Title: Particle swarm optimisation: time for uniformisation

Authors: Juan Luis Fernández-Martínez; Esperanza García-Gonzalo

Addresses: Department of Mathematics, Oviedo University, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain ' Department of Mathematics, Oviedo University, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

Abstract: Particle swarm optimisation (PSO) is an evolutionary algorithm that has been successfully applied to many optimisation problems in different fields. PSO has been heuristically proposed based in a social analogy for large groups in nature. Since its publication, research has been carried to understand the PSO convergence and improving its numerical performance. Accordingly several modifications of the basic PSO have been proposed, mostly in a heuristic way. Nevertheless, many of these modifications were not really needed, since they were proposed based on a deficient mathematical analysis of the PSO stability conditions. PSO trajectories are stochastic processes and PSO can be considered as a discrete stochastic gradient algorithm. Nevertheless, PSO is not heuristic, since its convergence and the stability of particle trajectories are related. In conclusion, it is time for uniformisation, because paradoxically this wide range of PSO versions have generated mistrust, providing the impression that PSO success depends more on the version that has been adopted and on the skills of the PSO designer.

Keywords: particle swarm optimisation; PSO variants; stability; convergence; PSO parameters.

DOI: 10.1504/IJCSM.2013.054671

International Journal of Computing Science and Mathematics, 2013 Vol.4 No.1, pp.16 - 33

Received: 13 Nov 2012
Accepted: 20 Nov 2012
Published online: 10 May 2014 *

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