 Under neutral selection, where formula_186, we find that

and under some mild additional assumptions on the initial conditions

and with an additional minor correction in the covariance matrix update for the case where the indicator function evaluates to zero, we find

Invariance properties imply uniform performance on a class of objective functions.They have been argued to be an advantage, because they allow to generalize and predict the behavior of the algorithm and therefore strengthen the meaning of empirical results obtained on single functions.The following invariance properties have been established for CMA-ES.