Invariance, Self-Adaptation and Correlated Mutations in
                Evolution Strategies

                  Nikolaus Hansen

 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.


In: Sixth International Conference on Parallel Problem
Solving from Nature (PPSN VI) 2000, Proceedings, 
pp. 355-364. 

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