Evolution Strategies, Network Random Keys, and the One-Max Tree Problem

  • Barbara Schindler
  • Franz Rothlauf
  • Hans-Josef Pesch
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2279)


Evolution strategies (ES)are efficient optimization methods for continuous problems. However, many combinatorial optimization methods can not be represented by using continuous representations. The development of the network random key representation which represents trees by using real numbers allows one to use ES for combinatorial tree problems.

In this paper we apply ES to tree problems using the network random key representation. We examine whether existing recommendations regarding optimal parameter settings for ES, which were developed for the easy sphere and corridor model, are also valid for the easy one-max tree problem.

The results show that the \( \frac{1} {5} \)-success rule for the (1+1)-ES results in low performance because the standard deviation is continuously reduced and we get early convergence. However, for the (μ+λ)-ES and the (μ, λ)-ES the recommendations from the literature are confirmed for the parameters of mutation \( \tau _1 \) and \( \tau _2 \) and the ratio μ/λ. This paper illustrates how existing theory about ES is helpful in finding good parameter settings for new problems like the one-max tree problem.


Evolution Strategy Strategy Parameter Success Rule Evolution Strategy Node Problem 
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 2002

Authors and Affiliations

  • Barbara Schindler
    • 1
  • Franz Rothlauf
    • 1
  • Hans-Josef Pesch
    • 2
  1. 1.Department of Information SystemsUniversity of BayreuthGermany
  2. 2.Department of Applied MathematicsUniversity of BayreuthGermany

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