Genetic programming: on the programming of computers by means of natural selection
Genetic programming: on the programming of computers by means of natural selection
Genetic programming II: automatic discovery of reusable programs
Genetic programming II: automatic discovery of reusable programs
Genetic programming: an introduction: on the automatic evolution of computer programs and its applications
Foundations of genetic programming
Foundations of genetic programming
EuroGP '02 Proceedings of the 5th European Conference on Genetic Programming
General schema theory for genetic programming with subtree-swapping crossover: part I
Evolutionary Computation
Proceedings of the 9th annual conference on Genetic and evolutionary computation
On the limiting distribution of program sizes in tree-based genetic programming
EuroGP'07 Proceedings of the 10th European conference on Genetic programming
Crossover, sampling, bloat and the harmful effects of size limits
EuroGP'08 Proceedings of the 11th European conference on Genetic programming
A Field Guide to Genetic Programming
A Field Guide to Genetic Programming
Sub-tree swapping crossover and arity histogram distributions
EuroGP'10 Proceedings of the 13th European conference on Genetic Programming
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We provide strong evidence that sub-tree swapping crossover when applied to tree-based representations will cause alleles (node labels) to diffuse within length classes. For a-ary trees we provide further confirmation that all programs are equally likely to be sampled within any length class when sub-tree swapping crossover is applied in the absence of selection and mutation. Therefore, we propose that this form of search is unbiased - within length classes - for a-ary trees. Unexpectedly, however, for mixed-arity trees this is not found and a more complicated form of search is taking place where certain tree shapes, hence programs, are more likely to be sampled than others within each class. We examine the reasons for such shape bias in mixed arity representations and provide the practitioner with a thorough examination of sub-tree swapping crossover bias. The results of this, when combined with crossover length bias research, explain Genetic Programming's lack of structural convergence during later stages of an experimental run. Several operators are discussed where a broader form of convergence may be detected in a similar way to that found in Genetic Algorithm experimentation.