부산대학교 도서관

The optimization behavior of the self-adaptation (SA) evolution strategy (ES) with intermediate multirecombination $[\left(\mu/\mu_{I},\lambda\right)\hbox{-}\sigma{\rm SA}\hbox{-}{\rm ES}]$ 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 $\left(\mu/\mu_{I},\lambda\right)\hbox{-}\sigma{\rm SA}\hbox{-}{\rm ES}$ 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 $\left(\mu/\mu_{I},\lambda\right)\hbox{-}\sigma{\rm SA}\hbox{-}{\rm ES}$ on objective functions with changing local condition numbers as often encountered in practical problems with complex fitness landscapes.