Differential evolution with multi-stage strategies for global optimization

Differential evolution is a fast, robust, and simple population-based stochastic search algorithm for global optimization, which has been widely applied in various fields. However, there are many mutation strategies in DE, which have their own characteristics. Therefore, choosing a best mutation strategy is not easy for a specific problem. Different mutation strategies may be appropriate during different stages of the evolution. In this paper, we propose a DE with multi-stage strategies (DEMS). In DEMS, the evolution process of DE is divided into multiple stages according to the average distance between each individual in the initial population. Each stage has its own strategy candidate pool which includes multiple effective strategies. At the beginning of each generation, the average distance between each individual is first calculated to determine the evolution stage. Then for each target vector in the current population, a mutation strategy is randomly selected from the strategy candidate pool with respect to the stage to produce a offspring vector. Numerical experiments on 15 well-known benchmark functions and the CEC 2015 benchmark sets show that the proposed DEMS is significantly better than, or at least comparable to several state-of-the-art DE variants, in terms of the quality of the final solutions and the convergence rate.