Table of Contents
Journal of Artificial Evolution and Applications
Volume 2008, Article ID 761459, 10 pages
http://dx.doi.org/10.1155/2008/761459
Research Article

Dynamics and Stability of the Sampling Distribution of Particle Swarm Optimisers via Moment Analysis

Department of Computing and Electronic Systems, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK

Received 23 July 2007; Accepted 3 December 2007

Academic Editor: T. Blackwell

Copyright © 2008 Riccardo Poli. 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.

Linked References

  1. J. Kennedy, “The behavior of particles,” in Proceedings of the 7th International Conference on Evolutionary Programming (EP '98), V. W. Porto, N. Saravanan, D. Waagen, and A. E. Eiben, Eds., p. 581, Springer, San Diego, Calif, USA, March 1998.
  2. M. Clerc and J. Kennedy, “The particle swarm—explosion, stability, and convergence in a multidimensional complex space,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 1, 58 pages, 2002. View at Publisher · View at Google Scholar
  3. E. Ozcan and C. K. Mohan, “Analysis of a simple particle swarm optimization system,” in Intelligent Engineering Systems Through Artificial Neural Networks, vol. 8, p. 253, ASME Press, St. Louis, Mo, USA, 1998. View at Google Scholar
  4. E. Ozcan and C. K. Mohan, “Particle swarm optimization: surfing the waves,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '99), vol. 3, p. 1939, IEEE Service Center, Washington, DC, USA, July 1999. View at Publisher · View at Google Scholar
  5. F. van den Bergh, An analysis of particle swarm optimizers, Ph.D. thesis, Department of Computer Science, University of Pretoria, Pretoria, South Africa, 2002.
  6. A. P. Engelbrecht, Fundamentals of Computational Swarm Intelligence, John Wiley & Sons, New York, NY, USA, 2005.
  7. K. Yasuda, A. Ide, and N. Iwasaki, “Adaptive particle swarm optimization,” in Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, vol. 2, p. 1554, Washington, DC, USA, October 2003.
  8. T. M. Blackwell, “Particle swarms and population diversity,” Soft Computing, vol. 9, no. 11, 793 pages, 2005. View at Publisher · View at Google Scholar
  9. B. Brandstatter and U. Baumgartner, “Particle swarm optimization—mass-spring system analogon,” IEEE Transactions on Magnetics, vol. 38, no. 2, 997 pages, 2002. View at Publisher · View at Google Scholar
  10. I. C. Trelea, “The particle swarm optimization algorithm: convergence analysis and parameter selection,” Information Processing Letters, vol. 85, no. 6, 317 pages, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. E. F. Campana, G. Fasano, and A. Pinto, “Dynamic system analysis and initial particles position in particle swarm optimization,” in Proceedings of the IEEE Swarm Intelligence Symposium (SIS '06), Indianapolis, Ind, USA, May 2006.
  12. E. F. Campana, G. Fasano, D. Peri, and A. Pinto, “Particle swarm optimization: efficient globally convergent modifications,” in Proceedings of the 3rd European Conference on Computational Mechanics, Solids, Structures and Coupled Problems in Engineering (ECCM '06), C. A. Mota Soares, J. A. C. Martins, H. C. Rodrigues, and J. A. C. Ambrosio, Eds., Lisbon, Portugal, June 2006.
  13. M. Clerc, “Stagnation analysis in particle swarm optimisation or what happens when nothing happens,” Tech. Rep. CSM-460, Department of Computer Science, University of Essex, Colchester, UK, August 2006. View at Google Scholar
  14. V. Kadirkamanathan, K. Selvarajah, and P. J. Fleming, “Stability analysis of the particle dynamics in particle swarm optimizer,” IEEE Transactions on Evolutionary Computation, vol. 10, no. 3, 245 pages, 2006. View at Publisher · View at Google Scholar
  15. D. H. Wolpert and W. G. Macready, “No free lunch theorems for search,” IEEE Transactions on Evolutionary Computation, vol. 1, no. 1, 67 pages, 1997. View at Publisher · View at Google Scholar
  16. R. Poli and D. Broomhead, “Exact analysis of the sampling distribution for the canonical particle swarm optimiser and its convergence during stagnation,” in Proceedings of the 9th Genetic and Evolutionary Computation Conference (GECCO '07), p. 134, ACM Press, London, UK, July 2007. View at Publisher · View at Google Scholar
  17. J. Kennedy, “Bare bones particle swarms,” in Proceedings of the IEEE Swarm Intelligence Symposium (SIS '03), p. 80, Indianapolis, Ind, USA, April 2003. View at Publisher · View at Google Scholar
  18. J. Kennedy and R. Mendes, “Population structure and particle swarm performance,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '02), vol. 2, p. 1671, Honolulu, Hawaii, USA, May 2002. View at Publisher · View at Google Scholar
  19. R. Mendes, Population topologies and their influence in particle swarm performance, Ph.D. thesis, Departamento de Informatica, Escola de Engenharia, Universidade do Minho, Braga, Portugal, 2004.
  20. J. S. Ramberg, P. R. Tadikamalla, E. J. Dudewicz, and E. F. Mykytka, “A probability distribution and its uses in fitting data,” Technometrics, vol. 21, no. 2, 201 pages, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. A. Lakhany and H. Mausser, “Estimating the parameters of the generalized lambda distribution,” Algo Research Quarterly, vol. 3, no. 3, 47 pages, 2000. View at Google Scholar
  22. S. W. M. AuYeung, Finding probability distributions from moments, M.S. thesis, Imperial College, London, UK, 2003.
  23. R. Poli, D. Bratton, T. M. Blackwell, and J. Kennedy, “Theoretical derivation, analysis and empirical evaluation of a simpler particle swarm optimiser,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC '07), IEEE Press, Singapore, September 2007.
  24. P. Larrañaga and J. A. Lozano, Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation, Kluwer Academic Publishers, Boston, Mass, USA, 2002.