On the analysis of the (1+ 1) evolutionary algorithm

  • Authors:
  • Stefan Droste;Thomas Jansen;Ingo Wegener

  • Affiliations:
  • Univ. Dortmund, Dortmund, Germany;Univ. Dortmund, Dortmund, Germany;Univ. Dortmund, Dortmund, Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2002

Quantified Score

Hi-index 5.25

Visualization

Abstract

Many experimental results are reported on all types of Evolutionary Algorithms but only few results have been proved. A step towards a theory on Evolutionary Algorithms, in particular, the so-called (1+1) Evolutionary Algorithm, is performed. Linear functions are proved to be optimized in expected time O(nlnn) but only mutation rates of size (1/n) can ensure this behavior. For some polynomial of degree 2 the optimization needs exponential time. The same is proved for a unimodal function. Both results were not expected by several other authors. Finally, a hierarchy result is proved. Moreover, methods are presented to analyze the behavior of the (1+1) Evolutionary Algorithm.