Accessible Requires Authentication Published by De Gruyter Oldenbourg October 19, 2019

Theory of particle swarm optimization: A survey of the power of the swarm’s potential

Bernd Bassimir ORCID logo, Alexander Raß ORCID logo and Manuel Schmitt

Abstract

This paper presents a survey on different showcases for potential measures on particle swarm optimization (PSO). First, a potential is analyzed to prove convergence to non-optimal points. Second, one can apply a minor modification to PSO to prevent convergence to non-optimal points by using an easy potential measure. Finally, analyzing this potential measure yields a reliable stopping criterion for the modified PSO.

ACM CCS:

References

1. B. Bassimir, M. Schmitt, and R. Wanka. How much forcing is necessary to let the results of particle swarms converge? In Proc. Int. Conf. on Swarm Intelligence Based Optimization (ICSIBO), pages 98–105, 2014. Search in Google Scholar

2. B. Bassimir, M. Schmitt, and R. Wanka. Self-adaptive potential-based stopping criteria for particle swarm optimization. arXiv, abs/1906.08867, 2019. Search in Google Scholar

3. M. Clerc and J. Kennedy. The particle swarm – explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6:58–73, 2002. Search in Google Scholar

4. R. C. Eberhart and J. Kennedy. A new optimizer using particle swarm theory. In Proc. 6th International Symposium on Micro Machine and Human Science, pages 39–43, 1995. Search in Google Scholar

5. M. Jiang, Y. P. Luo, and S. Y. Yang. Particle swarm optimization – stochastic trajectory analysis and parameter selection. In F. T. S. Chan and M. K. Tiwari, editors, Swarm Intelligence – Focus on Ant and Particle Swarm Optimization, pages 179–198. 2007. Corrected version of [6]. Search in Google Scholar

6. M. Jiang, Y. P. Luo, and S. Y. Yang. Stochastic convergence analysis and parameter selection of the standard particle swarm optimization algorithm. Information Processing Letters, 102:8–16, 2007. Corrected by [5]. Search in Google Scholar

7. J. Kennedy and R. C. Eberhart. Particle swarm optimization. In Proc. IEEE International Conference on Neural Networks, volume 4, pages 1942–1948, 1995. Search in Google Scholar

8. P. K. Lehre and C. Witt. Finite first hitting time versus stochastic convergence in particle swarm optimisation. arXiv:1105.5540, 2011. Search in Google Scholar

9. A. Raß. High precision particle swarm optimization (HiPPSO). https://github.com/alexander-rass/HiPPSO/, 2018. Search in Google Scholar

10. A. Raß, M. Schmitt, and R. Wanka. Explanation of stagnation at points that are not local optima in particle swarm optimization by potential analysis. arXiv, abs/1504.08241, 2015. Search in Google Scholar

11. A. Raß, M. Schmitt, and R. Wanka. Explanation of Stagnation at Points that are not Local Optima in Particle Swarm Optimization by Potential Analysis. In Companion of Proc. 17th Genetic and Evolutionary Computation Conference (GECCO), pages 1463–1464, U. ACM New York, NY, 2015. Search in Google Scholar

12. C. C. Ribeiro, I. Rosseti, and R. C. Souza. Effective probabilistic stopping rules for randomized metaheuristics: GRASP implementations. In Proc. 5th Int. Conf. on Learning and Intelligent Optimization (LION), pages 146–160, 2011. Search in Google Scholar

13. M. Schmitt and R. Wanka. Particle swarm optimization almost surely finds local optima. In Proc. 15th Genetic and Evolutionary Computation Conference (GECCO), pages 1629–1636, 2013. Search in Google Scholar

14. M. Schmitt and R. Wanka. Particle swarm optimization almost surely finds local optima. Theoretical Computer Science, Part A, 561:57–72, 2015. Search in Google Scholar

15. 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, 2005. Search in Google Scholar

16. F. van den Bergh and A. P. Engelbrecht. A new locally convergent particle swarm optimiser. In Proc. IEEE Int. Conf. on Systems, Man and Cybernetics (SMC), volume 3, pages 94–99, 2002. Search in Google Scholar

17. C. Witt. Why standard particle swarm optimisers elude a theoretical runtime analysis. In Proceedings of the 10th ACM SIGEVO Workshop on Foundations of Genetic Algorithms (FOGA), pages 13–20, 2009. 10.1145/1527125.1527128. Search in Google Scholar

18. K. Zielinski and R. Laur. Stopping criteria for a constrained single-objective particle swarm optimization algorithm. Informatica, (31):51–59, 2007. Search in Google Scholar

Received: 2019-01-18
Revised: 2019-09-18
Accepted: 2019-10-10
Published Online: 2019-10-19
Published in Print: 2019-08-27

© 2019 Walter de Gruyter GmbH, Berlin/Boston