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On the Optimization of Monotone Polynomials by the (1+1) EA and Randomized Local Search

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Genetic and Evolutionary Computation — GECCO 2003 (GECCO 2003)

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Abstract

Randomized search heuristics like evolutionary algorithms and simulated annealing find many applications, especially in situations where no full information on the problem instance is available. In order to understand how these heuristics work, it is necessary to analyze their behavior on classes of functions. Such an analysis is performed here for the class of monotone pseudo-boolean polynomials. Results depending on the degree and the number of terms of the polynomial are obtained. The class of monotone polynomials is of special interest since simple functions of this kind can have an image set of exponential size, improvements can increase the Hamming distance to the optimum and, in order to find a better search point, it can be necessary to search within a large plateau of search points with the same fitness value.

Supported in part by the Deutsche Forschungsgemeinschaft as a part of the Collaborative Research Center “Computational Intelligence” (SFB 531).

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Authors and Affiliations

  1. FB Informatik, LS 2, Univ. Dortmund, 44221, Dortmund, Germany

    Ingo Wegener & Carsten Witt

Authors
  1. Ingo Wegener
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  2. Carsten Witt
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Editors and Affiliations

  1. Lawrence Livermore National Laboratory, Center for Applied Scientific Computing (CASC), 7000 East Avenue, L-561, Livermore, CA, 94550, USA

    Erick Cantú-Paz

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© 2003 Springer-Verlag Berlin Heidelberg

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Wegener, I., Witt, C. (2003). On the Optimization of Monotone Polynomials by the (1+1) EA and Randomized Local Search. In: Cantú-Paz, E., et al. Genetic and Evolutionary Computation — GECCO 2003. GECCO 2003. Lecture Notes in Computer Science, vol 2723. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45105-6_73

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  • DOI: https://doi.org/10.1007/3-540-45105-6_73

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40602-0

  • Online ISBN: 978-3-540-45105-1

  • eBook Packages: Springer Book Archive

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