On Convergence and Parameter Selection of an Improved Particle Swarm Optimization

  • Chen, Xin (School of Information Science and Engineering, Central South University) ;
  • Li, Yangmin (Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau)
  • Published : 2008.08.31

Abstract

This paper proposes an improved particle swarm optimization named PSO with Controllable Random Exploration Velocity (PSO-CREV) behaving an additional exploration behavior. Different from other improvements on PSO, the updating principle of PSO-CREV is constructed in terms of stochastic approximation diagram. Hence a stochastic velocity independent on cognitive and social components of PSO can be added to the updating principle, so that particles have strong exploration ability than those of conventional PSO. The conditions and main behaviors of PSO-CREV are described. Two properties in terms of "divergence before convergence" and "controllable exploration behavior" are presented, which promote the performance of PSO-CREV. An experimental method based on a complex test function is proposed by which the proper parameters of PSO-CREV used in practice are figured out, which guarantees the high exploration ability, as well as the convergence rate is concerned. The benchmarks and applications on FCRNN training verify the improvements brought by PSO-CREV.

Keywords

References

  1. R. C. Eberhart and J. Kennedy, "A new optimizer using particle swarm theory," Proc. of 6th Int. Symp. on Micro Machine and Human Science, Nagoya, Japan, pp. 39-43, 1995
  2. J. Kennedy and R. C. Eberhart, "Particle swarm optimization," Proc. of IEEE Int. Conf. on Neural Network, Perth, Australia, pp. 1942-1948, 1995
  3. C. F. Juang, "A hybrid of genetic algorithm and particle swarm optimization for recurrent network design," IEEE Trans. on Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 34, no. 2, pp. 997-1006, 2004 https://doi.org/10.1109/TSMCB.2003.818557
  4. M. A. Abido, "Particle swarm optimization for multimachine power system stabilizer design," Proc. of Power Engineering Society Summer Meeting, pp. 1346-1351, 2001
  5. L. Messerschmidt and A. P. Engelbrecht, "Learning to play games using a PSO-based competitive learning approach," IEEE Trans. on Evolutionary Computation, vol. 8, no. 3, pp. 280-288, 2004 https://doi.org/10.1109/TEVC.2004.826070
  6. Y. Li and X. Chen, "Mobile robot navigation using particle swarm optimization and adaptive NN," Proc. of the First Int. Conf. on Natural Computation, Changsha, China, LNCS 3612, pp. 554-559, 2005
  7. H. M. Emara and H. A. Fattah, "Continuous swarm optimization technique with stability analysis," Proc. of American Control Conference, vol. 3, pp. 2811-2817, 2004
  8. M. Clerc and J. Kennedy, "The particle swarm: Explosion, stability, and convergence in a multidimensional complex space," IEEE Trans. on Evolutionary Computation, vol. 6, no. 1, pp. 58- 73, 2002 https://doi.org/10.1109/4235.985692
  9. K. Yasuda, A. Ide, and N. Iwasaki, "Adaptive particle swarm optimization," Proc. of IEEE Int. Conf. on Systems, Man and Cybernetics, pp. 1554-1559, 2003
  10. I. C. Trelea, "The particle swarm optimization algorithm: Convergence analysis and parameter selection," Information Processing Letters, vol. 85, no. 6, pp. 317-325, 2003 https://doi.org/10.1016/S0020-0190(02)00447-7
  11. B. Brandstäter and U. Baumgartner, "Particle swarm optimization-mass-spring system analogon," IEEE Trans. on Magnetics, vol. 38, no. 2, pp. 997-1000, 2002 https://doi.org/10.1109/20.996256
  12. Y. Shi and R. C. Eberhart, "A modified particle swarm optimizer," Proc. of IEEE Int. Conf. Evolutionary Computation, Anchorage, AK, pp. 69-73, 1998
  13. F. van den Bergh and A. P. Engelbrecht, "A cooperative approach to particle swarm optimization," IEEE Trans. on Evolutionary Computation, vol. 8, no. 3, pp. 225-239, 2004 https://doi.org/10.1109/TEVC.2004.826069
  14. A. Ratnaweera, S. K. Halgamuge, and H. C. Watson, "Self-organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients," IEEE Trans. on Evolutionary Computation, vol. 8, no. 3, pp. 240-254, 2004
  15. F. van den Bergh, An Analysis of Particle Swarm Optimizers, Ph.D. dissertation, Dept. Comput. Sci., Univ. Pretoria, Pretoria, South Africa, 2002
  16. B. Liu, L. Wang, Y. H. Jin, F. Tang, and D. X. Huang, "Improved particle swarm optimization combined with chaos," Chaos, Solitons and Fractals, vol. 25, no. 5, pp. 1261-1271, 2005 https://doi.org/10.1016/j.chaos.2004.11.095
  17. H. Robbins and S. Monro, "A stochastic approximation method," Ann Math. Stat., vol. 22, pp. 400-407, 1951 https://doi.org/10.1214/aoms/1177729586
  18. H. J. Kushner and G. G. Yin, Stochastic Approximation and Recursive Algorithms and Applications, 2nd Edition, Springer, 2003
  19. P. N. Suganthan, N. Hansen, J. J. Liang, K. Deb, Y. P. Chen, A. Auger, and S. Tiwari, "Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization," Technical Report, Nanyang Technological University, Singapore, May 2005 and KanGAL Report #2005005, IIT Kanpur, India
  20. R. Mendes, J. Kennedy, and J. Neves, "The fully informed particle swarm: Simple, maybe better," IEEE Trans. on Evolutionary Computation, vol. 8, no. 3. pp. 204-210, 2004 https://doi.org/10.1109/TEVC.2004.826074