Invariance, Self-Adaptation and Correlated Mutations and Evolution Strategies

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 identified. 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.