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Parameter Selection in Particle Swarm Optimisation from Stochastic Stability Analysis

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Swarm Intelligence (ANTS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9882))

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Abstract

Particle swarm optimisation is a metaheuristic algorithm which finds reasonable solutions in a wide range of applied problems if suitable parameters are used. We study the properties of the algorithm in the framework of random dynamical systems (RDS) which, due to the quasi-linear swarm dynamics, yields exact analytical results for the stability properties in the single particle case. The calculated stability region in the parameter space extends beyond the region determined by earlier approximations. This is also evidenced by simulations which indicate that the algorithm performs best in the asymptotic case if parameterised near the margin of instability predicted by the RDS approach.

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References

  1. Bonyadi, M.R., Michalewicz, Z.: Particle swarm optimization for single objective continuous space problems: a review. Evol. Comput (2016). doi:10.1162/EVCO_r_00180

    Google Scholar 

  2. Cleghorn, C.W., Engelbrecht, A.P.: A generalized theoretical deterministic particle swarm model. Swarm Intell. 8(1), 35–59 (2014)

    Article  Google Scholar 

  3. Cleghorn, C.W., Engelbrecht, A.P.: Particle swarm convergence: an empirical investigation. In: IEEE Congress on Evolutionary Computation, pp. 2524–2530 (2014)

    Google Scholar 

  4. Clerc, M., Kennedy, J.: The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Trans. Evol. Comput. 6(1), 58–73 (2002)

    Article  Google Scholar 

  5. Erskine, A., Herrmann, J.M.: Cell-division behavior in a heterogeneous swarm environment. Artif. Life 21(4), 481–500 (2015)

    Article  Google Scholar 

  6. Erskine, A., Herrmann, J.M.: CriPS: Critical particle swarm optimisation. In: Andrews, P., Caves, L., Doursat, R., Hickinbotham, S., Polack, F., Stepney, S., Taylor, T., Timmis, J. (eds.) Proceedings of European Conference Artificial Life, pp. 207–214 (2015)

    Google Scholar 

  7. Furstenberg, H., Kesten, H.: Products of random matrices. Ann. Math. Stat. 31(2), 457–469 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gazi, V.: Stochastic stability analysis of the particle dynamics in the PSO algorithm. In: IEEE International Symposium on Intelligent Control (2012)

    Google Scholar 

  9. Hu, M., Wu, T.F., Weir, J.D.: An adaptive particle swarm optimization with multiple adaptive methods. IEEE Trans. Evol. Comput. 17(5), 705–720 (2013)

    Article  Google Scholar 

  10. Jiang, M., Luo, Y., Yang, S.: Stagnation analysis in particle swarm optimization. In: IEEE Swarm Intelligence Symposium, pp. 92–99 (2007)

    Google Scholar 

  11. Kadirkamanathan, V., Selvarajah, K., Fleming, P.J.: Stability analysis of the particle dynamics in particle swarm optimizer. IEEE Trans. Evol. Comput. 10(3), 245–255 (2006)

    Article  Google Scholar 

  12. Kennedy, J.: The behavior of particles. In: Porto, V.W., Saravanan, N., Waagen, D., Eiben, A.E. (eds.) Evolutionary Programming VII. LNCS, vol. 1447, pp. 579–589. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  13. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948 (1995)

    Google Scholar 

  14. Khas’minskii, R.Z.: Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems. Theory Prob. Appl. 12(1), 144–147 (1967)

    Article  MathSciNet  Google Scholar 

  15. Liang, J.J., Qu, B.Y., Suganthan, P.N., Hernández-Díaz, A.G.: Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization. Technical report, 201212, Comput. Intelligence Lab., Zhengzhou Univ. (2013)

    Google Scholar 

  16. Liu, Q.: Order-2 stability analysis of particle swarm optimization. Evol. Comput. 23(2), 187–216 (2014)

    Article  Google Scholar 

  17. Poli, R.: Mean and variance of the sampling distribution of particle swarm optimizers during stagnation. IEEE Trans. Evol. Comput. 13(4), 712–721 (2009)

    Article  Google Scholar 

  18. Poli, R., Broomhead, D.: Exact analysis of the sampling distribution for the canonical particle swarm optimiser and its convergence during stagnation. In: Proceedings of the 9th Annual Conference Genetic and Evolutionary Computation, pp. 134–141. ACM (2007)

    Google Scholar 

  19. Trelea, I.C.: The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf. Process. Lett. 85(6), 317–325 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhan, Z.H., Zhang, J., Li, Y., Chung, H.S.H.: Adaptive particle swarm optimization. IEEE Trans. Syst. Man Cybern. B 39(6), 1362–1381 (2009)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Engineering and Physical Sciences Research Council (EPSRC), grant number EP/K503034/1.

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Authors and Affiliations

  1. School of Informatics, Institute for Perception, Action and Behaviour, The University of Edinburgh, Edinburgh, Scotland, UK

    Adam Erskine, Thomas Joyce & J. Michael Herrmann

Authors
  1. Adam Erskine
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  2. Thomas Joyce
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  3. J. Michael Herrmann
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Corresponding author

Correspondence to J. Michael Herrmann .

Editor information

Editors and Affiliations

  1. Université Libre de Bruxelles , Bruxelles, Belgium

    Marco Dorigo

  2. Université Libre de Bruxelles , Bruxelles, Belgium

    Mauro Birattari

  3. RMIT University , Melbourne, Victoria, Australia

    Xiaodong Li

  4. University of Manchester, Manchester, United Kingdom

    Manuel López-Ibáñez

  5. Hiroshima University , Hiroshima, Japan

    Kazuhiro Ohkura

  6. École Polytechnique de Montréal , Montréal, Québec, Canada

    Carlo Pinciroli

  7. Université Libre de Bruxelles IRIDIA, CoDE, Brüssel, Belgium

    Thomas Stützle

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Erskine, A., Joyce, T., Herrmann, J.M. (2016). Parameter Selection in Particle Swarm Optimisation from Stochastic Stability Analysis. In: Dorigo, M., et al. Swarm Intelligence. ANTS 2016. Lecture Notes in Computer Science(), vol 9882. Springer, Cham. https://doi.org/10.1007/978-3-319-44427-7_14

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  • DOI: https://doi.org/10.1007/978-3-319-44427-7_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44426-0

  • Online ISBN: 978-3-319-44427-7

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