorithms on these SMMF functions. This highlights the efficacy of the proposed block optimization and switchable hybrid clustering strategies in solving MMOPs with translation characteristics.