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Advances in genetic programming
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General Schema Theory for Genetic Programming with Subtree-Swapping Crossover
EuroGP '01 Proceedings of the 4th European Conference on Genetic Programming
Schema theory for genetic programming with one-point crossover and point mutation
Evolutionary Computation
Genetic Programming and Evolvable Machines
A Schema Theory Analysis of the Evolution of Size in Genetic Programming with Linear Representations
EuroGP '01 Proceedings of the 4th European Conference on Genetic Programming
General Schema Theory for Genetic Programming with Subtree-Swapping Crossover
EuroGP '01 Proceedings of the 4th European Conference on 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
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General schema theory for genetic programming with subtree-swapping crossover: Part II
Evolutionary Computation
Basic principles for understanding evolutionary algorithms
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Implicitly controlling bloat in genetic programming
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Natural Computing: an international journal
Size control with maximum homologous crossover
EA'05 Proceedings of the 7th international conference on Artificial Evolution
Sub-tree swapping crossover and arity histogram distributions
EuroGP'10 Proceedings of the 13th European conference on Genetic Programming
Basic principles for understanding evolutionary algorithms
Fundamenta Informaticae
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In this paper, firstly we specialise the exact GP schema theorem for one-point crossover to the case of linear structures of variable length, for example binary strings or programs with arity-1 primitives only. Secondly, we extend this to an exact schema theorem for GP with standard crossover applicable to the case of linear structures. Then we study, both mathematically and numerically, the schema equations and their fixed points for infinite populations for both a constant and a length-related fitness function. This allows us to characterise the bias induced by standard crossover. This is very peculiar. In the case of a constant fitness function, at the fixed-point, structures of any length are present with non-zero probability. However, shorter structures are sampled exponentially much more frequently than longer ones.