Abstract
Path length, or search complexity, is an understudied property of trees in genetic programming. Unlike size and depth measures, path length directly measures the balancedness or skewedness of a tree. Here a close relative to path length, called visitation length, is studied. It is shown that a population undergoing standard crossover will introduce a crossover bias in the visitation length. This bias is due to inserting variable length subtrees at various levels of the tree. The crossover bias takes the form of a covariance between the sizes and levels in the trees that form a population. It is conjectured that the crossover bias directly determines the size distribution of trees in genetic programming. Theorems are presented for the one-generation evolution of visitation length both with and without selection. The connection between path length and visitation length is made explicit.
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Keijzer, M., Foster, J. (2007). Crossover Bias in Genetic Programming. In: Ebner, M., O’Neill, M., Ekárt, A., Vanneschi, L., Esparcia-Alcázar, A.I. (eds) Genetic Programming. EuroGP 2007. Lecture Notes in Computer Science, vol 4445. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71605-1_4
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DOI: https://doi.org/10.1007/978-3-540-71605-1_4
Publisher Name: Springer, Berlin, Heidelberg
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