Understanding the Biases of Generalised Recombination: Part II

Authors:
Riccardo Poli;Christopher R. Stephens
Affiliations:
Department Computer Science, University of Essex, Colchester, CO4 3SQ, UK rpoli@essex.ac.uk;Department of Computer Science, University of Essex, UK, and Instituto de Ciencias Nucleares, UNAM, A. Postal 70-543,México, D.F. 04510 csteph@essex.ac.uk
Venue:
Evolutionary Computation
Year:
2007

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Abstract

This is the second part of a two-part paper where 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. In Part I, we derived both microscopic and coarse-grained evolution equations for strings and schemata for a selecto-recombinative GA using generalised recombination, and we explained the hierarchical nature of the schema evolution equations. In this part, we provide a variety of fixed points for evolution in the case where recombination is used alone, thereby generalising 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.