Lower Bounds for Evolution Strategies Using VC-Dimension

  • Olivier Teytaud
  • Hervé Fournier
Conference paper

DOI: 10.1007/978-3-540-87700-4_11

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)
Cite this paper as:
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

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.

Keywords

Evolution Strategies Convergence ratio VC-dimension Sign conditions 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Olivier Teytaud
    • 1
  • Hervé Fournier
    • 2
  1. 1.TAO (Inria), LRI, UMR 8623 (CNRS - Univ. Paris-Sud) ,Bât 490, Univ. Paris-SudOrsayFrance
  2. 2.Laboratoire PRiSM, CNRS UMR 8144 and Univ. Versailles St-Quentin en YvelinesVersaillesFrance

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