A niching differential evolution with Hilbert curve for multimodal multi-objective optimization

Abstract

Multimodal multi-objective optimization problems have a many-to-one relationship between the decision space and the objective space. That is, distinct solutions in the decision space share the same objective value. How to coordinate population convergence and diversity while locating multimodal solutions is a challenging research topic. Some evolutionary algorithms using niching techniques have been reported in the literature. These algorithms prefer to induce multiple niches based on population information. Owing to the impact of convergence-first principle, the population tends to gather in easier-to-search regions, making it tough to yield more dispersed solutions in different niches. To remedy this situation, this paper proposes a niching differential evolution with Hilbert curve. First, a neighborhood-driven reproduction method is presented based on Hilbert curve, which features a two-layer architecture to capture promising regions and identify multimodal solutions. Second, a convergence-based density indicator is designed as a selection criterion to distinguish between convergence solutions and diversity solutions in the decision space. Moreover, fifteen intricate multimodal multi-objective test functions are devised. The experiments are performed on a series of test functions and a map-based practical problem. Empirical results attest that the proposed algorithm is competitive in dealing with multimodality compared with ten multimodal multi-objective algorithms.