Abstract
Cartesian Genetic Programming (CGP) is applied to solving differential equations (DE). We illustrate that repeated elements in analytic solutions to DE can be exploited under GP. An analysis is carried out of the search space in tree and CGP frameworks, examining the complexity of different DE problems. Experimental results are provided against benchmark ordinary and partial differential equations. A system of ordinary differential equations (SODE) is solved using multiple outputs from a genome. We discuss best heuristics when generating DE solutions through evolutionary search.
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References
Sobolob, S.L.: Partial Differential Equations of Mathematical Physics. Pergamen Press, Oxford (1964)
Abell, M.L., Braselton, J.P.: Differential Equations with Maple V. Academic Press, London (2000)
Diver, D.A.: Applications of genetic algorithms to the solution of ordinary differential equations. J. Phys. A: Math. Gen. 26, 3503–3513 (1993)
Koza, J.R.: Genetic Programming, on the Programming of Computers By Means of Natural Selection. MIT Press, Cambridge (1992)
Cao, H., Lishan, K., Chen, Y.: Evolutionary Modelling of Systems of Ordinary Differential Equations with Genetic Programming (2000)
Tsoulos, I., Lagaris, I.E.: Solving differential equations with genetic programming. Genet. Program. Evolvable Mach. 7, 33–54 (2006)
Kirstukas, S.J., Bryden, K.M., Ashlock, D.A.: A hybrid genetic programming approach for the analytical solution of differential equations. International Journal of General Systems 34, 279–299 (2005)
Miller, J.F., Thomson, P.: Cartesian Genetic Programming. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., Fogarty, T.C. (eds.) EuroGP 2000. LNCS, vol. 1802, pp. 121–132. Springer, Heidelberg (2000)
Walker, J., Miller, J.F.: Investigating the performance of module acquisition in cartesian genetic programming. In: Genetic and Evolutionary Computation Conference, pp.1649–1655, 25-06 (2005)
Durrbaum, A., Klier, W., Hahn, H.: Comparison of Automatic and Symbolic Differentiation in Mathematical Modeling and Computer Simulation of Rigid-Body Systems. Multibody System Dynamics 7, 331–355 (2002)
Scmidt, M., Hod, L.: Comparison of Tree and Graph Encodings as Function of Problem Complexity. In: Genetic and Evolutionary Computation Conference, pp. 1674–1679 (2007)
Keijzer, M.: Scientific Discovery using Genetic Programming. PhD thesis, Department for Mathematical Modelling, Technical University of Denmark (2001)
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Seaton, T., Brown, G., Miller, J.F. (2010). Analytic Solutions to Differential Equations under Graph-Based 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_20
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DOI: https://doi.org/10.1007/978-3-642-12148-7_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12147-0
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