Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation

Abstract

A new formulation for coordinate system independentadaptation of arbitrary normal mutation distributionswith zero mean is presented. This enables the evolutionstrategy (ES) to adapt the correct scaling of a givenproblem and also ensures invariance with respect to any rotationof the fitness function (or the coordinate system). Especiallyrotation invariance, here resulting directly from thecoordinate system independent adaptation of the mutationdistribution, is an essential feature of the ...