On the Adaptation of Arbitrary Normal Mutation Distributions in
Evolution Strategies: The Generating Set Adaptation
Nikolaus Hansen, Andreas Ostermeier and Andreas Gawelczyk
ABSTRACT: A new adaptation scheme for adapting arbitrary normal
mutation distributions in evolution strategies is
introduced. It can adapt correct scaling and correlations
between object parameters. Furthermore, it is independent of
any rotation of the objective function and reliably adapts
mutation distributions corresponding to hyperellipsoids with
high axis ratio. In simulations, the generating set
adaptation is compared to two other schemes which also can
produce non axis-parallel mutation ellipsoids. It turns out
to be the only adaptation scheme which is completely
independent of the chosen coordinate system.
In: Eshelman, L.J. (ed.), Proceedings of the Sixth International
Conference on Genetic Algorithms (ICGA): 57-64, 1995.
CORRECTIONS
Sec.2, P.58: "However, generating the mutation vector in AI and
AIII takes computational time in order of n^3." must be corrected to
"However, generating the mutation vector in AI, AII and AIII
takes computational time in order of n^3, n and n^2 respectively.".
(Remark: This drawback of AI was resolved by the covariance matrix
adaptation (CMA) which uses a different representation for the
distribution.)
Sec.2.5.2, P.61: Use rather $c_r=3/(n+3)$ and $\beta=1/n$.