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A Blend of Markov-Chain and Drift Analysis

  • Jens Jägersküpper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)

Abstract

In their seminal article [Theo. Comp. Sci. 276(2002):51–82] Droste, Jansen, and Wegener present the first theoretical analysis of the expected runtime of a basic direct-search heuristic with a global search operator, namely the (1+1) Evolutionary Algorithm (EA), for the class of linear functions over the search space {0,1} n . In a rather long and involved proof they show that, for any linear function, the expected runtime of the EA is O(nlogn), i.e., that there are two constants c and n′ such that, for n ≥ n′, the expected number of iterations until a global optimum is generated is bound above by c·nlogn. However, neither c nor n′ are specified – they would be pretty large. Here we reconsider this optimization scenario to demonstrate the potential of an analytical method that makes use not only of the drift (w.r.t. a potential function, here the number of bits set correctly), but also of the distribution of the evolving candidate solution over the search space {0,1} n : An invariance property of this distribution is proved, which is then used to derive a significantly better lower bound on the drift. Finally, this better estimate of the drift results in an upper bound on the expected number of iterations of 3.8 nlog2 n + 7.6log2 n for n ≥ 2.

Keywords

Search Space Invariance Property Search Point Elitist Selection Drift Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jens Jägersküpper
    • 1
  1. 1.Technische Universität DortmundDortmundGermany

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