Hybrid Operator and Strengthened Diversity Improving for Multimodal Multi-Objective Optimization

Multimodal multi-objective optimization problems (MMOPs) contain multiple equivalent Pareto subsets (PSs) corresponding to a single Pareto front (PF), resulting in difficulty in maintaining promising diversities in both objective and decision spaces to find these PSs. Widely used to solve MMOPs, evolutionary algorithms mainly consist of evolutionary operators that generate new solutions and fitness evaluations of the solutions. To enhance performance in solving MMOPs, this paper proposes a multimodal multi-objective optimization evolutionary algorithm based on a hybrid operator and strengthened diversity improving. Specifically, a hybrid operator mechanism is devised to ensure the exploration of the decision space in the early stage and approximation to the optima in the latter stage. Moreover, an elitist-assisted differential evolution mechanism is designed for the early exploration stage. In addition, a new fitness function is proposed and used in environmental and mating selections to simultaneously evaluate diversities for PF and PSs. Experimental studies on 11 widely used benchmark instances from a test suite verify the superiority or at least competitiveness of the proposed methods compared to five state-of-the-art algorithms tailored for MMOPs.