Dynamic multi-swarm differential learning particle swarm optimizer

Because different optimization algorithms have different search behaviors and advantages, hybrid strategy is one of the main research directions to improve the performance of PSO. Inspired by this idea, a dynamic multi-swarm differential learning particle swarm optimizer (DMSDL-PSO) is proposed in this paper. We propose a novel method to merge the differential evolution operator into each sub-swarm of the DMSDL-PSO. Combining the exploration capability of the differential mutation and employing Quasi-Newton method as a local searcher to enhance the exploitation capability, DMSDL-PSO has a good exploration and exploitation capability. According to the characteristics of the DMSDL-PSO, three modified differential mutation operators are discussed. Differential mutation is adopted for the personal historically best particle. Because the velocity updating equation of the particles in PSO has some shortcomings, a modified velocity updating equation is adopted in DMSDL-PSO. In DMSDL-PSO, in which the particles are divided into several small and dynamic sub-swarms. The dynamic change of sub-swarms can promote the information exchange of the whole swarm. In order to test the performance of DMSDL-PSO, 41 benchmark functions are adopted. Lots of numerical experiments are conducted to compare DMSDL-PSO with other popular algorithms. The numerical results demonstrate that DMSDL-PSO performs better on some benchmark functions.