Distances that are bound to (or consistent with) genetic operators are measures that quantify the difficulty of reaching and individual (or a population) starting from another individual (or population) and applying the genetic operator iteratively. Defining distance measures bound to genetic operators is a very important task in evolutionary computation. In fact these distances usually make the analysis of some indicators of the the search process, like for instance population diversity or well-known measures of problem hardness such as fitness distance correlation, more accurate. In this paper, we introduce a distance measure bound to one point standard crossover for genetic algorithms. This measure quantifies the minimum number of crossover operations that have to be applied to a population to tranform it into another population. It is based on the definition of a lattice over some particular schemata that represent the individuals in the population and on the construction of a discrete dynamic system that models the dynamics of the genetic algorithm under the sole effect of crossover. Using this distance measure, it is also possible to build a family of distances between individuals.
