Random drift particle swarm optimization algorithm: convergence analysis and parameter selection

Abstract

The random drift particle swarm optimization (RDPSO) algorithm is a PSO variant inspired by the free electron model in metal conductors placed in an external electric field. Based on the preliminary work on the RDPSO algorithm, this paper makes systematical analyses and empirical studies of the algorithm. Firstly, the motivation of the RDPSO algorithm is presented and the design of the particle's velocity equation is described in detail. Secondly, a comprehensive analysis of the algorithm is made in order to gain a deep insight into how the RDPSO algorithm works. It involves a theoretical analysis and the simulation of the stochastic dynamical behavior of a single particle in the RDPSO algorithm. The search behavior of the algorithm itself is also investigated in detail, by analyzing the interaction among the particles. Then, some variants of the RDPSO algorithm are presented by incorporating different random velocity components with different neighborhood topologies. Finally, empirical studies of the RDPSO algorithm are performed by using a set of benchmark functions from the CEC2005 benchmark suite. Based on the theoretical analysis of the particle's behavior, two methods of controlling the algorithmic parameters are employed, followed by an experimental analysis on how to select the parameter values, in order to obtain a satisfactory overall performance of the RDPSO algorithm and its variants in real-world applications. A further performance comparison between the RDPSO algorithm and other variants of PSO is made to prove the effectiveness of the RDPSO.