Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation

  • Pietro S. Oliveto
  • Carsten Witt
Conference paper

DOI: 10.1007/978-3-540-87700-4_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)
Cite this paper as:
Oliveto P.S., Witt C. (2008) Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation. 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

Drift analysis is a powerful tool used to bound the optimization time of evolutionary algorithms (EAs). Various previous works apply a drift theorem going back to Hajek in order to show exponential lower bounds on the optimization time of EAs. However, this drift theorem is tedious to read and to apply since it requires two bounds on the moment-generating (exponential) function of the drift. A recent work identifies a specialization of this drift theorem that is much easier to apply. Nevertheless, it is not as simple and not as general as possible. The present paper picks up Hajek’s line of thought to prove a drift theorem that is very easy to use in evolutionary computation. Only two conditions have to be verified, one of which holds for virtually all EAs with standard mutation. The other condition is a bound on what is really relevant, the drift. Applications show how previous analyses involving the complicated theorem can be redone in a much simpler and clearer way. Therefore, the simplified theorem is also a didactical contribution to the runtime analysis of EAs.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Pietro S. Oliveto
    • 1
  • Carsten Witt
    • 2
  1. 1.Centre of Excellence for Research in Computational Intelligence and Applications (CERCIA), School of Computer ScienceUniversity of BirminghamBirminghamUK
  2. 2.Fakultät für InformatikLS 2, Technische Universität DortmundDortmundGermany

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