On the search biases of homologous crossover in linear genetic programming and variable-length genetic algorithms
Riccardo Poli, Christopher Rhodes Stephens, Alden H. Wright, Jonathan E. Rowe · 2002
In this paper we study with a schema-theoretic approach and experiments the search biases produced by GP/GA homologous crossovers when applied to linear, variable-length representations. By specialising the schema theory for homologous crossovers we show that these operators are totally unbiased with respect to string length. Then, we provide a fixed point for the schema evolution equations where the population presents a statistically independent distribution of primitives. This is an important step towards generalising Geiringer's theorem and the notion of linkage equilibrium, previously applied only to fixed-length representations.