The Dynamics of Self-Adaptive Multirecombinant Evolution Strategies on the General Ellipsoid Model.

The optimization behavior of the self-adaptation (SA) evolution strategy (ES) with intermediate multirecombination [\left(\mu/\muI,\lambda\right)\-\sigmaSA\-ES] using isotropic mutations is investigated on convex-quadratic functions (referred to as ellipsoid model). 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 $\tau$ . The theoretical results are compared and validated by comparison with real \left(\mu/\muI,\lambda\right)\-\sigmaSA\-ES runs on two ellipsoid test model cases. The theoretical results clearly indicate that using a model-independent learning parameter \tau$ leads to suboptimal performance of the \left(\mu/\muI,\lambda\right)\-\sigmaSA\-ES on objective functions with changing local condition numbers as often encountered in practical problems with complex fitness landscapes. [ABSTRACT FROM AUTHOR]