A multi-modal multi-objective evolutionary algorithm based on scaled niche distance

Multi-modal multi-objective optimization problems (MMOPs) refer to several solutions in the decision space that share the same or similar objective value. Balancing the diversity of the objective space and decision space while maintaining the convergence of the population is a challenging and important problem. To address this issue, a novel multi-modal multi-objective evolutionary algorithm (MMEA) named MMEA-SND is proposed in this study. In the MMEA-SND, to locate Pareto-optimal solutions, and improve the diversity of solutions in the decision space, a diversity fitness is designed by the niche method to calculate the fitness of solutions in the diversity archive. In order to balance the diversity of solutions in the objective space and decision space, a scaled niche distance (SND) method is proposed in environmental selection. In this context, SND are utilized to measure the distances between each solution in the objective space and decision space. Furthermore, a parameter is implemented to avoid disregarding locally optimal solutions. To verify the performance of MMEA-SND, six state-ofthe-art MMEAs are adopted to make a comparison on 42 benchmark problems. The experimental results show that the proposed MMEA-SND achieves a competitive performance in solving MMOPs.