Stability Analysis of the Particle Swarm Optimization Algorithm

Abstract

Stability of the particle swarm optimization algorithm is analyzed without any simplifying assumptions made in the previous works. To evaluate the convergence speed of the algorithm, the decay rate is introduced, and a method for finding the largest lower bound of the decay rate is presented. The proposed method is based on linear matrix inequality techniques, and therefore is carried out efficiently by using convex optimization tools. Numerical examples are given to show that the analysis method is reasonable and effective to select the parameters in the algorithm.