A Generalized Crossover Operation for Genetic Algorithms

The recombination of solut ions (crossover) is probably the most specific operat ion in opt imizat ion by genet ic algorit hms. We consider a very genera l way of recombining two solut ions using concepts relat ed to ort hogonal project ions. This includes most of the commonly used crossover opera tors such as, for example, one-po int or uniform crossover. We examine symmetry properties of the operator, genera lize the classical schema-oriented app roach to our setting, and study th e distribution of the offspring both geometr ically and stochas t ically. In par ticular we show that expectat ion and variance of the population (defined in appropriate terms) are invariant und er crossover. It t urns out th at the import ant features of the classical crossover operat ors hold in much more general mode ls, including cont inuous space.