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Algorithmica

, Volume 65, Issue 1, pp 224–250 | Cite as

Adaptive Drift Analysis

  • Benjamin Doerr
  • Leslie Ann Goldberg
Article

Abstract

We show that, for any c>0, the (1+1) evolutionary algorithm using an arbitrary mutation rate p n =c/n finds the optimum of a linear objective function over bit strings of length n in expected time Θ(nlogn). Previously, this was only known for c≤1. Since previous work also shows that universal drift functions cannot exist for c larger than a certain constant, we instead define drift functions which depend crucially on the relevant objective functions (and also on c itself). Using these carefully-constructed drift functions, we prove that the expected optimisation time is Θ(nlogn). By giving an alternative proof of the multiplicative drift theorem, we also show that our optimisation-time bound holds with high probability.

Keywords

Objective Function Evolutionary Algorithm Mutation Probability Short Block Linear Objective Function 
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 Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Max Planck Institute for Computer ScienceSaarbrückenGermany
  2. 2.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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