Abstract
Particle swarm optimization (PSO) algorithm can be viewed as a series of iterative matrix computation and its population diversity can be considered as an observation of the distribution of matrix elements. In this paper, PSO algorithm is first represented in the matrix format, then the PSO normalized population diversities are defined and discussed based on matrix analysis. Based on the analysis of the relationship between pairs of vectors in PSO solution matrix, different population diversities are defined for separable and non-separable problems, respectively. Experiments on benchmark functions are conducted and simulation results illustrate the effectiveness and usefulness of the proposed normalized population diversities.
The authors’ work was supported by National Natural Science Foundation of China under grant No. 60975080, and Suzhou Science and Technology Project under Grant No. SYJG0919.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Processings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39–43 (1995)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Processings of IEEE International Conference on Neural Networks (ICNN), pp. 1942–1948 (1995)
Eberhart, R., Shi, Y.: Computational Intelligence: Concepts to Implementations, 1st edn. Morgan Kaufmann Publisher, San Francisco (2007)
Shi, Y., Eberhart, R.C.: Population diversity of particle swarms. In: Proceedings of the 2008 Congress on Evolutionary Computation, pp. 1063–1067 (2008)
Olorunda, O., Engelbrecht, A.P.: Measuring exploration/exploitation in particle swarms using swarm diversity. In: Proceedings of the 2008 Congress on Evolutionary Computation, pp. 1128–1134 (2008)
Eberhart, R., Shi, Y.: Particle swarm optimization: Developments, applications and resources. In: Proceedings of the 2001 Congress on Evolutionary Computation, pp. 81–86 (2001)
Shi, Y., Eberhart, R.: Monitoring of particle swarm optimization. Frontiers of Computer Science 3(1), 31–37 (2009)
Cheng, S., Shi, Y.: Diversity control in particle swarm optimization. In: Proceedings of IEEE Swarm Intelligence Symposium 2011, Paris, France (April 2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cheng, S., Shi, Y. (2011). Normalized Population Diversity in Particle Swarm Optimization. In: Tan, Y., Shi, Y., Chai, Y., Wang, G. (eds) Advances in Swarm Intelligence. ICSI 2011. Lecture Notes in Computer Science, vol 6728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21515-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-21515-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21514-8
Online ISBN: 978-3-642-21515-5
eBook Packages: Computer ScienceComputer Science (R0)