Set-Based Particle Swarm Optimisation: A Review

The set-based particle swarm optimisation algorithm is a swarm-based meta-heuristic that has gained popularity in recent years. In contrast to the original particle swarm optimisation algorithm, the set-based particle swarm optimisation algorithm is used to solve discrete and combinatorial optimisation problems. The main objective of this paper is to review the set-based particle swarm optimisation algorithm and to provide an overview of the problems to which the algorithm has been applied. This paper starts with an examination of previous attempts to create a set-based particle swarm optimisation algorithm and discusses the shortcomings of the existing attempts. The set-based particle swarm optimisation algorithm is established as the only suitable particle swarm variant that is both based on true set theory and does not require problem-specific modifications. In-depth explanations are given regarding the general position and velocity update equations, the mechanisms used to control the exploration–exploitation trade-off, and the quantifiers of swarm diversity. After the various existing applications of set-based particle swarm optimisation are presented, this paper concludes with a discussion on potential future research.