A Decomposition-based Hybrid Evolutionary Algorithm for Multi-modal Multi-objective Optimization

Abstract

Multi-modal multi-objective optimization problems (MMOPs) have received increasing attention from the evolutionary multi-objective optimization community. To solve MMOPs, an optimizer is required to locate multiple sets of Pareto optimal solutions in the decision space. In this paper, a novel decomposition-based hybrid evolutionary algorithm is proposed for handling MMOPs efficiently. In the proposed algorithm, each reference vector is associated with a sub-population. In this manner, each reference vector is able to preserve multiple optima of the corresponding sub-problem in its own sub-population. In each generation, the following three procedures are used to update each sub-population. First, the sub-population evolves independently based on the deterministic crowding mechanism to maintain the diversity in the decision space. Second, the sub-population evolves in a collaborative manner with neighboring sub-populations. Subsequently, solutions that are converging to the same optimal solution are identified. All identified solutions except for the best one are re-initialized. This mechanism impels the solutions in each sub-population to converge to different optima in the decision space. Experimental results show that the proposed algorithm achieves superior performance in comparison with four state-of-the-art algorithms on various test problems.