Understanding the Biases of Generalised Recombination

In this paper we propose, model theoretically and study a general notion of recombination for fixed-length strings where homologous recombination, inversion, gene duplication, gene deletion, diploidy and more are just special cases. The analysis of the model reveals that the notion of schema emerges naturally from the model’s equations. The study provides a variety of fixed points for the case where recombination is used alone, which generalise Geiringer’s theorem. In addition, we numerically integrate the infinite-population schema equations for some interesting problems, where selection and recombination are used together to illustrate how these operators interact. Finally, to assess by how much genetic drift can make a system deviate from the infinite-population-model predictions we discuss the results of real GA runs for the same model problems with generalised recombination, selection and finite populations of different sizes.