Mixed-Integer NK Landscapes

  • Rui Li
  • Michael T. M. Emmerich
  • Jeroen Eggermont
  • Ernst G. P. Bovenkamp
  • Thomas Bäck
  • Jouke Dijkstra
  • Johan H. C. Reiber
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4193)

Abstract

NK landscapes (NKL) are stochastically generated pseudo-boolean functions with N bits (genes) and K interactions between genes. By means of the parameter K ruggedness as well as the epistasis can be controlled. NKL are particularly useful to understand the dynamics of evolutionary search. We extend NKL from the traditional binary case to a mixed variable case with continuous, nominal discrete, and integer variables. The resulting test function generator is a suitable test model for mixed-integer evolutionary algorithms (MI-EA) – i. e. instantiations of evolution algorithms that can deal with the aforementioned variable types. We provide a comprehensive introduction to mixed-integer NKL and characteristics of the model (global/local optima, computation, etc.). Finally, a first study of the performance of mixed-integer evolution strategies on this problem family is provided, the results of which underpin its applicability for optimization algorithm design.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Rui Li
    • 1
  • Michael T. M. Emmerich
    • 1
  • Jeroen Eggermont
    • 2
  • Ernst G. P. Bovenkamp
    • 2
  • Thomas Bäck
    • 1
  • Jouke Dijkstra
    • 2
  • Johan H. C. Reiber
    • 2
  1. 1.Natural Computing GroupLeiden UniversityLeidenThe Netherlands
  2. 2.Division of Image Processing, Department of Radiology C2SLeiden University Medical CenterLeidenThe Netherlands

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