Abstract
Particle Swarm Optimization (PSO) is a stochastic optimization approach that originated from simulations of bird flocking, and that has been successfully used in many applications as an optimization tool. Estimation of distribution algorithms (EDAs) are a class of evolutionary algorithms which perform a two-step process: building a probabilistic model from which good solutions may be generated and then using this model to generate new individuals. Two distinct research trends that emerged in the past few years are the hybridization of PSO and EDA algorithms and the parallelization of EDAs to exploit the idea of exchanging the probabilistic model information. In this work, we propose the use of a cooperative PSO/EDA algorithm based on the exchange of heterogeneous probabilistic models. The model is heterogeneous because the cooperating PSO/EDA algorithms use different methods to sample the search space. Three different exchange approaches are tested and compared in this work. In all these approaches, the amount of information exchanged is adapted based on the performance of the two cooperating swarms. The performance of the cooperative model is compared to the existing state-of-the-art PSO cooperative approaches using a suite of well-known benchmark optimization functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahn, C. W., Goldberg, D. E., & Ramakrishna, R. S. (2004). Multiple-deme parallel estimation of distribution algorithms: basic framework and applications. In Lecture notes in computer science : Vol. 3019. Proceedings of international conference on parallel processing and applied mathematics (pp. 544–551). Berlin: Springer.
Clerc, M. (2006a). Particle swarm optimization. London: ISTE.
Clerc, M. (2006b). Tribes-d code. http://clerc.maurice.free.fr/pso/Tribes/TRIBES-D.zip.
Cooren, Y., Clerc, M., & Siarry, P. (2009). Performance evaluation of tribes, an adaptive particle swarm optimization algorithm. Swarm Intelligence, 3(2), 149–178.
de la Ossa, L., Gamez, J., & Puerta, J. (2004). Migration of probability models instead of individuals: an alternative when applying the island models to EDAs. In X. Yao, E. Burke, J. A. Lozano, J. Smith, J. J. Merelo-Guervo’s, J. A. Bullinaria, J. Rowe, P. Tino, A. Kaba’n, & H. P. Schwefel (Eds.), Lecture notes in computer science : Vol. 3242. Proceedings of parallel problem solving from nature (pp. 242–252). Berlin: Springer.
de la Ossa, L., Gamez, J., & Puerta, J. (2006). Initial approaches to the application of island-based parallel edas in continuous domains. Journal of Parallel and Distributed Computing, 66(8), 991–1001.
El-Abd, M., & Kamel, M. S. (2007). Particle swarm optimization with varying bounds. In Proceedings of IEEE congress on evolutionary computation (pp. 4757–4761). Piscataway: IEEE Press.
El-Abd, M., & Kamel, M. S. (2008). A taxonomy of cooperative search algorithms. International Journal of Computational Intelligence Research, 4(2), 137–144.
Gallagher, M., Frean, M., & Downs, T. (1999). Real-valued evolutionary optimization using a flexible probability density estimator. In Proceedings of genetic and evolutionary computation conference (Vol. 1, pp. 840–846). San Francisco: Morgan Kaufmann.
Grahl, J., Bosman, P. A. N., & Rothlauf, F. (2006). The correlation-triggered adaptive variance scaling idea. In Proceedings of genetic and evolutionary computation conference (pp. 397–404). New York: ACM.
Hiroyaso, T., Miki, M., Sano, M., Shimosaka, H., Tsutsui, S., & Dongarra, J. (2003). Distributed probabilistic model-building genetic algorithm. In Lecture notes in computer science : Vol. 2724. Proceedings of genetic and evolutionary computation conference (pp. 1015–1028). Berlin: Springer.
Iqbal, M. & Montes de Oca, M. A. (2006). An estimation of distribution particle swarm optimization algorithm. In M. Dorigo, L. M. Gambardella, M. Birattari, A. Martinoli, R. Poli, & T. Stützle (Eds.), Lecture notes in computer science : Vol. 4150. Proceedings of the fifth international workshop on ant colony optimization and swarm intelligence (pp. 72–83). Berlin: Springer.
Jaros, J. & Schwarz, J. (2007). Parallel BMDA with probability model migration. In Proceedings of IEEE congress on evolutionary computation (pp. 1059–1066). Piscataway: IEEE Press.
Kennedy, J., & Eberhart, R. C. (1995). Particle swarm optimization. In Proceedings of IEEE international conference on neural networks (Vol. 4, pp. 1942–1948). Piscataway: IEEE Press.
Kennedy, J., & Mendes, R. (2002). Population structure and particle swarm performance. In Proceedings of IEEE congress on evolutionary computation (Vol. 2, pp. 1671–1676). Washington: IEEE Computer Society.
Larrañaga, P., & Lozano, J. A. (2001). Estimation of distribution algorithms. A new tool for evolutionary computation, genetic algorithms and evolutionary computation (Vol. 2). Berlin: Springer.
Liang, J. J., & Suganthan, P. N. (2005a). Dynamic multi-swarm particle swarm optimizer. In Proceedings of IEEE swarm intelligence symposium (pp. 124–129). Piscataway: IEEE Press.
Liang, J. J., & Suganthan, P. N. (2005b). Dynamic multi-swarm particle swarm optimizer with local search. In Proceedings of IEEE congress on evolutionary computation (pp. 522–528). Washington: IEEE Computer Society.
Madera, J., Alba, E., & Ochoa, A. (2006). A parallel island model for estimation of distribution algorithms. In J. A. Lozano, P. Larrañaga, I. Inza, & E. Bengoetxea (Eds.), Advances in the estimation of distribution algorithms, studies in fuzziness and soft computing : Vol. 192. Towards a new evolutionary computation (pp. 159–186). Berlin: Springer.
Monson, C. K., & Seppi, K. D. (2005). Exposing origin-seeking bias in PSO. In Proceedings of genetic and evolutionary computation conference (pp. 241–248). New York: ACM Press.
Mühlenbein, H. (1998). The equation for response to selection and its use for prediction. IEEE Transactions on Evolutionary Computation, 5(3), 303–346.
Rudolph, S., & Köppen, M. (1996). Stochastic hill climbing with learning by vectors of normal distributions. In First on-line workshop on soft computing (pp. 60–70), Nagoya, Japan, Nagoya University.
Schwarz, J., Jaros, J., & Ocenasek, J. (2007). Migration of probabilistic models for island-based bivariate EDA algorithm. In Proceedings of genetic and evolutionary computational conference (Vol. 1, p. 631). New York: ACM.
Sebag, M., & Ducoulombier, A. (1998). Extending population-based incremental learning to continuous search spaces. In Lecture notes in computer science : Vol. 1498. Proceedings of parallel problem solving from nature (pp. 418–427). Berlin: Springer.
Servet, I., Trave-Massuyes, L., & Stern, D. (1997). Telephone network traffic overloading diagnosis and evolutionary computation technique. In Lecture notes in computer science : Vol. 1363. Proceedings of artificial evolution (pp. 137–144). Berlin: Springer.
Socha, K., & Dorigo, M. (2005). Ant colony optimization for continuous domains (Technical Report TR/IRIDIA/2005-037). Université Libre de Bruxelles, Brussels, Belgium.
Socha, K., & Dorigo, M. (2008). Ant colony optimization for continuous domains. European Journal of Operational Research, 185(3), 1155–1173.
Suganthan, P. N., Hansen, N., Liang, J. J., Deb, K., Chen, Y. P., Auger, A., & Tiwari, S. (2005a). CEC05 benchmark functions. http://staffx.webstore.ntu.edu.sg/MySite/Public.aspx?accountname=epnsugan.
Suganthan, P. N., Hansen, N., Liang, J. J., Deb, K., Chen, Y. P., Auger, A., & Tiwari, S. (2005b). Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization (Technical Report 2005005). ITT Kanpur, India.
van den Bergh, F., & Engelbrecht, A. P. (2004). A cooperative approach to particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8(3), 225–239.
Yuan, B., & Gallagher, M. (2005). Experimental results for the special session on real-parameter optimization at CEC 2005: a simple, continuous EDA. In Proceedings IEEE congress on evolutionary computation (Vol. 2, pp. 1792–1799). Washington: IEEE Computer Society.
Zhou, Y., & Jin, J. (2006). EDA/PSO—a new hybrid intelligent optimization algorithm. In Proceedings of the university of Michigan graduate student symposium (p. 231). Michigan. http://www.engin.umich.edu/students/gradsymposium/2006pamphlet.pdf.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
El-Abd, M., Kamel, M.S. A cooperative particle swarm optimizer with migration of heterogeneous probabilistic models. Swarm Intell 4, 57–89 (2010). https://doi.org/10.1007/s11721-009-0037-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11721-009-0037-5