A Local Pareto Front Guided Microscale Search Algorithm for Multi-Modal Multi-Objective Optimization

Multimodal multiobjective optimization problems, characterized by multiple solutions mapping to identical objective vectors, are ubiquitous in real-world applications. Despite their prevalence, most existing multimodal multiobjective evolutionary algorithms (MMOEAs) predominantly focus on identifying global Pareto sets, often overlooking the equally significant local Pareto sets. While some algorithms attempt to address local Pareto sets, their performance in the objective space remains suboptimal. The inherent challenge lies in the fact that a single strategy cannot effectively tackle problems with and without local Pareto fronts. This study proposes a novel approach that first detects the presence of local Pareto fronts using a neural network, thereby enabling adaptive adjustments to the algorithm’s selection strategy and search scope. Based on this detection mechanism, we design a microscale searching multimodal multiobjective evolutionary algorithm (MMOEA_MS). Through extensive experiments on twenty-two benchmark problems, MMOEA_MS demonstrates superior performance in identifying local Pareto fronts and outperforms existing algorithms in the objective space. This study highlights the effectiveness of MMOEA_MS in solving multimodal multiobjective optimization problems with diverse Pareto front characteristics, thereby addressing key limitations of current methodologies.