CMA-ES

  The optimization behavior of the self-adaptation (SA) evolution strategy (ES) with intermediate multirecombination (the (=I )-SA-ES) using isotropic mutations is investigated on the general elliptic objective function. An asymptotically exact quadratic progress rate formula is derived. This is used to model the dynamical ES system by a set of difference equations. The solutions of this system are used to analytically calculate the optimal learning parameter  . The theoretical results are compared and validated by comparison with real (=I )-SA-ES runs on typical elliptic test model cases. The theoretical results clearly indicate that using a model-independent learning parameter  leads to suboptimal performance of the (=I )-SA-ES on objective functions with changing local condition numbers as often encountered in practical problems with complex fitness landscapes.