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

A self-adaptation of arbitrary normal mutation distributions within the concept of muta-tive 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.