Abstract
Particle swarm optimization (PSO) is originally developed as an unconstrained optimization technique, therefore lacks an explicit mechanism for handling constraints. When solving constrained optimization problems (COPs) with PSO, the existing research mainly focuses on how to handle constraints, and the impact of constraints on the inherent search mechanism of PSO has been scarcely explored. Motivated by this fact, in this paper we mainly investigate how to utilize the impact of constraints (or the knowledge about the feasible region) to improve the optimization ability of the particles. Based on these investigations, we present a modified PSO, called self-adaptive velocity particle swarm optimization (SAVPSO), for solving COPs. To handle constraints, in SAVPSO we adopt our recently proposed dynamic-objective constraint-handling method (DOCHM), which is essentially a constituent part of the inherent search mechanism of the integrated SAVPSO, i.e., DOCHM + SAVPSO. The performance of the integrated SAVPSO is tested on a well-known benchmark suite and the experimental results show that appropriately utilizing the knowledge about the feasible region can substantially improve the performance of the underlying algorithm in solving COPs.
Similar content being viewed by others
References
Floudas, C.A., Pardalos, P.M.: A collection of test problems for constrained global optimization algorithms. Lect. Notes Comput. Sci. 455, Springer-Verlag (1987)
Himmelblau, D.M.: Applied Nonlinear Programming. McGraw-Hill (1972)
Coello Coello C.A. (2002). Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: A survey of the state of the art. Comput. Meth. Appl. Mech. Eng. 191: 1245–1287
Dong Y., Tang J.-F., Xu B.-D. and Wang D.-W. (2005). An application of swarm optimization to nonlinear programming. Comput. Math. Appl. 49: 1655–1668
Hu, X., Eberhart, R.C., Shi, Y.: Engineering optimization with particle swarm. In: Proceedings of 2003 IEEE Swarm Intelligence Symposium, pp. 53–57 (2003)
Parsopoulos K.E. and Vrahatis M.N. (2005). Unified particle swarm optimization for solving constrained engineering optimization problems. Lect. Notes Comput. Sci. 3612: 582–591
Yeniay Ö. (2005). Penalty function methods for constrained optimization with genetic algorithms. Math. Comput. Appl. 10: 45–56
Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, Perth, Australia, pp. 1942–1948 (1995)
Eberhart, R.C., Kennedy, J.: A new Optimizer using particle swarm theory. In: Proceedings of 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, pp. 39–43 (1995)
Michalewicz Z. and Schoenauer M. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evol. Comput. 4: 1–32
Coello Coello C.A. (2000). Treating constraints as objectives for single objective evolutionary computations. Eng. Optim. 32: 275–308
Hu, X., Eberhart, R.C.: Solving constrained nonlinear optimization problems with particle swarm optimization. In: Proceedings of 6th World Multiconference on Systemics, Cybernetics and Informatics (SCI 2002), Orlando, USA (2002)
Toscano, G., Coello Coello, C.A.: A constraint-handling mechanism for particle swarm optimization. In: Proceedings of the 2004 Congress on Evolutionary Computation, June, IEEE, pp. 1396–1403 (2004)
Sedlaczek, K., Eberhart, P.: Constrained particle swarm optimization of mechanical systems. In: Proceedings of Sixth World Congresses of Structural and Multidisciplinary Optimization. Rio de Janeiro, Brizil (2005)
Parsopoulos, K.E., Vrahatis, M.N.: Particle swarm optimization method for constrained optimization problems. In: Proceedings of the Euro-International Symposium on Computational Intelligence (E-ISCI 2002) (2002)
Runarsson T.P. and Yao X. (2000). Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput. 4: 284–294
Koziel S. and Michalewicz Z. (1999). Evolutionary algorithms, homomorphous mappings and constrained parameter optimization. Evol. Comput. 7: 19–44
Zhang, W.-J., Xie, X.-F.: DEPSO: hybrid particle swarm with differential evolution operator. In: Proceedings of IEEE International Conference on Systems, Man and Cybernetics, October, IEEE, pp. 3816–3821 (2003)
Lu H.Y. and Chen W.Q. (2006). Dynamic-objective particle swarm optimization for constrained optimization problems. J. Comb. Optim. 12: 409–419
Kennedy, J.: Dynamic-probabilistic particle swarms. GECCO’05, June 2005, Washington, DC, USA, pp. 201–207 (2005)
Eberhart R.C. and Shi Y. (1998). Comparison between genetic algorithms and particle swarm optimization. In: Porto, V.W., Saravanan, N., Waagen, D. and Eiben, A.E. (eds) Evolutionary Programming, Vol. 7, pp 611–616. Springer-Verlag, Berlin
Shi Y. and Eberhart R.C. (1998). Parameter selection in particle swarm optimization. In: Porto, V.W., Saravanan, N., Waagen, D. and Eiben, A.E. (eds) Evolutionary Programming, vol. 7, pp 591–600. Springer-Verlag, Berlin
Shi, Y., Eberhart, R.C.: A modified particle swarm optimizer. In: Proceeding of IEEE Conference on Evolutionary Computation, Anchorage, AK, pp. 69–73 (1998)
Shi, Y.: Particle swarm optimization. IEEE Neural Networks Society, February, pp. 8–13 (2004)
Muñoz Zavala, A.E., Hernández Aguirre, A., Villa Diharce, E.R.: Constrained optimization via particle evolutionary swarm optimization algorithm (PESO), GECCO’05, Washington, DC, USA, 25–27 June, pp. 209–216 (2005)
Storn R. and Price K. (1997). Differential evolution—a simple andd efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11: 341–359
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Lu, H., Chen, W. Self-adaptive velocity particle swarm optimization for solving constrained optimization problems. J Glob Optim 41, 427–445 (2008). https://doi.org/10.1007/s10898-007-9255-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10898-007-9255-9