A Convergence Proof for the Particle Swarm Optimiser

Article type: Research Article

Authors: van den Bergh, Frans | Engelbrecht, Andries Petrus

Affiliations: CSIR, Meiring Naude Road, Pretoria, South Africa. [email protected] | Department of Computer Science, University of Pretoria, Pretoria, South Africa. [email protected]

Note: [] Address for correspondence: University of Pretoria, Pretoria, South Africa

Abstract: The Particle Swarm Optimiser (PSO) is a population based stochastic optimisation algorithm, empirically shown to be efficient and robust. This paper provides a proof to show that the original PSO does not have guaranteed convergence to a local optimum. A flaw in the original PSO is identified which causes stagnation of the swarm. Correction of this flaw results in a PSO algorithm with guaranteed convergence to a local minimum. Further extensions with provable global convergence are also described. Experimental results are provided to elucidate the behavior of the modified PSO as well as PSO variations with global convergence.

Keywords: Particle swarm optimisation, convergence proofs, stochastic optimisation, local convergence, global convergence

DOI: 10.3233/FI-2010-370

Journal: Fundamenta Informaticae, vol. 105, no. 4, pp. 341-374, 2010