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 $\beta=1/n$.