Abstract
We propose a novel approach to program simplification in tree-based Genetic Programming, based upon numerical relaxations of algebraic rules. We also separate proposal of simplifications from an acceptance criterion that checks the effect of proposed simplifications on the evaluation of training examples, looking several levels up the tree. We test our simplification method on three classification datasets and conclude that the success of linear regression is dataset dependent, that looking further up the tree can catch ineffective simplifications, and that CPU time can be significantly reduced while maintaining classification accuracy on unseen examples.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)
Blickle, T., Thiele, L.: Genetic programming and redundancy. In: Hopf, J. (ed.) Genetic Algorithms within the Framework of Evolutionary Computation, Max-Planck-Institut für Informatik (MPI-I-94-241), pp. 33–38 (1994)
Dignum, S., Poli, R.: Operator equalisation and bloat free GP. 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. 110–121. Springer, Heidelberg (2008)
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)
Poli, R.: A simple but theoretically-motivated method to control bloat in genetic programming. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 204–217. Springer, Heidelberg (2003)
Soule, T., Foster, J.A., Dickinson, J.: Code growth in genetic programming. In: Koza, J.R., et al. (eds.) Genetic Programming 1996: Proceedings of the First Annual Conference, Stanford University, CA, USA, pp. 215–223. MIT Press, Cambridge (1996)
Soule, T., Heckendorn, R.B.: An analysis of the causes of code growth in genetic programming. Genetic Programming and Evolvable Machines, 283–309 (2002)
Streeter, M.J.: The root causes of code growth in genetic programming. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 443–454. Springer, Heidelberg (2003)
Crane, E.F., McPhee, N.F.: The effects of size and depth limits on tree based genetic programming. In: Yu, T., et al. (eds.) Genetic Programming Theory and Practice III. Genetic Programming, vol. 9, pp. 223–240. Springer, Heidelberg (2005)
Nordin, P., Banzhaf, W.: Complexity compression and evolution. In: Eshelman, L. (ed.) Genetic Algorithms: Proceedings of the Sixth International Conference (ICGA 1995), Pittsburgh, PA, USA, pp. 310–317. Morgan Kaufmann, San Francisco (1995)
Zhang, B.T., Mühlenbein, H.: Balancing accuracy and parsimony in genetic programming. Evolutionary Computation 3(1), 17–38 (1995)
Luke, S., Panait, L.: Lexicographic parsimony pressure. In: Langdon, W.B., et al. (eds.) Proceedings of the 4th Annual Conference on Genetic and Evolutionary Computation (GECCO 2002), New York, pp. 829–836. Morgan Kaufmann, San Francisco (2002)
Hooper, D., Flann, N.S.: Improving the accuracy and robustness of genetic programming through expression simplification. In: Koza, J.R., et al. (eds.) Genetic Programming 1996: Proceedings of the First Annual Conference, p. 428 (1996)
Wong, P., Zhang, M.: Algebraic simplification of GP programs during evolution. In: Keijzer, M., et al. (eds.) Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation (GECCO 2006), Seattle, Washington, USA, July 8–12, vol. 1, pp. 927–934. ACM Press, New York (2006)
Zhang, M., Wong, P., Qian, D.: Online program simplification in genetic programming. In: Wang, T.-D., Li, X., Chen, S.-H., Wang, X., Abbass, H.A., Iba, H., Chen, G.-L., Yao, X. (eds.) SEAL 2006. LNCS, vol. 4247, pp. 592–600. Springer, Heidelberg (2006)
Kinzett, D., Zhang, M., Johnston, M.: Using numerical simplification to control bloat in genetic programming. In: Li, X., Kirley, M., Zhang, M., Green, D., Ciesielski, V., Abbass, H.A., Michalewicz, Z., Hendtlass, T., Deb, K., Tan, K.C., Branke, J., Shi, Y. (eds.) SEAL 2008. LNCS, vol. 5361, pp. 493–502. Springer, Heidelberg (2008)
Song, A., Chen, D., Zhang, M.: Bloat control in genetic programming by evaluating contribution of nodes. In: Raidl, G., et al. (eds.) Proceedings of the 11th Annual Conference on Genetic and Evolutionary Computation (GECCO 2009), Montreal, pp. 1893–1894. ACM, New York (2009)
Forina, M., Leardi, R., Armanino, C., Lanteri, S.: PARVUS: An Extendable Package of Programs for Data Exploration, Classification and Correlation. Elsevier, Amsterdam (1988)
Asuncion, A., Newman, D.J.: UCI Machine Learning Repository (2007), http://www.ics.uci.edu/~mlearn/MLRepository.html
Zhang, M., Ciesielski, V.: Genetic programming for multiple class object detection. In: Foo, N.Y. (ed.) AI 1999. LNCS (LNAI), vol. 1747, pp. 180–192. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Johnston, M., Liddle, T., Zhang, M. (2010). A Relaxed Approach to Simplification in Genetic Programming. In: Esparcia-Alcázar, A.I., Ekárt, A., Silva, S., Dignum, S., Uyar, A.Ş. (eds) Genetic Programming. EuroGP 2010. Lecture Notes in Computer Science, vol 6021. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12148-7_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-12148-7_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12147-0
Online ISBN: 978-3-642-12148-7
eBook Packages: Computer ScienceComputer Science (R0)