Skip to main content
SpringerLink
Log in

Improved Particle Swarm Optimization in Constrained Numerical Search Spaces

  • Chapter
Nature-Inspired Algorithms for Optimisation

Part of the book series: Studies in Computational Intelligence ((SCI,volume 193))

Abstract

This chapter presents a study about the behavior of Particle Swarm Optimization (PSO) in constrained search spaces. A comparison of four well-known PSO variants used to solve a set of test problems is presented. Based on the information obtained, the most competitive PSO variant is detected. From this preliminary analysis, the performance of this variant is improved with two simple modifications related with the dynamic control of some parameters and a variation in the constraint-handling technique. These changes keep the simplicity of PSO i.e. no extra parameters, mechanisms controlled by the user or combination of PSO variants are added. This Improved PSO (IPSO) is extensively compared against the original PSO variants, based on the quality and consistency of the final results and also on two performance measures and convergence graphs to analyze their on-line behavior. Finally, IPSO is compared against some state-of-the-art PSO-based approaches for constrained optimization. Statistical tests are used in the experiments in order to add support to the findings and conclusions established.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York (1996)

    MATH  Google Scholar 

  2. Cagnina, L.C., Esquivel, S.C., Coello, C.A.C.: A Particle Swarm Optimizer for Constrained Numerical Optimization. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 910–919. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Clerc, M., Kennedy, J.: The Particle Swarm-Explosion, Stability, and Convergence in a Multidimensional Complex Space. IEEE Transactions on Evolutionary Computation 6(1), 58–73 (2002)

    Article  Google Scholar 

  4. 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)

    Article  MATH  MathSciNet  Google Scholar 

  5. Deb, K.: An Efficient Constraint Handling Method for Genetic Algorithms. Computer Methods in Applied Mechanics and Engineering 186(2/4), 311–338 (2000)

    Article  MATH  Google Scholar 

  6. Dorigo, M., Maniezzo, V., Colorni, A.: The Ant System: Optimization by a Colony of Cooperating Agents. IEEE Transactions of Systems, Man and Cybernetics-Part B 26(1), 29–41 (1996)

    Article  Google Scholar 

  7. Eiben, A., Smith, J.E.: Introduction to Evolutionary Computing. Natural Computing Series. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  8. Eiben, G., Schut, M.C.: New Ways to Calibrate Evolutionary Algorithms. In: Siarry, P., Michalewicz, Z. (eds.) Advances in Metaheuristics for Hard Optimization. Natural Computing Series, pp. 153–177. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Engelbrecht, A.: Fundamentals of Computational Swarm Intelligence. John Wiley & Sons, Chichester (2005)

    Google Scholar 

  10. Fogel, L.: Autonomous Automata. Industrial Research 4(12), 14–19 (1962)

    Google Scholar 

  11. Glover, F., Laguna, F.: Tabu Search. Kluwer Academic Publishers, Norwell (1997)

    MATH  Google Scholar 

  12. Glover, F., Laguna, M., Ri, M.: Scatter Search. In: Advances in Evolutionary Computing: Theory and Applications, pp. 519–537. Springer, New York (2003)

    Google Scholar 

  13. He, S., Prempain, E., Wu, Q.H.: An Improved Particle Swarm Optimizer for Mechanical Design Optimization Problems. Engineering Optimization 36(5), 585–605 (2004)

    Article  MathSciNet  Google Scholar 

  14. Holland, J.H.: Concerning Efficient Adaptive Systems. In: Yovits, M.C., Jacobi, G.T., Goldstein, G.D. (eds.) Self-Organizing Systems, pp. 215–230. Spartan Books, Washington (1962)

    Google Scholar 

  15. Kennedy, J., Eberhart, R.C.: Swarm Intelligence. Morgan Kaufmann, UK (2001)

    Google Scholar 

  16. Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by Simulated Annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  17. Koza, J.R.: Genetic Programming. On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)

    MATH  Google Scholar 

  18. Krohling, R.A., dos Santos Coelho, L.: Coevolutionary Particle Swarm Optimization Using Gaussian Distribution for Solving Constrained Optimization Problems. IEEE Transactions on Systems, Man and Cybernetics Part B 36(6), 1407–1416 (2006)

    Article  Google Scholar 

  19. Lampinen, J.: A Constraint Handling Approach for the Diifferential Evolution Algorithm. In: Proceedings of the Congress on Evolutionary Computation (CEC 2002), vol. 2, pp. 1468–1473. IEEE, Piscataway (2002)

    Chapter  Google Scholar 

  20. Li, H., Jiao, Y.C., Wang, Y.: Integrating the Simplified Interpolation into the Genetic Algorithm for Constrained Optimization problems. In: Hao, Y., Liu, J., Wang, Y.-P., Cheung, Y.-m., Yin, H., Jiao, L., Ma, J., Jiao, Y.-C. (eds.) CIS 2005. LNCS, vol. 3801, pp. 247–254. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Li, X., Tian, P., Kong, M.: Novel Particle Swarm Optimization for Constrained Optimization Problems. In: Zhang, S., Jarvis, R. (eds.) AI 2005. LNCS, vol. 3809, pp. 1305–1310. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  22. Li, X., Tian, P., Min, X.: A Hierarchical Particle Swarm Optimization for Solving Bilevel Programming Problems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS, vol. 4029, pp. 1169–1178. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  23. Liang, J.J., Suganthan, P.N.: Dynamic Multi-Swarm Particle Swarm Optimizer with a Novel Constrain-Handling Mechanism. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2006), pp. 316–323. IEEE, Vancouver (2006)

    Google Scholar 

  24. Liang, J.J., Runarsson, T., Mezura-Montes, E., Clerc, M., Suganthan, P.N., Coello, C.C., Deb, K.: Problem Definitions and Evaluation Criteria for the CEC 2006, Special Session on Constrained Real-Parameter Optimization. Tech. rep. (2006), http://www3.ntu.edu.sg/home/EPNSugan/

  25. Lu, H., Chen, W.: Dynamic-Objective Particle Swarm Optimization for Constrained Optimization Problems. Journal of Combinatorial Optimization 12(4), 409–419 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  26. Mendes, R., Kennedy, J., Neves, J.: The Fully Informed Particle Swarm: Simpler, Maybe Better. IEEE Transactions on Evolutionary Computation 8(3), 204–210 (2004)

    Article  Google Scholar 

  27. Mezura-Montes, E., Coello, C.A.C.: Identifying On-line Behavior and Some Sources of Difficulty in Two Competitive Approaches for Constrained Optimization. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2005), vol. 2, pp. 1477–1484. IEEE, Edinburgh (2005)

    Chapter  Google Scholar 

  28. Mezura-Montes, E., Coello-Coello, C.A.: Constrained Optimization via Multiobjective Evolutionary Algorithms. In: Multiobjective Problems Solving from Nature: From Concepts to Applications. Natural Computing Series, pp. 53–76. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  29. Mezura-Montes, E., López-Ramírez, B.C.: Comparing Bio-Inspired Algorithms in Constrained Optimization problems. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2007), pp. 662–669. IEEE, Singapore (2007)

    Chapter  Google Scholar 

  30. Michalewicz, Z., Schoenauer, M.: Evolutionary Algorithms for Constrained Parameter Optimization Problems. Evolutionary Computation 4(1), 1–32 (1996)

    Article  Google Scholar 

  31. Paquet, U., Engelbrecht, A.P.: A New Particle Swarm Optimiser for Linearly Constrained Optimization. In: Proceedings of the Congress on Evolutionary Computation (CEC 2003), vol. 1, pp. 227–233. IEEE, Canberra (2003)

    Chapter  Google Scholar 

  32. Parsopoulos, K., Vrahatis, M.: Unified Particle Swarm Optimization for Solving Constrained Engineering Optimization Problems. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3612, pp. 582–591. Springer, Heidelberg (2005)

    Google Scholar 

  33. Powell, D., Skolnick, M.M.: Using Genetic Algorithms in Engineering Design Optimization with Non-Linear Constraints. In: Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms (ICGA 1993), University of Illinois at Urbana-Champaign, pp. 424–431. Morgan Kaufmann Publishers, San Mateo (1993)

    Google Scholar 

  34. Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution. In: A practical Approach to Global Optimization. Springer, Heidelberg (2005)

    Google Scholar 

  35. Runarsson, T.P., Yao, X.: Stochastic Ranking for Constrained Evolutionary Optimization. IEEE Transactions on Evolutionary Computation 4(3), 284–294 (2000)

    Article  Google Scholar 

  36. Schoenauer, M., Xanthakis, S.: Constrained GA Optimization. In: Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms (ICGA 1993), University of Illinois at Urbana-Champaign, pp. 573–580. Morgan Kauffman Publishers, San Mateo (1993)

    Google Scholar 

  37. Schwefel, H.P. (ed.): Evolution and Optimization Seeking. Wiley, New York (1995)

    Google Scholar 

  38. Shi, Y., Eberhart, R.: A Modified Particle Swarm Optimizer. In: Proceedings of the IEEE World Congress on Computational Intelligence, pp. 69–73 (1998)

    Google Scholar 

  39. Shi Y., Eberhart, R.C.: Parameter Selection in Particle Swarm Optimization (1998), http://www.engriupui.edu/shi/PSO/Paper/EP98/psof6/ep98_pso.html

  40. Takahama, T., Sakai, S., Iwane, N.: Solving Nonlinear Constrained Optimization Problems by the ε Constrained Differential Evolution. In: Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, Taipei, Taiwan, pp. 2322–2327 (2006)

    Google Scholar 

  41. Tessema, B., Yen, G.G.: A Self Adaptative Penalty Function Based Algorithm for Constrained Optimization. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2006), pp. 950–957. IEEE, Vancouver (2006)

    Google Scholar 

  42. Toscano-Pulido, G., Coello Coello, C.A.: A Constraint-Handling Mechanism for Particle Swarm Optimization. In: Proceedings of the Congress on Evolutionary Computation (CEC 2004), vol. 2, pp. 1396–1403. IEEE, Portland (2004)

    Chapter  Google Scholar 

  43. Wei, J., Wang, Y.: A novel multi-objective PSO algorithm for constrained optimization problems. In: Wang, T.-D., Li, X.-D., Chen, S.-H., Wang, X., Abbass, H.A., Iba, H., Chen, G.-L., Yao, X. (eds.) SEAL 2006. LNCS, vol. 4247, pp. 174–180. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratorio Nacional de Informática Avanzada (LANIA A.C.), Rébsamen 80, Centro, Xalapa, Veracruz, 91000, México

    Efrén Mezura-Montes & Jorge Isacc Flores-Mendoza

Authors
  1. Efrén Mezura-Montes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jorge Isacc Flores-Mendoza
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Swinburne University of Technology, Sarawak Campus, Jalan Simpang Tiga, 93350, Kuching, Sarawak, Malaysia

    Raymond Chiong

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Mezura-Montes, E., Flores-Mendoza, J.I. (2009). Improved Particle Swarm Optimization in Constrained Numerical Search Spaces. In: Chiong, R. (eds) Nature-Inspired Algorithms for Optimisation. Studies in Computational Intelligence, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00267-0_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00267-0_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00266-3

  • Online ISBN: 978-3-642-00267-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation