Abstract
In this paper we study, theoretically, the search biases produced by GP subtree crossover when applied to linear representations, such as those used in linear GP or in variable length GAs. The study naturally leads to generalisations of Geiringer’s theorem and of the notion of linkage equilibrium, which, until now, were applicable only to fixed-length representations. This indicates the presence of a diffusion process by which, even in the absence of selective pressure and mutation, the alleles in a particular individual tend not just to be swapped with those of other individuals in the population, but also to diffuse within the representation of each individual. More precisely, crossover attempts to push the population towards distributions of primitives where each primitive is equally likely to be found in any position in any individual.
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Poli, R., Rowe, J.E., Stephens, C.R., Wright, A.H. (2002). Allele Diffusion in Linear Genetic Programming and Variable-Length Genetic Algorithms with Subtree Crossover. In: Foster, J.A., Lutton, E., Miller, J., Ryan, C., Tettamanzi, A. (eds) Genetic Programming. EuroGP 2002. Lecture Notes in Computer Science, vol 2278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45984-7_21
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DOI: https://doi.org/10.1007/3-540-45984-7_21
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