Abstract
This work has the aim of exploring the area of symbolic regression problems by means of Genetic Programming. It is known that symbolic regression is a widely used method for mathematical function approximation. Previous works based on Genetic Programming have already dealt with this problem, but considering Koza’s GP approach. This paper introduces a novel GP encoding based on multi-branches. In order to show the use of the proposed multi-branches representation, a set of testing equations has been selected. Results presented in this paper show the advantages of using this novel multi-branches version of GP.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Angeline, P.J.: Parse trees. In: Back, T., Fogel, D.B., Michalewickz, T. (eds.) Evolutionary Computation 1, basic algorithms and operators (1996)
Angeline, P.J., Pollack, J.B.: Co – evolving high level representation. In: Langton, C.G. (ed.) Artificial life III, pp. 55–71. Addison Wesley, Reading (1994)
Cramer, N.L.: A representation for the adaptative generation of simple sequencial programs. In: Grefenstette, J.J. (ed.) Proc. 1st. Int. Conference on Genetic Algorithms, Pittsburg, PA, Hillsdale, NJ, pp 183 –187 (July 1985)
Harries, K., Smith, P.W.H.: Code Growth, Explicitly Defined Introns and Alternative Selection Schemes. Evolutionary Computation 6(4), 346–364 (1998)
Hinchiffe, M., Hiden, H., McKay, B., Willis, M., Tham, M., Barton, G.: Modelling Chemical Process System using multi-gene Programming Algorithm. In: Koza, J.R. (ed.) Late Breaking Papers at the Genetic Programming 1996 Conference, Stanford University, C.A, pp. 56–65. Stanford Bookstore, Stanford (1996)
Ivakhnenko, A.G.: Polynomial theory of complex systems IEEE Transactions on Systems, Man, and Cybernetics, 364–378 (1971)
Keijzer, M.: Improving Symbolic Regression with Interval Arithmetic and Linear Scaling. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, Springer, Heidelberg (2003)
Keijzer, M., Babovic, V.: Genetic Programming, Ensemble Methods and the Bias/Variance Tradeoff – introductory Investigations. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., Fogarty, T.C. (eds.) EuroGP 2000. LNCS, vol. 1802, pp. 76–90. Springer, Heidelberg (2000)
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.: Size Fair and Homologous Tree Genetic Programming Crossovers. In: Morgan Kaufmannm, Banzhaf, W., Daida, J., Eiben, A.E., Garzon, M.H., Honavar, V., Jakiela, M., Smith, R.E. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference, vol. 2, pp. 1092–1097 (1999)
Langdon, W.B., Poli, R.: Fitness Causes Bloat. In: Chawdhry, P.K., Roy, R., Pan, R.K. (eds.) Second On-line World Conference on Soft Computing in Engineering Design and Manufacturing, pp. 13–22. Springer, London (1997)
Nordin, P., Francone, F., Banzhaf, W.: Explicitly defined introns and destructive crossover in genetic programming. In: Angeline, P.J., Kinnear Jr., K.E. (eds.) Advances in Genetic Programming 2, ch. 6, pp. 111–134. MIT Press, Cambridge (1996)
Nordin, J.P., Banzhaf, W.: Complexity Compression and Evolution. In: Eshelman, L. (ed.) Proceedings of Sixth International Conference of Genetic Algorithms, Pittsburgh, Morgan Kaufmann, San Mateo (1995)
Nikolaev, I.N., Iba, H.: Accelerated Genetic Programming of Polynomials. Genetic Programming and Evolvable Machines 2(3), 231–258 (2001)
Oliver, M.C.: Programación Genética Multi - Ramas en el Modelado y Predicción de Datos Climatológicos. Tesis de Maestría. Universidad Autonoma de México, D.F., México, spanish (2002)
Oliver, M.C., y Rodríguez, K.V.: Estructuta de Arbol vs Estructura Polinomial con Programación Genética en el Modelado de Variables Climatológicas. en el 1er Congreso Español de Algoritmos Geneticos y Bioinspirados. Del 6 al 8 de Febrero de, Merida, España (2002)
Poli, R.: Genetic programming for image analysis. In: Koza, J.R., Goldberg, D.E., Fogel, D.B., Riolo, R.L. (eds.) Proc. Genetic Programming 1996, pp. 363–368. MIT Press, Cambridge (1996)
Rodríguez, V.K., Oliver, M.C.: Divide and Conquer: Genetic Programming Based on Multiple Branches Encoding. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, Springer, Heidelberg (2003)
Rosca, J.P., Ballard, D.H.: Discovery of subroutines in genetic programming. In: Angeline, P.J., Kinnear, K. (eds.) Advances in Genetic Programming, vol. 2, pp. 177–202. MIT press, Cambridge (1996)
Salustowicks, R.P., Schmidhuber, J.: Probabilistc Incremental Program Evolution. Evolutionary Computation 5(2), 123–141 (1997)
Streeter, M., Becker, L.A.: Automated Discovery of Numerical Aproximation Formulae via Genetic Programming. In: Spector, L., Goodman, E.D., Wu, A., Langdom, W.B., Voigth, H.M., Gen, M., Sen, S., Dorigo, M., Pezeshk, S., Garzon, M.H., Burke, E. (eds.) Proceedings of the Genetic and Evolutionary Conference (GECCO 2001), San Francisco CA, July 7-11, pp. 147–154. Morgam Kaufmann, San Francisco (2001)
Soule, T., Foster, J.A., Dickinson, J.: Code growth in genetic programming. In: Koza, J.R., Goldberg, D.E., Fogel, D.B., Riolo, R.L. (eds.) Genetic Programming 1996: Proceedings of the First Annual Conference, Stanford University, CA, USA, July 28-31, pp. 215–223. MIT Press, Cambridge (1996)
Topchy, A., Punch, W.F.: Faster Genetic Based on Local Gradient Search of Numeric Leaf Values. In: Spector, L., Goodman, E.D., Wu, A., Langdom, W.B., Voigth, H.M., Gen, M., Sen, S., Dorigo, M., Pezeshk, S., Garzon, M.H., Burke, E. (eds.) Proceedings of the Genetic and Evolutionary Conference (GECCO 2001), San Francisco CA, July 7-11, pp. 155–162. Morgam Kaufmann, San Francisco (2001)
Sims, K.: Interactive Evolution of Equations for Procedural Models. The Visual Computer 9, 466–476 (1993)
Zhang, B.-T., Muhlenbein, H.: Balancing Accuracy and Parsimony in Genetic Programming. Evolutionary Computation 3(1), 17–38
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Oliver Morales, C., Rodríguez Vázquez, K. (2004). Symbolic Regression Problems by Genetic Programming with Multi-branches. In: Monroy, R., Arroyo-Figueroa, G., Sucar, L.E., Sossa, H. (eds) MICAI 2004: Advances in Artificial Intelligence. MICAI 2004. Lecture Notes in Computer Science(), vol 2972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24694-7_74
Download citation
DOI: https://doi.org/10.1007/978-3-540-24694-7_74
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21459-5
Online ISBN: 978-3-540-24694-7
eBook Packages: Springer Book Archive