The CMA Evolution Strategy: A Comparing Review
Nikolaus Hansen
Derived from the concept of self-adaptation in evolution strategies,
the CMA (Covariance Matrix Adaptation) adapts the covariance matrix
of a multi-variate normal search distribution. The CMA was
originally designed to perform well with small populations. In this
review, the argument starts out with large population sizes,
reflecting recent extensions of the CMA algorithm. Commonalities and
differences to continuous Estimation of Distribution Algorithms are
analyzed. The aspects of reliability of the estimation, overall step
size control, and independence from the coordinate system
(invariance) become particularly important in small populations
sizes. Consequently, performing the adaptation task with small
populations is more intricate.
In Lozano et al, Towards a new evolutionary computation. Advances on
estimation of distribution algorithms, pp. 75--102, Springer, 2006.
Erratum: "..., we focus on algorithms with a multivariate normal
search distribution, where the covariance matrix of the distribution
\emph{is not restricted to a priori}, e.g., not a diagonal matrix."
The emphasized phrase must read "is not restricted a priori".