Particle swarm optimization (PSO) is a population-based intelligent algorithm for solving optimization problems. Since the fast convergence and easy implementation, PSO has been successfully applied in some areas. However, the standard PSO also has some inherent drawbacks, and the premature convergence is the main issue. Many PSO variants have been developed to solve this problem. Unlike the previous studies, this paper focuses on the communications among different particles, based on the graph theory and information theory, a new analytical method for PSO topology was proposed. By analysing three typical topologies (star, ring, and von-Neumann), the influence of different topologies was revealed. Therefore, an improved topology combines the advantages of three typical topologies was developed, and the iterations of PSO were divided into three stages. The different stages have different topologies. The benchmark test results show that the improved topology is effective. It applies to both convex and nonconvex optimizations.
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