Markov Models for GP and Variable-length GAs with Homologous Crossover

Abstract

In this paper we present a Markov model for GP and variable-length GAs with homologous crossover: a set of operators where the offspring are created preserving the position of the genetic material taken from the parents. We obtain this result by using the core of Vose’s model for GAs in conjunction with a specialisation of recent schema theory for such operators. The model is then specialised for the case of GAs operating on variable-length strings, where symmetries can be exploited to obtain further simplifications. In the absence of mutation, the theory presented here generalises Vose’s GA model to GP and variable-length GAs.

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