Abstract
This paper has two primary aims. Firstly, to empirically verify the use of a specially designed objective function for particle swarm optimization (PSO) convergence analysis. Secondly, to investigate the impact of PSO’s social topology on the parameter region needed to ensure convergent particle behavior. At present there exists a large number of theoretical PSO studies, however, all stochastic PSO models contain the stagnation assumption, which implicitly removes the social topology from the model, making this empirical study necessary. It was found that using a specially designed objective function for convergence analysis is both a simple and valid method for convergence analysis. It was also found that the derived region needed to ensure convergent particle behavior remains valid regardless of the selected social topology.
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References
Poli, R.: Analysis of the publications on the applications of particle swarm optimisation. Journal of Artificial Evolution and Applications 2008, 1–10 (2008)
Ozcan, E., Mohan, C.: Analysis of a simple particle swarm optimization system. Intelligent Engineering Systems through Artificial Neural Networks 8, 253–258 (1998)
Ozcan, E., Mohan, C.: Particle swarm optimization: Surfing the waves. In: Proceedings of the IEEE Congress on Evolutionary Computation, vol. 3. IEEE Press, Piscataway (1999)
Clerc, M., Kennedy, J.: The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation 6(1), 58–73 (2002)
Zheng, Y., Ma, L., Zhang, L., Qian, J.: On the convergence analysis and parameter selection in particle swarm optimization. In: Proceedings of the International Conference on Machine Learning and Cybernetics, Xi’an, China, vol. 3, pp. 1802–1907 (2003)
Van den Bergh, F., Engelbrecht, A.: A study of particle swarm optimization particle trajectories. Information Sciences 176(8), 937–971 (2006)
Trelea, I.: The particle swarm optimization algorithm: Convergence analysis and parameter selection. Information Processing Letters 85(6), 317–325 (2003)
Cleghorn, C., Engelbrecht, A.: A generalized theoretical deterministic particle swarm model. Swarm Intelligence Journal, 1–25 (2014)
Kadirkamanathan, V., Selvarajah, K., Fleming, P.: Stability analysis of the particle dynamics in particle swarm optimizer. IEEE Transactions on Evolutionary Computation 10(3), 245–255 (2006)
Gazi, V.: Stochastic stability analysis of the particle dynamics in the PSO algorithm. In: Proceedings of the IEEE International Symposium on Intelligent Control, pp. 708–713. IEEE Press, Dubrovnik (2012)
Poli, R.: Mean and variance of the sampling distribution of particle swarm optimizers during stagnation. IEEE Transactions on Evolutionary Computation 13(4), 712–721 (2009)
Campana, E., Fasano, G., Pinto, A.: Dynamic analysis for the selection of parameters and initial population, in particle swarm optimization. Journal of Global Optimization 48, 347–397 (2010)
Kennedy, J., Eberhart, R.: Particle swarm optimization, pp. 1942–1948. IEEE Press, Piscataway (1995)
Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 69–73. IEEE Press, Piscataway (1998)
Kennedy, J.: Small worlds and mega-minds: effects of neighborhood topology on particle swarm performance. In: Proceedings of the IEEE Congress on Evolutionary Computation, vol. 3, pp. 1931–1938. IEEE Press, Piscataway (1999)
Kennedy, J., Mendes, R.: Population structure and particle performance. In: Proceedings of the IEEE Congress on Evolutionary Computation, pp. 1671–1676. IEEE Press, Piscataway (2002)
Engelbrecht, A.: Particle swarm optimization: Global best or local best. In: 1st BRICS Countries Congress on Computational Intelligence. IEEE Press, Piscataway (2013)
Van den Bergh, F.: An analysis of particle swarm optimizers. PhD thesis, Department of Computer Science, University of Pretoria, Pretoria, South Africa (2002)
Kisacanin, B., Agarwal, G.: Linear Control Systems: With Solved Problems and Matlab Examples. Springer, New York (2001)
Cleghorn, C., Engelbrecht, A.: Particle swarm convergence: An empirical investigation. In: Proceedings of the Congress on Evolutionary Computation, pp. 1–7. IEEE Press, Piscataway (accepted at, 2014)
Liang, J., Qu, B., Suganthan, P.: Problem definitions and evaluation criteria for the cec 2014 special session and competition on single objective real-parameter numerical optimization. Technical Report 201311, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Nanyang Technological University, Singapore (2013)
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Cleghorn, C.W., Engelbrecht, A.P. (2014). Particle Swarm Convergence: Standardized Analysis and Topological Influence. In: Dorigo, M., et al. Swarm Intelligence. ANTS 2014. Lecture Notes in Computer Science, vol 8667. Springer, Cham. https://doi.org/10.1007/978-3-319-09952-1_12
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DOI: https://doi.org/10.1007/978-3-319-09952-1_12
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09951-4
Online ISBN: 978-3-319-09952-1
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