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Evolution Strategies

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Springer Handbook of Computational Intelligence

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Abstract

Evolution strategies (GlossaryTerm

ES

) are evolutionary algorithms that date back to the 1960s and that are most commonly applied to black-box optimization problems in continuous search spaces. Inspired by biological evolution, their original formulation is based on the application of mutation, recombination and selection in populations of candidate solutions. From the algorithmic viewpoint, GlossaryTerm

ES

are optimization methods that sample new candidate solutions stochastically, most commonly from a multivariate normal probability distribution. Their two most prominent design principles are unbiasedness and adaptive control of parameters of the sample distribution. In this overview, the important concepts of success based step-size control, self-adaptation, and derandomization are covered, as well as more recent developments such as covariance matrix adaptation and natural GlossaryTerm

ES

. The latter give new insights into the fundamental mathematical rationale behind GlossaryTerm

ES

. A broad discussion of theoretical results includes progress rate results on various function classes and convergence proofs for evolution

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Abbreviations

CMA:

covariance matrix adaptation

CSA:

cumulative step-size adaptation

ES:

evolution strategy

i.i.d.:

independent, identically distributed

IPOP:

increasing population size

NES:

natural evolution strategy

xNES:

exponential natural evolution strategy

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Author information

Authors and Affiliations

  1. Machine Learning and Optimization Group (TAO), Universitè Paris-Sud, Rue Noetzlin, 91405, Orsay Cedex, France

    Nikolaus Hansen

  2. Faculty of Computer Science, Dalhousie University, 6050 University Avenue, B3H 4R2, Halifax, Nova Scotia, Canada

    Dirk V. Arnold

  3. CR Inria, University Paris-Sud Orsay, LRI (UMR 8623), 91405, Orsay Cedex, France

    Anne Auger

Authors
  1. Nikolaus Hansen
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  2. Dirk V. Arnold
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  3. Anne Auger
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Correspondence to Nikolaus Hansen .

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Editors and Affiliations

  1. Systems Research Inst., Polish Academy of Sciences, ul. Newelska 6, 01-447, Warsaw, Poland

    Janusz Kacprzyk

  2. Dep. Electrical and Computer Engineering, University of Alberta, 116 Street 9107, T6J 2V4, Edmonton, Alberta, Canada

    Witold Pedrycz

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Hansen, N., Arnold, D.V., Auger, A. (2015). Evolution Strategies. In: Kacprzyk, J., Pedrycz, W. (eds) Springer Handbook of Computational Intelligence. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43505-2_44

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