Abstract
This paper presents a particle swarm optimizer for solving constrained optimization problems which adopts a very small population size (five particles). The proposed approach uses a reinitialization process for preserving diversity, and does not use a penalty function nor it requires feasible solutions in the initial population. The leader selection scheme adopted is based on the distance of a solution to the feasible region. In addition, a mutation operator is incorporated to improve the exploratory capabilities of the algorithm. The approach is tested with a well-know benchmark commonly adopted to validate constraint-handling approaches for evolutionary algorithms. The results show that the proposed algorithm is competitive with respect to state-of-the-art constraint-handling techniques. The number of fitness function evaluations that the proposed approach requires is almost the same (or lower) than the number required by the techniques of the state-of-the-art in the area.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Andrews, P.S.: An investigation into mutation operators for particle swarm optimization. In: CEC 2006. Proceedings of the 2006 IEEE Congress on Evolutionary Computation, Vancouver, Canada, July, pp. 3789–3796 (2006)
Coello, C.A.C., Pulido, G.T.: Multiobjective optimization using a micro-genetic algorithm. In: Spector, L., Goodman, E.D., Wu, A., Langdon, W., Voigt, H.M., Gen, M., Sen, S., Dorigo, M., Pezeshk, S., Garzon, M., Burke, E. (eds.) GECCO 2001. Genetic and Evolutionary Computation Conference, pp. 274–282. Morgan Kaufmann, San Francisco (2001)
Coello, C.A.C.: Theoretical and numerical constraint handling techniques used with evolutionary algorithms: A survey of the state of the art. Computer Methods in Applied Mechanics and Engineering 191(11–12), 1245–1287 (2002)
Eberhart, R., Kennedy, J.: Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, pp. 1942–1948. IEEE Computer Society Press, Los Alamitos (1995)
Esquivel, S.C., Coello Coello, C.A.: On the use of particle swarm optimization with multimodal functions. In: CEC 2003. Proceedings of the 2003 IEEE Congress on Evolutionary Computation, pp. 1130–1136. IEEE Computer Society Press, Los Alamitos (2003)
Aguirre, A.H., Muñoz Zavala, A.E., Villa Diharce, E., Botello Rionda, S.: COPSO: Constrained Optimization via PSO algorithm. Technical Report I-07-04, Center of Research in Mathematics (CIMAT), Guanajuato, México (2007)
Hu, X., Eberhart, R.: Solving Constrained Nonlinear Optimization Problems with Particle Swarm Optimization. In: SCI 2002. Proceedings of the 6th World Multiconference on Systemics, Cybernetics and Informatics, Orlando, USA IIIS, vol. 5(July 2002)
Hu, X., Eberhart, R.C., Shi, Y.: Engineering Optimization with Particle Swarm. In: Proceedings of the 2003 IEEE Swarm Intelligence Symposium, Indianapolis, Indiana, USA, pp. 53–57. IEEE Service Center (April 2003)
Kennedy, J., Mendes, R.: Population structure and particle swarm performance. In: Proceedings of the 2002 IEEE Congress on Evolutionary Computation, vol. 2, pp. 1671–1676. IEEE Press, Los Alamitos (2002)
Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kauffmann Publishers, San Francisco (2001)
Koziel, S., Michalewicz, Z.: Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization. Evolutionary Computation 7(1), 19–44 (1999)
Krishnakumar, K.: Micro-genetic algorithms for stationary and non-stationary function optimization. In: SPIE. Proceedings: Intelligent Control and Adaptive Systems, vol. 1196, pp. 289–296 (1989)
Liang, J.J., Runarsson, T.P., Mezura-Montes, E., Clerc, M., Suganthan, P.N., Coello Coello, C.A., Deb, K.: Problem definitions and evaluation criteria for the cec 2006 special session on constrained real-parameter optimization. Technical report, Nanyang Technological University, Singapore (2006)
Mezura-Montes, E., Coello Coello, C.A.: A simple multimembered evolution strategy to solve constrained optimization problems. Transactions on Evolutionary Computation 9(1), 1–17 (2005)
Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs. Springer, Heidelberg (1996)
Michalewicz, Z., Schoenauer, M.: Evolutionary Algorithms for Constrained Parameter Optimization Problems. Evolutionary Computation 4(1), 1–32 (1996)
Paquet, U., pEngelbrecht, A.: A New Particle Swarm Optimiser for Linearly Constrained Optimization. In: CEC 2003. Proceedings of the Congress on Evolutionary Computation 2003, Piscataway, New Jersey, vol. 1, pp. 227–233. IEEE Service Center, Canberra, Australia (2003)
Runanarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation 4(3), 248–249 (2000)
Shi, Y., Eberhart, R.C.: A modified particle swarm optimizer. In: Proceedings of the 1998 IEEE Congress on Evolutionary Computation, pp. 69–73. IEEE Computer Society Press, Los Alamitos (1998)
Pulido, G.T., Coello Coello, C.A.: A constraint-handling mechanism for particle swarm optimization. In: CEC 2004. Proceedings of the 2004 IEEE Congress on Evolutionary Computation, vol. 2, pp. 1396–1403. IEEE Press, Los Alamitos (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fuentes Cabrera, J.C., Coello Coello, C.A. (2007). Handling Constraints in Particle Swarm Optimization Using a Small Population Size. In: Gelbukh, A., Kuri Morales, Á.F. (eds) MICAI 2007: Advances in Artificial Intelligence. MICAI 2007. Lecture Notes in Computer Science(), vol 4827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76631-5_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-76631-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-76630-8
Online ISBN: 978-3-540-76631-5
eBook Packages: Computer ScienceComputer Science (R0)