Differential evolution, rotationally invariant, experimental comparison

We study a problem of the control parameter settings in differential evolution algorithm. Although differential evolution with basic setting (i.e.CR=0.5; F=0.5) works quite well, it starts to fail on rotated functions. In general we want to improve the convergence of algorithm primarily on rotatedfunctions. It is done by adapting crossover parameter CR whereas parameter F is fixed to 0.5. There is a recommendation to set CR=1 forrotated functions. It means that trial vectors are essentially composed from mutant. We verify the fact by running the algorithm with mentioned setting on some pairs of rotated and non-rotated functions from CEC2013 benchmark set in various levels of dimension space. This experimental study aims to reveal if such algorithm setting is invariant under a rotation.