ABSTRACT
Inducing equations based on theory and data is a time-honoured technique in science. This is usually done manually, based on theoretical understanding and previously established equations. In this work, for a particular problem in hydraulics, human induction of equations is compared with the use of genetic programming. It will be shown that even with the use of synthetic data for training, genetic programming was capable of identifying a relationship that was more concise and more accurate than the relationship uncovered by scientists. As such this is a human-competitive result. Furthermore it will be shown that the genetic programming induced expression could be embedded in a line of theoretical work, filling in a few gaps in an already established line of reasoning. The resulting equation is the most accurate and elegant formulation of vegetation induced resistance to date.
- Vladan Babovic and Maarten Keijzer. Genetic programming as a model induction engine. Journal of Hydroinformatics, 1(2):35--60, 2000.Google ScholarCross Ref
- Vladan Babovic and Maarten Keijzer. Rainfall runoff modelling based on genetic programming. Nordic Hydrology, 34(1), 2003.Google Scholar
- Vladan Babovic, Maarten Keijzer, David Rodriguez Aquilera, and Joe Harrington. An evolutionary approach to knowledge induction: Genetic programming in hydraulic engineering. In Don Phelps and Gerald Sehlke, editors, Proceedings of the World Water and Environmental Resources Congress, volume 111, pages 64--64. ASCE, 20-24 May 2001.Google Scholar
- M. J. Baptist. Modelling oodplain biogeomorphology. Ph.D. thesis, ISBN 90-407-2582-9, 193 pp., Delft University of Technology, Faculty of Civil Engineering and Geosciences, Section Hydraulic Engineering, 2005.Google Scholar
- T. R. Campana. Hydraulic resistance of submerged oodplain vegetation. M.Sc. thesis H.E.043, IHE-Delft, 1999.Google Scholar
- F. H. Dawson and F. G. Charlton. Bibliography on the hydraulic resistance of vegetated watercourses. Technical report, Freshwater Biological Association, Occasional Publication No. 25, ISNN 0308-6739, 25 pp., 1988. eigen kopie.Google Scholar
- O Giustolisi. Using genetic programming to determine chézy resistance coefficient in corrugated channels. Journal of Hydroinformatics, 6(3):157--173, 2004.Google ScholarCross Ref
- H. T. M. Hong. Hydraulic Resistance of Flexible Roughness. M.Sc thesis H.H.237, IHE Delft, 1995.Google Scholar
- Maarten Keijzer. Improving symbolic regression with interval arithmetic and linear scaling. In Conor Ryan, Terence Soule, Maarten Keijzer, Edward Tsang, Riccardo Poli, and Ernesto Costa, editors, Genetic Programming, Proceedings of EuroGP'2003, volume 2610 of LNCS, pages 71--83, Essex, 14-16 April 2003. Springer-Verlag. Google ScholarDigital Library
- Maarten Keijzer and Vladan Babovic. Dimensionally aware genetic programming. In Wolfgang Banzhaf, Jason Daida, Agoston E. Eiben, Max H. Garzon, Vasant Honavar, Mark Jakiela, and Robert E. Smith, editors, Proceedings of the Genetic and Evolutionary Computation Conference, volume 2, pages 1069--1076, Orlando, Florida, USA, 13-17 July 1999. Morgan Kaufmann.Google Scholar
- Maarten Keijzer and Vladan Babovic. Declarative and preferential bias in GP-based scientific discovery. Genetic Programming and Evolvable Machines, 3(1):41--79, March 2002. Google ScholarDigital Library
- Soon Thiam Khu, Shie-Yui Liong, Vladan Babovic, Henrik Madsen, and Nitin Muttil. Genetic programming and its application in real-time runoff forecasting. Journal of the American Water Resources Association, 37(2):439--451, April 2001.Google ScholarCross Ref
- G. J. Klaassen, C. Stolker, E. H. Van Velzen, and H. Verheij. Naar een ruwheidsvoorspeller voor moerasvegetatie op basis van riet en gras. Technical report, WL | Delft Hydraulics, RWS/RIZA, 1999.Google Scholar
- N. Kouwen, T. E. Unny, and H. M. Hill. Flow retarance in vegetated channals. Journal of Irrigation and Drainage Division, 95(IR2):329--342, 1969.Google Scholar
- Shie-Yui Liong, Tirtha Raj Gautam, Soon Thiam Khu, Vladan Babovic, Maarten Keijzer, and Nitin Muttil. Genetic programming: A new paradigm in rainfall runoff modeling. Journal of American Water Resources Association, 38(3):705--718, June 2002.Google ScholarCross Ref
- F. López and M. H. García. Mean ow and turbulence structure of open-channel ow through non-emergent vegetation. Journal of Hydraulic Engineering, 127(5):392--402, 2001.Google ScholarCross Ref
- D. G. Meijer and E. H. Van Velzen. Prototype-scale ume experiments on hydraulic roughness of submerged vegetation. In 28th International IAHR Conference, Graz, 1999.Google Scholar
- N. Muttil and S. Y. Liong. Improving runoff forecasting by input variable selection in genetic programming. In Don Phelps and Gerald Sehlke, editors, World Water Congress 2001, volume 111, pages 76--76, Orlando, Florida, USA, 20-24 May 2001. ASCE.Google Scholar
- H. M. Nepf and E. R. Vivoni. Flow structure in depth-limited, vegetated ow. Journal of Geophysical Research, 105(C12):28,547--28,557, 2000.Google Scholar
- J. Nikuradse. Turbulente strömung in nichtkreisförmigen rohren. Ing.-Arch., 1(306), 1930.Google Scholar
- Z. Shi and M. R. Hughes. Laboratory ume studies of microflow environments of aquatic plants. Hydrol. Process., 16:3279--3289, 2002.Google ScholarCross Ref
- B. M. Stone and H. T. Shen. Hydraulic resistance of flow in channels with cylindrical roughness. Journal of Hydraulic Engineering, 128(5):500--506, 2002.Google ScholarCross Ref
- R. Uittenbogaard. Modelling turbulence in vegetated aquatic flows. In International workshop on RIParian FORest vegetated channels: hydraulic, morphological and ecological aspects, 20-22 February 2003, Trento, Italy, 2003.Google Scholar
- L. F. Vernon-Harcourt. Rivers and Canals, Vol. 1 Rivers. the Clarendon Press, 1896.Google Scholar
Index Terms
- Determining equations for vegetation induced resistance using genetic programming
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