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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References
Altenberg, L.: The evolution of evolvability in genetic programming. In: Kinnear Jr., K.E. (ed.) Advances in Genetic Programming, pp. 47–74. MIT Press, Cambridge (1994)
Altenberg, L.: The Schema Theorem and Price’s Theorem. In: Whitley, L.D., Vose, M.D. (eds.) Foundations of Genetic Algorithms 3, Estes Park, Colorado, USA, 31 July–2 Aug. 1994, pp. 23–49. Morgan Kaufmann, Seattle (1995)
Langdon, W.B., Soule, T., Poli, R., Foster, J.A.: The evolution of size and shape. In: Spector, L., Langdon, W.B., O’Reilly, U.-M., Angeline, P.J. (eds.) Advances in Genetic Programming 3, pp. 163–190. MIT Press, Cambridge (1999)
McPhee, N.F., Poli, R.: A schema theory analysis of the evolution of size in genetic programming with linear representations. In: Miller, J., Tomassini, M., Lanzi, P.L., Ryan, C., Tetamanzi, A.G.B., Langdon, W.B. (eds.) EuroGP 2001. LNCS, vol. 2038, pp. 18–125. Springer, Heidelberg (2001)
Price, G.: Selection and covariance. Nature 227, 520–521 (1970)
Sedgewick, R., Flajolet, P.: An Introduction to the Analysis of Algorithms. Addison Wesley, London (1996)
Smits, G., Kotanchek, M.: Pareto-front exploitation in symbolic regression. In: O’Reilly, U.-M., et al. (eds.) Genetic Programming Theory and Practice II, vol. 17, Ann Arbor, 13-15 May 2004, Kluwer, Dordrecht (2004)
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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
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