Advertisement

Experimental Comparison of Methods to Handle Boundary Constraints in Differential Evolution

  • Jarosłlaw Arabas
  • Adam Szczepankiewicz
  • Tomasz Wroniak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6239)

Abstract

In this paper we show that the technique of handling boundary constraints has a significant influence on the efficiency of the Differential Evolution method. We study the effects of applying several such techniques taken from the literature. The comparison is based on experiments performed for a standard DE/rand/1/bin strategy using the CEC2005 benchmark. The paper reports the results of experiments and provides their simple statistical analysis. Among several constraint handling methods, a winning approach is to repeat the differential mutation by resampling the population until a feasible mutant is obtained. Coupling the aforementioned method with a simple DE/rand/1/bin strategy allows to achieve results that outperform in many cases results of almost all other methods tested during the CEC2005 competition, including the original DE/rand/1/bin strategy.

Keywords

Benchmark Function Constraint Handling Constraint Handling Technique Feasible Area Constraint Handling Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Price, K., et al.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  2. 2.
    Neri, F., Tirronen, V.: Recent advances in Differential Evolution: a survey and experimental analysis. Artificial Intelligence Rev. 33(1-2), 61–106 (2010)CrossRefGoogle Scholar
  3. 3.
    Qin, A.K., et al.: Differential Evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evolutionary Computation 13(2), 398–417 (2009)CrossRefGoogle Scholar
  4. 4.
    Liu, J., Lampinen, J.: A Fuzzy Adaptive Differential Evolution algorithm. Soft Computing 9(6), 448–462 (2005)zbMATHCrossRefGoogle Scholar
  5. 5.
    Zhang, J., Sanderson, A.C.: JADE: adaptive Differential Evolution with optional external archive. IEEE Trans. Evolutionary Computation 13(5), 945–958 (2009)CrossRefGoogle Scholar
  6. 6.
    Doumpos, M., et al.: An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method. Eur. J. of Operational Research 199(2), 496–505 (2009)zbMATHCrossRefGoogle Scholar
  7. 7.
    Rönkkönen, J., et al.: Real-parameter optimization with differential evolution. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  8. 8.
    Brest, J., et al.: Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. IEEE Trans. Evolutionary Computation 10(6), 646–657 (2006)CrossRefGoogle Scholar
  9. 9.
    Karabogal, N., Cetinkayal, B.: Design of digital FIR filters using Differential Evolution algorithm. Circuits, Systems, Signal Processing 25(5), 649–660 (2006)CrossRefGoogle Scholar
  10. 10.
    Hansen, N.: Compilation of results on the 2005 CEC benchmark function set (2005), http://www.ntu.edu.sg/home/epnsugan/index_files/CEC-05/compareresults.pdf
  11. 11.
    Suganthan, P.N., et al.: Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report, Nanyang Tech. Univ. (2005)Google Scholar
  12. 12.
    Bui, L.T., et al.: Comparing two versions of differential evolution in real parameter optimization. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  13. 13.
    Qin, A., Suganthan, P.: Self-adaptive differential evolution algorithm for numerical optimization. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  14. 14.
    Martines, C.G., Lozano, M.: Hybrid real-coded genetic algorithms with female and male differentiation. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  15. 15.
    Molina, D., et al.: Adaptive local search parameters for real-coded memetic algorithms. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  16. 16.
    Ballester, P., et al.: Real-parameter optimization performance study on the CEC-2005 benchmark with SPC-PNX. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  17. 17.
    Sinha, A., et al.: A population-based, steady-state procedure for real-parameter optimization. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  18. 18.
    Posik, P.: Real parameter optimization using mutation step co-evolution. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  19. 19.
    Liang, J., Suganthan, P.: Dynamic multi-swarm particle swarm optimizer with local search. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  20. 20.
    Yuan, B., Gallagher, M.: Experimental results for the special session on real-parameter optimization at CEC 2005: A simple, continuous EDA. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  21. 21.
    Auger, A., et al.: A restart CMA evolution strategy with increasing population size. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar
  22. 22.
    Auger, A., et al.: Performance evaluation of an advanced local search evolutionary algorithm. In: CEC 2005. IEEE, Los Alamitos (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Jarosłlaw Arabas
    • 1
  • Adam Szczepankiewicz
    • 2
  • Tomasz Wroniak
    • 2
  1. 1.Institute of Electronic SystemsWarsaw University of TechnologyPoland
  2. 2.Faculty of Electronics and Information TechnologyWarsaw University of TechnologyPoland

Personalised recommendations