Abstract
We show how affine arithmetic can be used to improve both the performance and the robustness of genetic programming for problems such as symbolic regression and time series prediction. Affine arithmetic is used to estimate conservative bounds on the output range of expressions during evolution, which allows us to discard trees with potentially infinite bounds, as well as those whose output range lies outside the desired range implied by the training dataset. Benchmark experiments are performed on 15 symbolic regression problems as well as 2 wellknown time series problems. Comparison with a baseline genetic programming system shows a reduced number of fitness evaluations during training and improved generalization on test data, completely eliminating extreme errors. We also apply this technique to the problem of forecasting wind speed on a real world dataset, and the use of affine arithmetic compares favorably with baseline genetic programming, feedforward neural networks and support vector machines.
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References
Comba, J. andStolfi, J. (1993).Affine arithmetic and its applications to computer graphics. In Anais do VI SIBGRAPI.
de Figueiredo, L. H. and Stolfi, J. (1997). Self-Validated Numerical Methods and Applications. Brazilian Mathematics Colloquium monographs. IMPA, Rio de Janeiro, Brazil.
de Figueiredo, L. H. and Stolfi, J. (2004). Affine arithmetic: Concepts and applications. Numerical Algoritms, 37:147–158.
Glass, L. and Mackey, M. (2010). Mackey-glass equation. Scholarpedia.
Hall, Mark, Frank, Eibe, Holmes, Geoffrey, Pfahringer, Bernhard, Reutemann, Peter, and Witten, Ian H. (2009). The weka data mining software: an update. SIGKDD Explor. Newsl., 11:10–18.
Keijzer, Maarten (2003). Improving symbolic regression with interval arithmetic and linear scaling. In Ryan, Conor et al., editors, Genetic Programming, Proceedings of EuroGP’2003, volume 2610 of LNCS, pages 70–82, Essex. Springer-Verlag.
Keijzer, Maarten (2004). Scaled symbolic regression. Genetic Programming and Evolvable Machines, 5(3):259–269.
Korns, Michael F. (2009). Symbolic regression of conditional target expressions. In Riolo, Rick L., O’Reilly, Una-May, and McConaghy, Trent, editors, Genetic Programming Theory and Practice VII, Genetic and Evolutionary Computation, chapter 13, pages 211–228. Springer, Ann Arbor.
Kotanchek,Mark, Smits,Guido, and Vladislavleva, Ekaterina (2007). Trustable symbolic regression models: using ensembles, interval arithmetic and pareto fronts to develop robust and trust-aware models. In Riolo, Rick L., Soule, Terence, and Worzel, Bill, editors, Genetic Programming Theory and Practice V, Genetic and Evolutionary Computation, chapter 12, pages 201–220. Springer, Ann Arbor.
Koza, John R. (1992). Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge, MA, USA.
Langdon, W. B. and Poli, Riccardo (2002). Foundations of Genetic Programming. Springer-Verlag.
Lei, Ma, Shiyan, Luan, Chuanwen, Jiang, Hongling, Liu, and Yan, Zhang (2009). A review on the forecasting of wind speed and generated power. Renewable and Sustainable Energy Reviews, 13(4):915 – 920.
Looks, M. (2010). PLOP: Probabilistic learning of programs. http://code. google.com/p/plop.
Messine, F. (2002). Extentions of affine arithmetic: Application to unconstrained global optimization. Journal of Universal Computer Science, 8(11):992–1015.
Michiorri, A. and Taylor, P.C. (2009). Forecasting real-time ratings for electricity distribution networks using weather forecast data. In 20th International Conference and Exhibition on Electricity Distribution (CIRED), pages 854– 854.
Moore, R. (1966). Interval Analysis. Prentice Hall.
Pennachin, Cassio L., Looks, Moshe, and de Vasconcelos, Joao A. (2010). Robust symbolic regression with affine arithmetic. In Branke, Juergen et al., editors, GECCO’10: Proceedings of the 12th annual conference onGenetic and evolutionary computation, pages 917–924, Portland, Oregon, USA. ACM.
Shou, Huahao, Lin, Hongwei, Martin, Ralph, and Wang, Guojin (2003). Modified affine arithmetic is more accurate than centered interval arithmetic or affine arithmetic. In Wilson, Michael J. and Martin, Ralph R., editors, 10th IMA International Conference on theMathematics of Surfaces, volume 2768 of Lecture Notes in Computer Science, pages 355–365. Springer.
Smits, Guido and Kotanchek, Mark (2004). Pareto-front exploitation in symbolic regression. InO’Reilly, Una-May, Yu, Tina, Riolo, Rick L., andWorzel, Bill, editors, Genetic Programming Theory and Practice II, chapter 17, pages 283–299. Springer, Ann Arbor.
Soman, S.S., Zareipour, H.,Malik, O., andMandal, P. (2010). A review of wind power and wind speed forecasting methods with different time horizons. In North American Power Symposium (NAPS).
Valigiani, Gregory, Fonlupt, Cyril, and Collet, Pierre (2004). Analysis of GP improvement techniques over the real-world inverse problem of ocean color. In Keijzer, Maarten et al., editors, Genetic Programming 7th European Conference, EuroGP 2004, Proceedings, volume 3003 of LNCS, pages 174–186, Coimbra, Portugal. Springer-Verlag.
Weigend, A. S., Huberman, B. A., and Rumelhart, D. E. (1992). Predicting sunspots and exchange rateswith connectionist networks. InCasdagli,M. and Eubank, S., editors, Nonlinear Modeling and Forecasting. Addison-Wesley.
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Pennachin, C., Looks, M., de Vasconcelos, J.A. (2011). Improved Time Series Prediction and Symbolic Regression with Affine Arithmetic. In: Riolo, R., Vladislavleva, E., Moore, J. (eds) Genetic Programming Theory and Practice IX. Genetic and Evolutionary Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1770-5_6
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DOI: https://doi.org/10.1007/978-1-4614-1770-5_6
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