The mating is exhaustive, i.e. there remains no individual chromosome that does not enter the crossover process in a generation. The mating is binary, without sex and absolutely stochastic. After couples are formed an n-point crossover is performed. The position of the n crossover points are totally determined randomly among gene boundaries. The value of n is among the dynamic parameters of the GA, set by the user before the run. Each couple will produce two off-springs. All of these off-springs form the new generation on which the reproduction operator will act. Hence the size of the population is invariant under the crossover operation.
If and are two chromosomes that are mated we formally define the crossover operator which will produce the two offsprings and as
where