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.-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.