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A Sniffer Technique for an Efficient Deduction of Model Dynamical Equations Using Genetic Programming

  • Dilip P. Ahalpara
  • Abhijit Sen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6621)

Abstract

A novel heuristic technique that enhances the search facility of the standard genetic programming (GP) algorithm is presented. The method provides a dynamic sniffing facility to optimize the local search in the vicinity of the current best chromosomes that emerge during GP iterations. Such a hybrid approach, that combines the GP method with the sniffer technique, is found to be very effective in the solution of inverse problems where one is trying to construct model dynamical equations from either finite time series data or knowledge of an analytic solution function. As illustrative examples, some special function ordinary differential equations (ODEs) and integrable nonlinear partial differential equations (PDEs) are shown to be efficiently and exactly recovered from known solution data. The method can also be used effectively for solution of model equations (the direct problem) and as a tool for generating multiple dynamical systems that share the same solution space.

Keywords

Local Search Genetic Programming Soliton Solution Good Chromosome Standard Genetic Programming 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Ahalpara, D.P., Parikh, J.C.: Genetic Programming Based Approach for Modeling Time Series Data of Real Systems. Int. J. Mod. Phys. C 19, 63 (2008)CrossRefzbMATHGoogle Scholar
  2. Ahalpara, D.P., Arora, S., Santhanam, M.S.: Genetic programming based approach for synchronization with parameter mismatches in EEG. In: Vanneschi, L., Gustafson, S., Moraglio, A., De Falco, I., Ebner, M. (eds.) EuroGP 2009. LNCS, vol. 5481, pp. 13–24. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  3. Cao, H., Kang, L., Chen, Y., Yu, J.: Evolutionary Modeling of Systems of Ordinary Differential Equations with Genetic Programming. Genetic Programming and Evolvable Machines 1, 309–337 (2000)CrossRefzbMATHGoogle Scholar
  4. Gray, G.J., Murray-Smith David, J., Li, Y., Sharman Ken, C.: Nonlinear Model Structure Identification Using Genetic Programming. In: Conference Proceedings Genetic Algorithms in Engineering Systems: Innovations and Applications GALESIA 1997 at Glasgow, pp. 308–313 (1997), ISBN: 0-85296-693-8Google Scholar
  5. Iba, H.: Inference of Differential Equation Models by Genetic Programming. Information Sciences, an International Journal archive 178(23), 4453–4468 (2008)CrossRefGoogle Scholar
  6. Korteweg, D.J., de Vries, F.: On the Change of Form of Long WavesAdvancing in a Rectangular Canal, and on a New Type of Soliton Waves. Philosophical Magazine 39, 422–443 (1895)MathSciNetCrossRefzbMATHGoogle Scholar
  7. Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural selection and Genetics. MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  8. Miles, J.W.: The Korteweg-De Vries equation: A Historical Essay. Journal of Fluid Mechanics 106, 131–147 (1981)CrossRefzbMATHGoogle Scholar
  9. Moscato, P.: New ideas in optimization. In: Corne, D., et al. (eds.) pp. 219–234. McGraw-Hill Ltd., UK (1999)Google Scholar
  10. Press, W.H., Teukolsky, S., Vetterling, W., Flannery, B.: Numerical Recipes in C++: The Art of Scientific Computing, 3rd edn. Cambridge University Press, Cambridge (2007), ISBN: 0-521-75033-4zbMATHGoogle Scholar
  11. Sakamoto, E., Iba, H.: Evolutionary Inference of a Biological Network as Differential Equations by Genetic Programming. Genome Informatics 12, 276–277 (2001)Google Scholar
  12. Sugimoto, N., Sakamoto, E., Iba, H.: Inference of Differential Equations by Using Genetic Programming by Genetic Programming. Genome Informatics 12, 276–277 (2001)Google Scholar
  13. Tsoulos, I.G., Lagaris, I.E.: Solving differential equations with genetic programming. Genetic Programming and Evolvable Machines 7(1), 33–54 (2006)CrossRefGoogle Scholar
  14. Zabusky, N.J., Kruskal, M.D.: Interaction of Solitons in a Collisionless Plasma and the Recurrence of Initial States. Physical Review Letters 15, 240–243 (1965)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dilip P. Ahalpara
    • 1
  • Abhijit Sen
    • 1
  1. 1.Institute for Plasma ResearchGandhinagarIndia

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