Multi-objective evolution strategy for multimodal multi-objective optimization

Abstract

In the past decades, various effective and efficient multi-objective evolutionary algorithms (MOEAs) have been proposed for solving multi-objective optimization problems. However, existing MOEAs cannot satisfactorily address multimodal multi-objective optimization problems that demand to find multiple groups of optimal solutions simultaneously. In this paper, we propose an evolution strategy to solve multimodal multi-objective optimization problems, named MMO-MOES. This paper focus on searching for well-converged and well-distributed solutions in the decision space. Firstly, a novel niching strategy in the decision space, which imitates the repulsive force among isotropic magnetic particles, is adopted to drive the individuals to preserve uniform distances from each other and spread to the whole Pareto set automatically. This strategy is effective in finding multiple groups of optimal solutions simultaneously. Secondly, MMO-MOES requires only a very small population size to obtain a well-distributed and well-converged set of Pareto optimal solutions in the decision space. The greater the population size, the clearer contour of the approximate Pareto sets and Pareto front will be. Finally, the MMO-MOES is compared against some chosen leading-edge MMOEAs. The experimental results demonstrate that MMO-MOES provides exceptional performance in searching for the complete Pareto subsets and Pareto front on Omni-test problem, Symmetrical Parts (SYM-PART) problems, and CEC 2019 Multimodal Multi-Objective Optimization Problems (MMOPs) test suite.