A neighborhood-assisted evolutionary algorithm for multimodal multi-objective optimization

Multi-modal multi-objective optimization problems (MMOPs) involve multiple Pareto sets (PSs) in decision space corresponding to the same Pareto front (PF) in objective space. The difficulty lies in locating multiple equivalent PSs while ensuring a well-converged and well-distributed PF. To address this, a neighborhood-assisted reproduction strategy is proposed. Through interactions with non-dominated solutions, the generated offspring could spread out along the PF, while ineractions with neighbors could improve the convergence ability. Importantly, individuals can participate in multiple neighborhoods, reducing the computational burden. Additionally, a neighborhood-assisted environmental selection strategy is prposed to encourage exploration of diverse solution regions, ensuring a balanced distribution of the population and preservation of multiple PSs. Comparative experiments are implemented on the CEC 2019 MMOPs test suite, and the superior performance of the proposed algorithm is demonstrated in comparison to several state-of-the-art approaches.