Skip to main content
SpringerLink
Log in

Modified Constrained Differential Evolution for Solving Nonlinear Global Optimization Problems

  • Conference paper
Computational Intelligence (IJCCI 2011)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 465))

Included in the following conference series:

Abstract

Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolution has shown to be very efficient when solving global optimization problems with simple bounds. In this paper, we propose a modified constrained differential evolution based on different constraints handling techniques, namely, feasibility and dominance rules, stochastic ranking and global competitive ranking and compare their performances on a benchmark set of problems. A comparison with other solution methods available in literature is also provided. The convergence behavior of the algorithm to handle discrete and integer variables is analyzed using four well-known mixed-integer engineering design problems. It is shown that our method is rather effective when solving nonlinear optimization problems.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
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. Ali, M.M., Khompatraporn, C., Zabinsky, Z.B.: A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems. J. Glob. Optim. 31, 635–672 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barbosa, H.J.C., Lemonge, A.C.C.: A new adaptive penalty scheme for genetic algorithms. Inf. Sci. 156, 215–251 (2003)

    Article  MathSciNet  Google Scholar 

  3. Brest, J., Greiner, S., Bošković, B., Mernik, M., Žumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10, 646–657 (2006)

    Article  Google Scholar 

  4. Coello Coello, C.A.: Constraint-handling using an evolutionary multiobjective optimization technique. Civ. Eng. Environ. Syst. 17, 319–346 (2000)

    Article  Google Scholar 

  5. Coello Coello, C.A., Cortés, N.C.: Hybridizing a genetic algorithm with an artificial immune system for global optimization. Eng. Optim. 36, 607–634 (2004)

    Article  MathSciNet  Google Scholar 

  6. Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186, 311–338 (2000)

    Article  MATH  Google Scholar 

  7. Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91, 201–213 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dong, Y., Tang, J., Xu, B., Wang, D.: An application of swarm optimization to nonlinear programming. Comput. Math. Appl. 49, 1655–1668 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Erbatur, F., Hasançebi, O., Tütüncü, İ., Kılıç, H.: Optimal design of planar and space structures with genetic algorithms. Comput. Struct. 75, 209–224 (2000)

    Article  Google Scholar 

  10. Fletcher, R., Leyffer, S.: Nonlinear programming without a penalty function. Math. Program. 91, 239–269 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  11. Fourer, R., Gay, D.M., Kernighan, B.W.: AMPL: A modeling language for mathematical programming. Boyd & Fraser Publishing Co., Massachusetts (1993)

    MATH  Google Scholar 

  12. Hedar, A.R., Fukushima, M.: Derivative-free filter simulated annealing method for constrained continuous global optimization. J. Glob. Optim. 35, 521–549 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  14. Kaelo, P., Ali, M.M.: A numerical study of some modified differential evolution algorithms. Eur. J. Oper. Res. 169, 1176–1184 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lampinen, J., Zelinka, I.: Mixed integer-discrete-continuous optimization by differential evolution. In: Proceedings of the 5th International Conference on Soft Computing, pp. 71–76 (1999)

    Google Scholar 

  16. Ray, T., Tai, K.: An evolutionary algorithm with a multilevel pairing strategy for single and multiobjective optimization. Found. Comput. Decis. Sci. 26, 75–98 (2001)

    Google Scholar 

  17. Ray, T., Liew, K.M.: Society and civilization: An optimization algorithm based on the simulation of social behavior. IEEE Trans. Evol. Comput. 7, 386–396 (2003)

    Article  Google Scholar 

  18. Rocha, A.M.A.C., Fernandes, E.M.G.P.: Feasibility and Dominance Rules in the Electromagnetism-Like Algorithm for Constrained Global Optimization. In: Gervasi, O., Murgante, B., Laganà, A., Taniar, D., Mun, Y., Gavrilova, M.L. (eds.) ICCSA 2008, Part II. LNCS, vol. 5073, pp. 768–783. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  19. Rocha, A.M.A.C., Fernandes, E.M.G.P.: Self adaptive penalties in the electromagnetism-like algorithm for constrained global optimization problems. In: Proceedings of the 8th World Congress on Structural and Multidisciplinary Optimization, pp. 1–10 (2009)

    Google Scholar 

  20. Rocha, A.M.A.C., Martins, T.F.M.C., Fernandes, E.M.G.P.: An augmented Lagrangian fish swarm based method for global optimization. J. Comput. Appl. Math. 235, 4611–4620 (2011)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  22. Runarsson, T.P., Yao, X.: Constrained evolutionary optimization – the penalty function approach. In: Sarker, et al. (eds.) Evolutionary Optimization. International Series in Operations Research and Management Science, vol. 48, pp. 87–113. Springer, New York (2003)

    Chapter  Google Scholar 

  23. Silva, E.K., Barbosa, H.J.C., Lemonge, A.C.C.: An adaptive constraint handling technique for differential evolution with dynamic use of variants in engineering optimization. Optim. Eng. 12, 31–54 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Storn, R., Price, K.: Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  25. Tomassetti, G.: A cost-effective algorithm for the solution of engineering problems with particle swarm optimization. Eng. Optim. 42(5), 471–495 (2010)

    Article  Google Scholar 

  26. Wang, J., Yin, Z.: A ranking selection-based particle swarm optimizer for engineering design optimization problems. Struct. Multidisc. Optim. 37(2), 131–147 (2008)

    Article  Google Scholar 

  27. Wang, P.-C., Tsai, J.-F.: Global optimization of mixed-integer nonlinear programming for engineering design problems. In: Proceedings of the International Conference on System Science and Engineering, pp. 255–259 (2011)

    Google Scholar 

  28. Zahara, E., Hu, C.-H.: Solving constrained optimization problems with hybrid particle swarm optimization. Eng. Optim. 40, 1031–1049 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Algoritmi R&D Centre, University of Minho, 4710-057, Braga, Portugal

    Md. Abul Kalam Azad & M. G. P. Fernandes

Authors
  1. Md. Abul Kalam Azad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. G. P. Fernandes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Md. Abul Kalam Azad .

Editor information

Editors and Affiliations

  1. , Images, Signals and, University PARIS-EST Creteil (UPEC), Paris 12, 3956, France

    Kurosh Madani

  2. , Departamento de Engenharia Informatica, University of Coimbra, Polo II - Pinhal de Marrocos, Coimbra, 3030, Portugal

    António Dourado

  3. Systems and Robotics Institute, Evolutionary Systems and, Instituto Superior Tecnico IST, Av. Rovisco Pais, Lisboa, 1049-001, Portugal

    Agostinho Rosa

  4. INSTICC, Polytechnic Institute of Setúbal /, Setubal, 2910-595, Portugal

    Joaquim Filipe

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Azad, M.A.K., Fernandes, M.G.P. (2013). Modified Constrained Differential Evolution for Solving Nonlinear Global Optimization Problems. In: Madani, K., Dourado, A., Rosa, A., Filipe, J. (eds) Computational Intelligence. IJCCI 2011. Studies in Computational Intelligence, vol 465. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35638-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-35638-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35637-7

  • Online ISBN: 978-3-642-35638-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation