Normalized population diversity in particle swarm optimization

Abstract

Particle swarm optimization (PSO) algorithm can be viewed as a series of iterative matrix computation and its population diversity can be considered as an observation of the distribution of matrix elements. In this paper, PSO algorithm is first represented in the matrix format, then the PSO normalized population diversities are defined and discussed based on matrix analysis. Based on the analysis of the relationship between pairs of vectors in PSO solution matrix, different population diversities are defined for separable and non-separable problems, respectively. Experiments on benchmark functions are conducted and simulation results illustrate the effectiveness and usefulness of the proposed normalized population diversities. © 2011 Springer-Verlag.