Multi-Dimensional Gaussian and Cauchy Mutations

  • Andrzej Obuchowicz
Conference paper
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 10)


The aim of this work is to focus the attention of researchers concerned with evolutionary algorithms on the fact that the most probable location of the mutated points in multi-dimensional Gaussian and Cauchy mutations is not in a close neighborhood of the origin, but at a certain distance from it. In the case of the Gaussian mutation this distance is proportional to the norm of the standard deviation vector and increases with the landscape dimension. This may cause a decrease in the sensitivity of the evolutionary algorithm to narrow peaks when the landscape dimension increases. Moreover, it is proved that the multi-dimensional Cauchy mutation is not isotropic and the directions parallel to the axes of the reference frame are preferred. The effectiveness of the evolutionary algorithm using the Cauchy mutation strongly depends on the choice of the reference frame. New Gaussian-like and Cauchy-like mutations are proposed in order to overcome the considered difficulties.


Reference Frame Evolutionary Algorithm Probable Location Narrow Peak Global Optimization Problem 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bäck, T., Fogel, D.B., and Michalewicz, Z., (Eds.) Handbook of Evolutionary Computation. Institute of Physics Publishing and Oxford University Press, NY, 1997.MATHCrossRefGoogle Scholar
  2. 2.
    Fogel, L.J., Owens, A.J., and Walsh, M.J., Artificial Intelligence through Simulated Evolution. Wiley, NY, 1966.Google Scholar
  3. 3.
    Galar, R., Handicapped individua in evolutionary processes. Biological Cybernetics, Vol. 51, 1985, pp. 1 - 9.CrossRefGoogle Scholar
  4. 4.
    Michalewicz, Z., Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin Heidelberg, 1996.MATHCrossRefGoogle Scholar
  5. 5.
    Rechenberg, I., Cybernetic solution path of an experimental problem. Roy. Aircr. Establ., libr. Transl. 1122, Farnborough, Hants., UK, 1965.Google Scholar
  6. 6.
    Yao, X., and Liu, Y., Fast evolutionary programming. Evolutionary Programming V: Proc. 5th Annual Conference on Evolutionary Programming, L.J. Fogel, P.J. Angeline, and T. Bäck, Eds. Cambridge, MIT Press, MA, 1996, pp. 419 - 429.Google Scholar
  7. 7.
    Yao, X., and Liu, Y., Evolutionary programming made faster. IEEE Trans. on Evolutionary Computation, Vol. 3, No. 2, 1999, pp. 82 - 102.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Andrzej Obuchowicz
    • 1
  1. 1.Institute of Control and Computation EngineeringTechnical University of Zielona GóraZielona GóraPoland

Personalised recommendations