A grid-guided particle swarm optimizer for multimodal multi-objective problems

This paper proposes a grid-guided particle swarm optimizer for solving multimodal multi-objective optimization problems that may have multiple disjoint Pareto sets corresponding to the same Pareto front. The concept of grid in the decision space is adopted to detect the special promising subregions, and accordingly to generate multiple subpopulations. The grid-guided technique can maintain the diversity of the population during the search process and improve the search efficiency. To obtain a well distributed Pareto optimal set, an external archive maintenance strategy is employed to select and store the solutions found in each generation. In addition, nine new multimodal multi-objective benchmark test functions are designed. The proposed algorithm is compared with ten state-of-the-art evolutionary algorithms on thirty-seven test functions. Moreover, the proposed algorithm is applied to solve a real-world problem. The experimental results demonstrate that the proposed algorithm is able to achieve superior performance compared with the alternative evolutionary methods considered. •A grid-based technique is employed to increase the population diversity and improve the search efficiency.•A self-adjusting parameter scheme and a leader selection strategy are introduced to improve the performance of the particle swarm optimizer.•A maintenance strategy for the external archive is proposed to promote the distribution of Pareto-optimal solutions.•Nine new test functions are designed to assess the performance of algorithms more comprehensively.•The proposed algorithm is applied to solve a real-world problem.