A multilevel sampling strategy based memetic differential evolution for multimodal optimization

Abstract

Multimodal optimization, aiming to locate multiple optima in parallel, is a challenging task. In this paper, a multilevel sampling strategy based memetic differential evolution algorithm is proposed to tackle the problem. In the proposed algorithm, a multilevel sampling strategy is devised to sample a subpopulation for evolution at each generation. In this strategy, the entire population is dynamically divided into multiple levels according to the fitness of individuals at each generation. A subpopulation is then adaptively sampled from the individuals at different levels to undergo a niching based evolution for identifying multiple optima in the search space. Further, a crossover-based local search scheme is designed to fine-tune the seed solutions of niches in the population during evolution. We evaluate the proposed method on 20 benchmark multimodal problems and compare it with state-of-the-art multimodal optimization algorithms. The results show that our proposed algorithm can effectively and accurately locate multiple optima, outperforming related methods to be compared.