Evolution Strategies with a Fourier Series Auxiliary Function for Difficult Function Optimization

  • Kwong-Sak Leung
  • Yong Liang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2690)


Through identifying the main causes of low efficiency of the currently known evolutionary algorithms for difficult function optimization problem, the complementary efficiency speed-up strategy—Fourier series auxiliary function technique is suggested, analyzed, and partially explored. The Fourier series auxiliary function could guide an algorithm to search for optima with small attraction basins efficiently. Incorporation of this technique with any known evolutionary algorithm leads to an accelerated version of the algorithm for the difficult function optimization. As a case study, the developed technique has been incorporated with evolution strategies (ES), yielding accelerated Fourier series auxiliary function evolution strategies: the FES. The experiments demonstrate that the FES consistently outperforms the standard ES in efficiency and solution quality.


Fourier Series Evolution Strategy Original Region Fourier Representation Attraction Basin 
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.
    Folland, G.B.: Fourier Analysis and its Applications. Wadsworth & Brooks/Cole Advanced Book & Software (1998)Google Scholar
  2. 2.
    Edwards, R.E.: Fourier Series, 2nd edn. Springer, Heidelberg (1999)Google Scholar
  3. 3.
    Schwefel, H.-P., Rudolph, G.: Contemparary Evolution Strategies. In: Morán, F., Merelo, J.J., Moreno, A., Chacon, P. (eds.) ECAL 1995. LNCS, vol. 929, pp. 893–907. Springer, Heidelberg (1995)Google Scholar
  4. 4.
    Yao, X.: Evolutionary computation: theory and applications, Singapore. World Scientific, New Jersey (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Kwong-Sak Leung
    • 1
  • Yong Liang
    • 1
  1. 1.Department of Computer Science & EngineeringThe Chinese University of Hong KongShatin, N.T., Hong Kong

Personalised recommendations