Mixed-Integer NK landscapes

  • Authors:
  • Rui Li;Michael T. M. Emmerich;Jeroen Eggermont;Ernst G. P. Bovenkamp;Thomas Bäck;Jouke Dijkstra;Johan H. C. Reiber

  • Affiliations:
  • Natural Computing Group, Leiden University, Leiden, CA, The Netherlands;Natural Computing Group, Leiden University, Leiden, CA, The Netherlands;Division of Image Processing, Department of Radiology C2S, Leiden University Medical Center, Leiden, RC, The Netherlands;Division of Image Processing, Department of Radiology C2S, Leiden University Medical Center, Leiden, RC, The Netherlands;Natural Computing Group, Leiden University, Leiden, CA, The Netherlands;Division of Image Processing, Department of Radiology C2S, Leiden University Medical Center, Leiden, RC, The Netherlands;Division of Image Processing, Department of Radiology C2S, Leiden University Medical Center, Leiden, RC, The Netherlands

  • Venue:
  • PPSN'06 Proceedings of the 9th international conference on Parallel Problem Solving from Nature
  • Year:
  • 2006

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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.