Invariance , Self - Adaptation and CorrelatedMutations in Evolution StrategiesNikolaus

i are transformed accordingly to f tablet(1) or f tablet(1) , as shown in Table 2." must be \.. . where x (0) and (0) i are transformed accordingly to f tablet(1) or f tablet(5) , as shown in Table 2." Abstract. A conceptual objective behind the self-adaptation of the mutation distribution is to achieve invariance against certain transformations of the search space. In this paper, a priori invariances of a simple evolution strategy and invariances, which can be introduced by self-adaptation, are identiied. In principle, correlated mutations can achieve invariance against any linear transformation of the search space. Correlated mutations, as typically implemented, are investigated with respect to both a priori and new invariances. Simulations reveal that neither all a priori invariances are retained, nor the invariance against linear transformation is achieved.