The stability analysis of particle swarm optimization-grey wolf optimization algorithm

Abstract

In order to overcome the problem that particles fall into local optimum in the iterative process of Particle Swarm Optimization (PSO) algorithm, the Gray Wolf Optimization (GWO) is added to particle swarm optimization and form Particle Swarm Optimization-Gray Wolf Optimization (PSO-GWO) algorithm. Aiming at the instability of the algorithm in the iterative process, two methods for judging the stability of the algorithm are proposed, namely, the asymptotic stability analysis method of the algorithm model perturbation system and the Input-to-State Stability (ISS) analysis method. First, the PSO-GWO algorithm is transformed into a Discrete Linear Time-Varying (DLTV) system model, and two stability analysis methods are used to judge the stability of the model. Through simulation experiments on nine benchmark functions under five different sets of algorithm parameters, that is, the stability of PSO-GWO algorithm in the iterative process is analyzed. The experimental results verify the effectiveness of the stability theory of the algorithm.