A Computational Efficient Covariance Matrix Update and a 
       (1+1)-CMA for Evolution Strategies

       C. Igel, T. Suttorp, and N. Hansen


Abstract. First, the covariance matrix adaptation (CMA) with rank-one
  update is introduced into the (1+1)-evolution strategy.  An improved
  implementation of the 1/5-th success rule is proposed for step size
  adaptation, which replaces cumulative path length control. Second,
  an incremental Cholesky update for the covariance matrix is
  developed replacing the computational demanding and numerically
  involved decomposition of the covariance matrix. The Cholesky update
  can replace the decomposition only for the update without evolution
  path and reduces the computational effort from O(n3) to O(n2). The
  resulting (1+1)-Cholesky-CMA-ES is an elegant algorithm and the
  perhaps simplest evolution strategy with covariance matrix and step
  size adaptation. Simulations compare the introduced algorithms to
  previously published CMA versions.


In: Proceedings of the Genetic and Evolutionary Computation Conference
  (GECCO 2006), ACM Press, 2006.

BIBTEX: 
@inproceedings{igel2006computational,
  title={A computational efficient covariance matrix update and a 
         (1+1)-{CMA} for evolution strategies},
  author={Igel, C. and Suttorp, T. and Hansen, N.},
  booktitle={Proceedings of the 8th annual conference on 
             genetic and evolutionary computation {GECCO}},
  pages={453--460},
  year={2006},
  organization={ACM}
}