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}
}