On the Behaviour of the (1+1)-ES for a Simple Constrained Problem

  • Dirk V. Arnold
  • Daniel Brauer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)


This paper studies the behaviour of the (1 + 1)-ES when applied to a linear problem with a single linear constraint. It goes beyond previous work by considering constraint planes that do not contain the gradient direction. The behaviour of the distance of the search point from the constraint plane forms a Markov chain. The limit distribution of that chain is approximated using an exponential model, and progress rates and success probabilities are derived. Consequences for the working of step length adaptation mechanisms based on success probabilities are discussed.


Evolution Strategy Evolutionary Computation Success Probability Candidate Solution Limit Distribution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Dirk V. Arnold
    • 1
  • Daniel Brauer
    • 1
  1. 1.Faculty of Computer ScienceDalhousie UniversityHalifaxCanada

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