The Progress Rate of the \(\left( {1\mathop ,\limits^ + \lambda } \right)\)-ES on the Sphere Model

  • Hans-Georg Beyer
Part of the Natural Computing Series book series (NCS)


This chapter analyzes the progress rate of the \(\left( {1\mathop ,\limits^ + \lambda } \right)\)-ES. The first section is devoted to the exact theory of the (1 + 1)-ES on the sphere model, including the results considering the N-dependency and noisy fitness data. In the second and third section, analytical progress rate formulae are derived for the asymptotic case N → ∞; moreover, the dynamics of the ES-process is investigated. The second section is dedicated to the ES without noise, whereas the third is concerned with the ES under the presence of noise on the fitness measurement process (fitness noise). The consequences are discussed, as well as ideas for the improvement of the convergence property. In the fourth section, the (1, λ)-ES is investigated again with the aim of finding a simpler approach to the derivation of N-dependent analytical progress rate formulae.


Asymptotic Formula Success Probability Sphere Model Progress Rate Fitness Landscape 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Hans-Georg Beyer
    • 1
  1. 1.Department of Computer ScienceUniversity of DortmundDortmundGermany

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