Exact Schema Theory for GP and Variable-length GAs with Homologous Crossover

In this paper we present a new exact schema theory for genetic programming and variable-length genetic algorithms which is applicable to the general class of homologous crossovers. These are a group of operators, including GP one-point crossover and GP uniform crossover, where the offspring are created preserving the position of the genetic material taken from the parents. The theory is based on the concepts of GP crossover masks and GP recombination distributions (both introduced here for the first time), as well as the notions of hyperschema and node reference systems introduced in other recent research. This theory generalises and refines previous work in GP and GA theory.