Covariance Matrix Adaptation Revisited – The CMSA Evolution Strategy –

  • Hans-Georg Beyer
  • Bernhard Sendhoff
Conference paper

DOI: 10.1007/978-3-540-87700-4_13

Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)
Cite this paper as:
Beyer HG., Sendhoff B. (2008) Covariance Matrix Adaptation Revisited – The CMSA Evolution Strategy –. In: Rudolph G., Jansen T., Beume N., Lucas S., Poloni C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg


The covariance matrix adaptation evolution strategy (CMA-ES) rates among the most successful evolutionary algorithms for continuous parameter optimization. Nevertheless, it is plagued with some drawbacks like the complexity of the adaptation process and the reliance on a number of sophisticatedly constructed strategy parameter formulae for which no or little theoretical substantiation is available. Furthermore, the CMA-ES does not work well for large population sizes. In this paper, we propose an alternative – simpler – adaptation step of the covariance matrix which is closer to the “traditional” mutative self-adaptation. We compare the newly proposed algorithm, which we term the CMSA-ES, with the CMA-ES on a number of different test functions and are able to demonstrate its superiority in particular for large population sizes.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hans-Georg Beyer
    • 1
  • Bernhard Sendhoff
    • 2
  1. 1.Vorarlberg University of Applied SciencesDornbirnAustria
  2. 2.Honda Research Institute Europe GmbHOffenbach/MainGermany

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