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A hierarchical particle swarm optimizer for noisy and dynamic environments

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Abstract

New Particle Swarm Optimization (PSO) methods for dynamic and noisy function optimization are studied in this paper. The new methods are based on the hierarchical PSO (H-PSO) and a new type of H-PSO algorithm, called Partitioned Hierarchical PSO (PH-PSO). PH-PSO maintains a hierarchy of particles that is partitioned into several sub-swarms for a limited number of generations after a change of the environment occurred. Different methods for determining the best time when to rejoin the sub-swarms and how to handle the topmost sub-swarm are discussed. A standard method for metaheuristics to cope with noise is to use function re-evaluations. To reduce the number of necessary re-evaluations a new method is proposed here which uses the hierarchy to find a subset of particles for which re-evaluations are particularly important. In addition, a new method to detect changes of the optimization function in the presence of noise is presented. It differs from conventional detection methods because it does not require additional function evaluations. Instead it relies on observations of changes that occur within the swarm hierarchy. The new algorithms are compared experimentally on different dynamic and noisy benchmark functions with a variant of standard PSO and H-PSO that are both provided with a change detection and response method.

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Notes

  1. We also tested PSO and H-PSO with 5 and 9 re-randomized particles, but the larger number of 16 particles always provided better results.

  2. Note, that for severity \(s=0\%\) PSO-g and H-PSO are reported in Table 3 to be significantly better than PSO-l, although the average offline performance value says differently. This is because the average value is determined by few large values, but still the majority of the PSO-g runs ranked better than PSO-l which is recorded by the statistical analysis (compare Section 6.3).

References

  1. T.M. Blackwell and P.J. Bentley, “Dynamic search with charged swarms,” in Proc. GECCO-2002, W.B. Langdon et al. (eds.), Morgan Kaufmann Publishers: San Mateo, 2002, pp. 19–26.

  2. T.M. Blackwell, “Swarms in dynamic environments,” in Proc. Genetic and Evolutionary Computation Conference (GECCO 2003), E. Cantú-Paz et al. (eds.): Springer, Heidelberg, 2003, pp. 1–12.

  3. T.M. Blackwell, “Particle swarms and population diversity I: analysis,” in Proc. Bird of a Feather Workshops (in EvoDOP2003), J. Branke (ed.), Springer: Heidelberg, Genetic and Evolutionary Computation Conference, 2003, pp. 103–107.

  4. T.M. Blackwell, “Particle swarms and population diversity II: experiments,” in Proc. Bird of a Feather Workshops, Genetic and Evolutionary Computation Conference (in EvoDOP2003), J. Branke (ed.), Springer: Heidelberg, 2003, pp. 108–112.

  5. T.M. Blackwell and J. Branke, “Multi-swarm optimization in dynamic environments,” in Applications of Evolutionary Computing, LNCS 3005, G.R. Raidl et al. (eds.), Springer: Heidelberg, 2004, pp. 489–500.

  6. J. Branke, “Memory enhanced evolutionary algorithms for changing optimization problems,” in Proc. Congress on Evolutionary Computation (CEC-1999), P. J. Angeline et al. (eds.), IEEE Press: Piscataway, NJ, 1999, pp. 1875–1882.

  7. J. Branke, Evolutionary Optimization in Dynamic Environments, Genetic Algorithms and Evolutionary Computation Series. Kluwer Academic Publishers: Boston, MA, 2001.

  8. A. Carlisle and G. Dozier, “Adapting particle swarm optimization to dynamic environments,” in Proc. International Conference on Artificial Intelligence (ICAI 2000), H. R. Arabnia (ed.), CSREA Press, 2000, pp. 429–434.

  9. A. Carlisle, “Applying the particle swarm optimizer to non-stationary environments,” PhD Dissertation, Auburn University, 2002.

  10. A. Carlisle and G. Dozier, “Tracking changing extrema with adaptive particle swarm optimizer,” in Proc. ISSCI, 2002 World Automation Congress, Orlando, USA, M. Jamshidi et al. (eds.), TSI Press: Albuquerque, NM, 2002, pp. 265–270.

  11. J. P. Coelho, P.B. De Moura Oliveira, and J. Boaventura Cunha, “Non-linear concentration system design using a new adaptive particle swarm optimiser,” in Proc. 5th Portuguese Conference on Automatic Control (Controlo 2002), 2002, pp. 132–137.

  12. R. C. Eberhart and Y. Shi, “Tracking and optimizing dynamic systems with particle swarms,” in Proc. Congress on Evolutionary Computation (CEC2001), J.-H. Kim et al. (eds.), IEEE Press: Piscataway, NJ, 2001, pp. 94–100.

  13. X. Hu and R. Eberhart, “Tracking dynamic systems with PSO: where’s the cheese,” in Proc. Workshop on Particle Swarm Optimization, Purdue School of Engineering, Indinapolis, USA, 2001, pp. 80–83.

  14. X. Hu and R. Eberhart, “Adaptive particle swarm optimization: detection and response to dynamic systems,” in Proc. Congress on Evolutionary Computation (CEC2002), X. Yao et al. (eds.), IEEE Press: Piscataway, NJ, 2002, pp. 1666–1670.

  15. S. Janson and M. Middendorf, “A hierarchical particle swarm optimizer and its adaptive variant,” IEEE Trans. Systems, Man and Cybernetics, Part B: Cybernetics, vol. 35, pp. 1272–1282, 2005.

  16. J. Kennedy and R.C. Eberhart, “Particle swarm optimization,” in Proc. IEEE International Conference on Neural Networks (ICNN'95), Y. Attikiouzel (ed.), IEEE Press: Piscataway, NJ, 1995, pp. 1942–1947.

  17. B. Kaewkamnerdpong and P.J. Bentley, “Perceptive particle swarm optimisation: an investigation,” in Proc. IEEE Swarm Intelligence Symposium, P. Arabshahi and A. Martinoli (eds.), IEEE Press: Piscataway, NJ, 2005.

  18. J. Kennedy, “Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance,” in Proc. Congress on Evolutionary Computation (CEC-1999), P.J. Angeline et al. (eds.), IEEE Press: Piscataway, NJ, 1999, pp. 1931–1938.

  19. X. Li and K.H. Dam, “Comparing particle swarms for tracking extrema in dynamic environments,” in Proc. IEEE Congress on Evolutionary Computation (CEC2003), R. Sarker, et al. (eds.), IEEE Press: Piscataway, NJ, 2003, pp. 1772–1779.

  20. R.W. Morrison, in Designing Evolutionary Algorithms for Dynamic Environments, Natural Computing Series, Springer Verlag: Heidelberg, 2004.

  21. D. Parrott and X. Li, “A particle swarm model for tracking multiple peaks in a dynamic environment using speciation,” in Proc. Congress on Evolutionary Computation (CEC'04), G. Greenwood (ed.), IEEE Press: Piscataway, NJ, 2004, pp. 98–103.

  22. K.E. Parsopoulos and M.N. Vrahatis, “Unified particle swarm optimization in dynamic environments,” in Proc. 2nd European Workshop on Evolutionary Algorithms in Stochastic and Dynamic Environments, LNCS 3449, F. Rothlauf et al. (eds.), Springer, Heidelberg, 2005, pp. 590–599.

  23. K.E. Parsopoulos and M.N. Vrahatis, “Particle swarm optimization for imprecise problems,” in Scattering and Biomedical Engineering, Modeling and Applications, D. Fotiadis and C. Massalas (eds.), World Scientific, Hackensack, NJ, 2002, pp. 254–264.

  24. K.E. Parsopoulos and M.N. Vrahatis, “Particle swarm optimizer in noisy and continuously changing environments,” in Artificial Intelligence and Soft Computing, M.H. Hamza (ed.), IASTED/ACTA Press: Anaheim, CA, 2001, pp. 289–294.

  25. P.N. Suganthan, “Particle swarm optimizer with neighborhood operator,” in Proc. Congress on Evolutionary Computation (CEC-1999), P.J. Angeline et al. (eds.), IEEE Press: Piscataway, NJ, 1999, pp. 1958–1962.

  26. I.C. Trelea, “The particle swarm optimization algorithm: convergence analysis and parameter selection,” Information Processing Letters, vol. 85, pp. 317–325, 2003.

  27. X. Zhang, L. Yu, Y. Zheng, Y. Shen, G. Zhou, L. Chen, L. Xi, T. Yuan, J. Zhang, and B. Yang, “Two-stage adaptive PMD compensation in a 10 Gbit/s optical communication system using particle swarm optimization algorithm,” Optics Communications, vol. 231, pp. 233–242, 2004.

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Acknowledgments

This work was supported by the German Research Foundation (DFG) through the project “Swarm Intelligence on Reconfigurable Architectures”.

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  1. Parallel Computing and Complex Systems Group, Department of Computer Science, University of Leipzig, Augustusplatz 10/11, D-04109, Leipzig, Germany

    Stefan Janson & Martin Middendorf

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  2. Martin Middendorf
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Correspondence to Stefan Janson.

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Janson, S., Middendorf, M. A hierarchical particle swarm optimizer for noisy and dynamic environments. Genet Program Evolvable Mach 7, 329–354 (2006). https://doi.org/10.1007/s10710-006-9014-6

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