A new joint spectral radius analysis of random PSO algorithm

The existing stability analysis of particle swarm optimization (PSO) algorithm is chiefly concluded by the assumption of constant transfer matrix or time-varying random transfer matrix. Firstly, one counterexample is provided to show that the existing convergence analysis is not possibly valid for PSO system involving random variables. Secondly, the joint spectral radius, mainly calculated by the maximum eigenvalue of the product of all asymmetric random transfer matrices, is introduced to analyze and discuss convergence condition and convergence rate from numerical viewpoint with the aid of Monte Carlo method. Numerical results show that there is one major discrepancy between some preview convergence results and our corresponding results, helping us to deeply understand the tradeoff between exploration ability and exploitation ability as well as providing certain guideline for parameter selection.