Covariance Matrix Adaptation Revisited – The CMSA Evolution Strategy –

  • Hans-Georg Beyer
  • Bernhard Sendhoff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5199)


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.


Strategy Parameter Robust Optimization Large Population Size Covariance Matrix Adaptation Evolution Strategy Covariance Matrix Adaptation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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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