Particle Convergence Time in the PSO Model with Inertia Weight

Krzysztof Trojanowski, Tomasz Kulpa

2015

Abstract

Particle Swarm Optimization (PSO) is a powerful heuristic optimization method being subject of continuous interest. Theoretical analysis of its properties concerns primarily the conditions necessary for guaranteeing its convergent behaviour. Particle behaviour depends on three groups of parameters: values of factors in a velocity update rule, initial localization and velocity and fitness landscape. The paper presents theoretical analysis of the particle convergence properties in the model with inertia weight respectively to different values of these parameters. A new measure for evaluation of a particle convergence time is proposed. For this measure an upper bound formula is derived and its four main types of characteristics are discussed. The way of the characteristics transformations respectively to changes of velocity equation parameters is presented as well.

References

  1. Bonyadi, M. R. and Michalewicz, Z. (2015). Analysis of stability, local convergence, and transformation sensitivity of a variant of particle swarm optimization algorithm. IEEE T. Evolut. Comput. Date of Publication: July 25, 2015.
  2. Cleghorn, C. W. and Engelbrecht, A. P. (2014a). A generalized theoretical deterministic particle swarm model. Swarm Intelligence, 8(1):35-59.
  3. Cleghorn, C. W. and Engelbrecht, A. P. (2014b). Particle swarm convergence: An empirical investigation. In Evolutionary Computation (CEC), 2014 IEEE Congress on, pages 2524 - 2530. IEEE Press.
  4. Clerc, M. and Kennedy, J. (2002). The particle swarmexplosion, stability, and convergence in a multidimensional complex space. IEEE T. Evolut. Comput., 6(1):58-73.
  5. Eberhart, R. C. and Shi, Y. (2000). Comparing inertia weights and constriction factors in particle swarm optimization. In Proc. of the 2000 Congress on Evolutionary Computation, pages 84-88, Piscataway, NJ. IEEE Service Center.
  6. Engelbrecht, A. P. (2010). Heterogeneous particle swarm optimization. In Swarm Intelligence, volume 6234 of Lecture Notes in Computer Science, pages 191-202. Springer Berlin Heidelberg.
  7. Gazi, V. (2012). Stochastic stability analysis of the particle dynamics in the pso algorithm. In Intelligent Control (ISIC), 2012 IEEE International Symposium on, pages 708 - 713. IEEE Press.
  8. Kadirkamanathan, V., Selvarajah, K., and Fleming, P. J. (2006). Stability analysis of the particle dynamics in particle swarm optimizer. IEEE T. Evolut. Comput., 10(3):245-255.
  9. Kennedy, J. and Eberhart, R. C. (1995). Particle swarm optimization. In Proc. of the IEEE Int. Conf. on Neural Networks, pages 1942-1948, Piscataway, NJ. IEEE.
  10. Li, C. and Yang, S. (2010). Adaptive learning particle swarm optimizer-II for global optimization. In IEEE Congress on Evolutionary Computation, pages 1-8. IEEE.
  11. Liu, Q. (2015). Order-2 stability analysis of particle swarm optimization. Evol. Comput., 23(2):187-216.
  12. Nepomuceno, F. V. and Engelbrecht, A. P. (2013a). Behavior changing schedules for heterogeneous particle swarms. In Computational Intelligence and 11th Brazilian Congress on Computational Intelligence, 2013 BRICS Congress on, pages 112 - 118. IEEE Press.
  13. Nepomuceno, F. V. and Engelbrecht, A. P. (2013b). A selfadaptive heterogeneous PSO for real-parameter optimization. In 2013 IEEE Conference on Evolutionary Computation, volume 1, pages 361-368.
  14. Poli, R. (2009). Mean and variance of the sampling distribution of particle swarm optimizers during stagnation. IEEE T. Evolut. Comput., 13(4):712-721.
  15. Shi, Y. and Eberhart, R. C. (1998). A modified particle swarm optimizer. In Proceedings of the IEEE Congress on Evolutionary Computation 1998, pages 69-73. IEEE Press.
  16. Trelea, I. C. (2003). The particle swarm optimization algorithm: convergence analysis and parameter selection. Inform. Process. Lett., 85(6):317 - 325.
  17. van den Bergh, F. and Engelbrecht, A. P. (2006). A study of particle swarm optimization particle trajectories. Inform. Sciences, 176(8):937-971.
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Paper Citation


in Harvard Style

Trojanowski K. and Kulpa T. (2015). Particle Convergence Time in the PSO Model with Inertia Weight . In Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: ECTA, ISBN 978-989-758-157-1, pages 122-130. DOI: 10.5220/0005629701220130


in Bibtex Style

@conference{ecta15,
author={Krzysztof Trojanowski and Tomasz Kulpa},
title={Particle Convergence Time in the PSO Model with Inertia Weight},
booktitle={Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: ECTA,},
year={2015},
pages={122-130},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005629701220130},
isbn={978-989-758-157-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 7th International Joint Conference on Computational Intelligence - Volume 1: ECTA,
TI - Particle Convergence Time in the PSO Model with Inertia Weight
SN - 978-989-758-157-1
AU - Trojanowski K.
AU - Kulpa T.
PY - 2015
SP - 122
EP - 130
DO - 10.5220/0005629701220130