Discrete Particle Swarm Optimization Algorithm: A Stability Study of Particle Trajectories under $c_1 $ and $c_2$

Abstract

Particle Swarm Optimization (PSO) is a robust, efficient and stable optimization algorithm. To solve different optimization problems in discrete spaces, in recent years various discrete PSO algorithms have been provided. As the studies of discrete PSO are mostly empirical, in this paper a theoretical analysis for particle trajectories of a discrete PSO is proposed, at the same time, a formal proof that each particle of a discrete PSO has stable trajectories is presented. And then trajectories of stochastic particles is also tested and verified in a 15 dimensional discrete space, as expected, the experimental results is consistent with the conclusions drawn from the theoretical analysis.