An Evolution Strategy with Coordinate System Invariant 
 Adaptation of Arbitrary Normal Mutation Distributions Within 
     the Concept of Mutative Strategy Parameter Control

          Andreas Ostermeier and Nikolaus Hansen


Abstract: A self-adaptation of arbitrary normal mutation
distributions within the concept of mutative strategy
parameter control (MSC) using a newly formulated mutation
operator is introduced. The coordinate system independent
formulation ensures the invariance of the algorithm towards
arbitrary linear transformations, which is a novelty for
self-adaptation within the concept of MSC. To enable a
sensible adaptation, the population size must scale
quadratically with the problem size $N$ -- according to the
number of adapted strategy parameters.  Because the
adaptation time (number of generations) also scales with
$\N^2$, the overall adaptation expense amounts to $N^4$
function evaluations.

In: Proceedings of the Genetic and Evolutionary Computation Conference
	  1999 (GECCO-99): 902-909.