Repair Methods for Box Constraints Revisited

  • Simon Wessing
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7835)


Box constraints are possibly the simplest kind of constraints one could think of in real-valued optimization, because it is trivial to detect and repair any violation of them. But so far, the topic has only received marginal attention in the literature compared to the more general formulations, although it is a frequent use case. It is experimentally shown here that different repair methods can have a huge impact on the optimizer’s performance when using the covariance matrix self-adaptation evolution strategy (CMSA-ES). Also, two novel repair methods, specially designed for this algorithm, sometimes outperform the traditional ones.


box constraints repair method Baldwin Lamarck 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Coello Coello, C.A.: 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)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Arabas, J., Szczepankiewicz, A., Wroniak, T.: Experimental Comparison of Methods to Handle Boundary Constraints in Differential Evolution. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6239, pp. 411–420. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Suganthan, P.N., Hansen, N., Liang, J.J., Deb, K., Chen, Y.P., Auger, A., Tiwari, S.: Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report, Nanyang Technological University, Singapore (May 2005),
  4. 4.
    Lewis, R.M., Torczon, V.: Pattern search algorithms for bound constrained minimization. SIAM Journal on Optimization 9(4), 1082–1099 (1999)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Langdon, W.B., Poli, R.: Evolving problems to learn about particle swarm optimizers and other search algorithms. IEEE Transactions on Evolutionary Computation 11(5), 561–578 (2007)CrossRefGoogle Scholar
  6. 6.
    Hansen, N., Niederberger, A.S., Guzzella, L., Koumoutsakos, P.: A method for handling uncertainty in evolutionary optimization with an application to feedback control of combustion. IEEE Transactions on Evolutionary Computation 13(1), 180–197 (2009)CrossRefGoogle Scholar
  7. 7.
    Purchla, M., Malanowski, M., Terlecki, P., Arabas, J.: Experimental comparison of repair methods for box constraints. In: Proceedings of the 7th National Conference on Evolutionary Computation and Global Optimization. Warsaw University of Technology Publishing House (2004)Google Scholar
  8. 8.
    Schwefel, H.P.: Evolution and Optimum Seeking. Wiley, New York (1995)Google Scholar
  9. 9.
    Fletcher, R., Powell, M.J.D.: A rapidly convergent descent method for minimization. The Computer Journal 6(2), 163–168 (1963)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Eiben, A.E., Smith, J.E.: Introduction to Evolutionary Computing. Springer (2003)Google Scholar
  11. 11.
    Michalewicz, Z., Nazhiyath, G.: Genocop III: a co-evolutionary algorithm for numerical optimization problems with nonlinear constraints. In: IEEE International Conference on Evolutionary Computation, pp. 647–651 (1995)Google Scholar
  12. 12.
    Beyer, H.-G., Sendhoff, B.: Covariance Matrix Adaptation Revisited – The CMSA Evolution Strategy –. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 123–132. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  13. 13.
    Hansen, N., Auger, A., Finck, S., Ros, R.: Real-parameter black-box optimization benchmarking 2010: Experimental setup. Technical Report RR-7215, INRIA (March 2010)Google Scholar
  14. 14.
    Koziel, S., Michalewicz, Z.: Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evolutionary Computation 7(1), 19–44 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Simon Wessing
    • 1
  1. 1.Fakultät für InformatikTechnische Universität DortmundGermany

Personalised recommendations