Table of Contents
Journal of Artificial Evolution and Applications
Volume 2008, Article ID 893237, 10 pages
Research Article

Examination of Particle Tails

Department of Computing Goldsmiths, University of London, New Cross, London SE14 6NW, UK

Received 20 July 2007; Accepted 29 November 2007

Academic Editor: Riccardo Poli

Copyright © 2008 Tim Blackwell and Dan Bratton. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The tail of the particle swarm optimisation (PSO) position distribution at stagnation is shown to be describable by a power law. This tail fattening is attributed to particle bursting on all length scales. The origin of the power law is concluded to lie in multiplicative randomness, previously encountered in the study of first-order stochastic difference equations, and generalised here to second-order equations. It is argued that recombinant PSO, a competitive PSO variant without multiplicative randomness, does not experience tail fattening at stagnation.