Complex Systems

A Generalized Crossover Operation for Genetic Algorithms Download PDF

Michael Kolonko
Institut für Mathematik, Universität Hildesheim,
Marienburger Platz 22, D-31141 Hildesheim, Germany


The recombination of solutions (crossover) is probably the most specific operation in optimization by genetic algorithms. We consider a very general way of recombining two solutions using concepts related to orthogonal projections. This includes most of the commonly used crossover operators such as, for example, one-point or uniform crossover.

We examine symmetry properties of the operator, generalize the classical schema-oriented approach to our setting, and study the distribution of the offspring both geometrically and stochastically. In particular we show that expectation and variance of the population (defined in appropriate terms) are invariant under crossover.

It turns out that the important features of the classical crossover operators hold in much more general models, including continuous space.