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 multi-recombination [(μ/μ_I, λ)-σSA-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 τ. The theoretical results are compared and validated by comparison with real (μ/μ_I, λ)-σSA-ES runs on two ellipsoid test model cases. The theoretical results clearly indicate that using a model-independent learning parameter τ leads to suboptimal performance of the (μ/μI, λ)-σSA-ES on objective functions with changing local condition numbers as often encountered in practical problems with complex fitness landscapes.