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:
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  recommends the following values:
n being the number of control variables.
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).