Differential evolution based on local grid search for multimodal multiobjective optimization with local Pareto fronts

Multimodal multiobjective optimization problems (MMOPs) are characterized by multiple Pareto optimal solutions corresponding to the same objective vector. MMOPs with local Pareto fronts (MMOPLs) are common in the real world. However, existing multimodal multiobjective evolutionary algorithms (MMEAs) face significant challenges in finding both global and local Pareto sets (PSs) when dealing with MMOPLs. For this purpose, we propose a differential evolution algorithm based on local grid search, called LGSDE. LGSDE establishes a local grid region for each solution, achieving a balanced distribution by judging the dominant relationship only among solutions within that local region. This approach enables the population to converge towards both global and local PSs. We compare LGSDE with other state-of-the-art MMEAs. Experimental results demonstrate LGSDE exhibits superiority in addressing MMOPLs.