Skip to main content
SpringerLink
Log in

Self-adaptive velocity particle swarm optimization for solving constrained optimization problems

  • Published:
Journal of Global Optimization Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Floudas, C.A., Pardalos, P.M.: A collection of test problems for constrained global optimization algorithms. Lect. Notes Comput. Sci. 455, Springer-Verlag (1987)

  2. Himmelblau, D.M.: Applied Nonlinear Programming. McGraw-Hill (1972)

  3. 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

    Article  Google Scholar 

  4. 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

    Article  Google Scholar 

  5. Hu, X., Eberhart, R.C., Shi, Y.: Engineering optimization with particle swarm. In: Proceedings of 2003 IEEE Swarm Intelligence Symposium, pp. 53–57 (2003)

  6. 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

    Article  Google Scholar 

  7. Yeniay Ö. (2005). Penalty function methods for constrained optimization with genetic algorithms. Math. Comput. Appl. 10: 45–56

    Google Scholar 

  8. Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, Perth, Australia, pp. 1942–1948 (1995)

  9. 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)

  10. Michalewicz Z. and Schoenauer M. (1996). Evolutionary algorithms for constrained parameter optimization problems. Evol. Comput. 4: 1–32

    Article  Google Scholar 

  11. Coello Coello C.A. (2000). Treating constraints as objectives for single objective evolutionary computations. Eng. Optim. 32: 275–308

    Article  Google Scholar 

  12. 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)

  13. 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)

  14. 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)

  15. 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)

  16. Runarsson T.P. and Yao X. (2000). Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput. 4: 284–294

    Article  Google Scholar 

  17. Koziel S. and Michalewicz Z. (1999). Evolutionary algorithms, homomorphous mappings and constrained parameter optimization. Evol. Comput. 7: 19–44

    Article  Google Scholar 

  18. 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)

  19. Lu H.Y. and Chen W.Q. (2006). Dynamic-objective particle swarm optimization for constrained optimization problems. J. Comb. Optim. 12: 409–419

    Article  Google Scholar 

  20. Kennedy, J.: Dynamic-probabilistic particle swarms. GECCO’05, June 2005, Washington, DC, USA, pp. 201–207 (2005)

  21. 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

    Chapter  Google Scholar 

  22. 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

    Chapter  Google Scholar 

  23. Shi, Y., Eberhart, R.C.: A modified particle swarm optimizer. In: Proceeding of IEEE Conference on Evolutionary Computation, Anchorage, AK, pp. 69–73 (1998)

  24. Shi, Y.: Particle swarm optimization. IEEE Neural Networks Society, February, pp. 8–13 (2004)

  25. 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)

  26. 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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Jiangnan University, Wuxi, 214122, P.R. China

    Haiyan Lu

  2. Department of Mathematics, Zhejiang University, Hangzhou, 310027, P.R. China

    Haiyan Lu

  3. School of Information Technology, Jiangnan University, Wuxi, 214122, P.R. China

    Weiqi Chen

  4. China Ship Scientific Research Center, Wuxi, 214082, P.R. China

    Weiqi Chen

Authors
  1. Haiyan Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weiqi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haiyan Lu.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10898-007-9255-9

Keywords

Search

Navigation