An Evolution Strategy with Coordinate System Invariant Adaptation of Arbitrary Normal Mutation Distr

A self-adaptation of arbitrary normal mutation distributions within the concept of mutative strategy parameter control (MSG) 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 MSG. 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 N2, the overall adaptation expense amounts to N4 function evaluations.