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International Conference on Parallel Problem Solving from Nature

PPSN 2008: Parallel Problem Solving from Nature – PPSN X pp 102–111Cite as

Lower Bounds for Evolution Strategies Using VC-Dimension

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5199))

Abstract

We derive lower bounds for comparison-based or selection-based algorithms, improving existing results in the continuous setting, and extending them to non-trivial results in the discrete case. This is achieved by considering the VC-dimension of the level sets of the fitness functions; results are then obtained through the use of Sauer’s lemma. In the special case of optimization of the sphere function, improved lower bounds are obtained by bounding the possible number of sign conditions realized by some systems of equations.

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Author information

Authors and Affiliations

  1. TAO (Inria), LRI, UMR 8623 (CNRS - Univ. Paris-Sud) ,Bât 490, Univ. Paris-Sud, 91405, Orsay, France

    Olivier Teytaud

  2. Laboratoire PRiSM, CNRS UMR 8144 and Univ. Versailles St-Quentin en Yvelines, 45 av. des États-Unis, 78035, Versailles, France

    Hervé Fournier

Authors
  1. Olivier Teytaud
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  2. Hervé Fournier
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Editor information

Editors and Affiliations

  1. Fakultät für Informatik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Günter Rudolph

  2. Fakultät für Informatik, Technische Universität Dortmund, 44221, Dortmund, Germany

    Thomas Jansen  & Nicola Beume  & 

  3. Department of Computing and Electronic Systems, University of Essex, CO4 3SQ, Colchester, Essex, UK

    Simon Lucas

  4. Dipartimento di Ingegneria Meccanica, Università degli Studi di Trieste, 34127, Trieste, Italy

    Carlo Poloni

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Teytaud, O., Fournier, H. (2008). Lower Bounds for Evolution Strategies Using VC-Dimension. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87700-4_11

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  • DOI: https://doi.org/10.1007/978-3-540-87700-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-87699-1

  • Online ISBN: 978-3-540-87700-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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