, Volume 75, Issue 3, pp 462–489 | Cite as

Robustness of Populations in Stochastic Environments

  • Christian GießenEmail author
  • Timo Kötzing


We consider stochastic versions of OneMax and LeadingOnes and analyze the performance of evolutionary algorithms with and without populations on these problems. It is known that the (\(1+1\)) EA on OneMax performs well in the presence of very small noise, but poorly for higher noise levels. We extend these results to LeadingOnes and to many different noise models, showing how the application of drift theory can significantly simplify and generalize previous analyses. Most surprisingly, even small populations (of size \(\varTheta (\log n)\)) can make evolutionary algorithms perform well for high noise levels, well outside the abilities of the (\(1+1\)) EA. Larger population sizes are even more beneficial; we consider both parent and offspring populations. In this sense, populations are robust in these stochastic settings.


Run time analysis Stochastic fitness function Evolutionary algorithm Populations Robustness 



The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/2007–2013) under Grant Agreement No. 618091 (SAGE) and by the Danish Council for Independent Research (DFF), through Grant 4002-00542. The authors would like to thank Benjamin Doerr and Tobias Friedrich for many useful discussions on the topic. Furthermore, the reviewers of both the conference and the journal version of this paper gave a lot of helpful feedback, for which we are very grateful.


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Technical University of DenmarkKongens LyngbyDenmark
  2. 2.Friedrich-Schiller-Universität JenaJenaGermany

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