In GA implementations mutation is usually a background operator, with crossover (recombination) being the primary search mechanism. In ES implementations mutation takes a much more central role. In its most general form the ES mutation operator works as follows:

- First, if they are used, the standard deviations and rotation angles
(strategy parameters) associated with the individual solution are mutated:
where the are (different) random numbers sampled from a normally distributed one-dimensional random variable with zero mean and unity standard deviation, and , and are algorithm control parameters for which Schwefel [69] recommends the following values:

**n**being the number of control variables. - Then the vector of control variables is mutated:
where

**n**is a vector of random numbers sampled from the**n**-dimensional normal distribution with zero means and the probability density function in equation (86).