Abstract
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.
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References
Banzhaf, W., Nordin, P., Keller, R.E., Francone, F.D.: Genetic Programming – An Introduction; On the Automatic Evolution of Computer Programs and its Applications. Morgan Kaufmann, San Francisco (1998)
Dignum, S., Poli, R.: Generalisation of the limiting distribution of program sizes in tree-based genetic programming and analysis of its effects on bloat. In: Thierens, D., et al. (eds.) GECCO 2007: Proceedings of the 9th annual conference on Genetic and evolutionary computation, London, vol. 2, pp. 1588–1595. ACM Press, New York (2007)
Dignum, S., Poli, R.: Crossover, sampling, bloat and the harmful effects of size limits. In: O’Neill, M., Vanneschi, L., Gustafson, S., Esparcia Alcázar, A.I., De Falco, I., Della Cioppa, A., Tarantino, E. (eds.) EuroGP 2008. LNCS, vol. 4971, pp. 158–169. Springer, Heidelberg (2008)
Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)
Koza, J.R.: Genetic Programming II: Automatic Discovery of Reusable Programs. MIT Press, Cambridge (1994)
Langdon, W.B., Poli, R.: Foundations of Genetic Programming. Springer, Heidelberg (2002)
Poli, R., Langdon, W.B., Dignum, S.: On the limiting distribution of program sizes in tree-based genetic programming. In: Ebner, M., O’Neill, M., Ekárt, A., Vanneschi, L., Esparcia-Alcázar, A.I. (eds.) EuroGP 2007. LNCS, vol. 4445, pp. 193–204. Springer, Heidelberg (2007)
Poli, R., Langdon, W.B., McPhee, N.F.: A field guide to genetic programming (With contributions by J. R. Koza) (2008), http://lulu.com , http://www.gp-field-guide.org.uk
Poli, R., McPhee, N.F.: General schema theory for genetic programming with subtree-swapping crossover: Part I. Evolutionary Computation 11(1), 53–66 (2003)
Poli, R., Rowe, J.E., Stephens, C.R., Wright, A.H.: 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.G.B. (eds.) EuroGP 2002. LNCS, vol. 2278, pp. 212–227. Springer, Heidelberg (2002)
Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82 (1997)
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Dignum, S., Poli, R. (2008). Sub-tree Swapping Crossover, Allele Diffusion and GP Convergence. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87700-4_37
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DOI: https://doi.org/10.1007/978-3-540-87700-4_37
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