Skip to main content
Log in

Accelerated Genetic Programming of Polynomials

  • Published:
Genetic Programming and Evolvable Machines Aims and scope Submit manuscript

Abstract

An accelerated polynomial construction technique for genetic programming is proposed. This is a horizontal technique for gradual expansion of a partial polynomial during traversal of its tree-structured representation. The coefficients of the partial polynomial and the coefficient of the new term are calculated by a rapid recurrent least squares (RLS) fitting method. When used for genetic programming (GP) of polynomials this technique enables us not only to achieve fast estimation of the coefficients, but also leads to power series models that differ from those of traditional Koza-style GP and from those of the previous GP with polynomials STROGANOFF. We demonstrate that the accelerated GP is sucessful in that it evolves solutions with greater generalization capacity than STROGANOFF and traditional GP on symbolic regression, pattern recognition, and financial time-series prediction tasks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. Banzhaf, P. Nordin, R. E. Keller, and F. D. Francone, Genetic Programming: An Introduction. On the Automatic Evolution of Computer Programs and Its Applications, Morgan Kaufmann: San Francisco, CA, 1998.

    Google Scholar 

  2. I. S. Berezin and N. P. Zhidkov, Computing Methods, Addison-Wesley: Reading, MA, 1965.

    Google Scholar 

  3. S.-H. Chen and C.-H. Yeh, “Option pricing with genetic programming,” in Genetic Programming 1998: Proc. Second Annual Conf., Madison, WI, J. R. Koza, W. Banzhaf, K. Chellapilla, K. Deb, M. Dorigo, D. B. Fogel, M. Garzon, D. Goldberg, H. Iba, and R. L. Riolo (eds.), Morgan Kaufmann: San Francisco, CA, 1998, pp. 32-37.

    Google Scholar 

  4. G. J. Deboeck and M. Cader, “Pre and postprocessing of financial data,” in Trading on the Edge: Neural, Genetic and Fuzzy Systems for Chaotic Financial Markets, G. J. Deboeck (ed.), John Wiley & Sons: New York, NY, 1994, Chapter 2, pp. 27-44.

    Google Scholar 

  5. D. K. Fadeev and V. N. Fadeeva, Computational Methods of Linear Algebra, W. H. Freeman: San Francisco, CA, 1963.

    Google Scholar 

  6. A. A. Freitas, “Genetic programming framework for two data mining tasks: classification and generalized rule regression,” in Genetic Programming 1997: Proc. Second Annual Conf., Stanford University, CA, J. R. Koza, K. Deb, M. Dorigo, D. B. Fogel, M. Garzon, H. Iba, and R. L. Riolo (eds.), Morgan Kaufmann: San Francisco CA, 1997, pp. 96-101.

    Google Scholar 

  7. D. Gabor, W. Wildes, and R. Woodcock, “A universal nonlinear filter, predictor and simulator which optimizes itself by a learning process,” Proc. IEE, vol. 108B, pp. 422-438, 1961.

    Google Scholar 

  8. Ch. Hafner and J. Fröhlich, “Generalized function analysis using hybrid evolutionary algorithms,” in Proc. 1999 Congress on Evolutionary Computation, IEEE Press: Piscataway, NJ, 1999, pp. 287-294.

    Google Scholar 

  9. H. Hiden, B. McKay, M. Willis, and G. Montague, “Non-linear partial least squares using genetic programming,” in Genetic Programming 1998: Proc. Second Annual Conf., Madison, WI, J. R. Koza, W. Banzhaf, K. Chellapilla, K. Deb, M. Dorigo, D. B. Fogel, M. Garzon, D. Goldberg, H. Iba, and R. L. Riolo (eds.), Morgan Kaufmann: San Francisco, CA, 1998, pp. 128-133.

    Google Scholar 

  10. A. E. Hoerl and R. W. Kennard, “Ridge regression: biased estimation of nonorthogonal problems,” Technometrics vol. 12, pp. 55-67, 1970.

    Google Scholar 

  11. W. Hordijk, “A measure of landscapes,” Evolutionary Computation vol. 4, no. 4, pp. 335-360, 1996.

    Google Scholar 

  12. H. Iba, H. de Garis, and T. Sato, “Genetic programming using a minimum description length principle,” in Advances in Genetic Programming, K. Kinnear, Jr. (ed.), The MIT Press: Cambridge, MA, 1994, pp. 265-284.

    Google Scholar 

  13. H. Iba and H. de Garis, “Extending genetic programming with recombinative guidance,” in Advances in Genetic Programming 2, P. J. Angeline and K. Kinnear (eds.), The MIT Press: Cambridge, MA, 1996, pp. 69-88.

    Google Scholar 

  14. H. Iba and T. Sasaki, “Using genetic programming to predict financial data,” in Proc. 1999 Congress on Evolutionary Computation, IEEE Press: Piscataway, NJ, 1999, pp. 244-251.

    Google Scholar 

  15. A. G. Ivakhnenko, “Polynomial theory of complex systems,” IEEE Trans. Systems Man Cybernet. vol. 1(4), pp. 364-378, 1971.

    Google Scholar 

  16. J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection, The MIT Press: Cambridge, MA, 1992.

    Google Scholar 

  17. J. R. Koza, “Genetic programming for economic modeling,” in Intelligent Systems for Finance and Business, S. Goonatilaje and P. Treleaven (eds.), John Wiley Sons: London, UK, 1995, pp. 251-269.

    Google Scholar 

  18. G. Y. Lee, “Genetic recursive regression for modeling and forecasting real-world chaotic time series,” in Advances in Genetic Programming 3, L. Spector, W. B. Langdon, U.-M. O'Reilly, and P. J. Angeline (eds.), The MIT Press: Cambridge, MA, 1999, pp. 401-423.

    Google Scholar 

  19. H. R. Madala and A. G. Ivakhnenko, Inductive Learning Algorithms for Complex Systems Modeling, CRC Press: Boca Raton, FL, 1994.

    Google Scholar 

  20. B. Manderick, W. de Weger, and P. Spiessens, “The genetic algorithm and the structure of the fitness landscape,” in Proc. Fourth Int. Conf. Genetic Algorithms, R. K. Belewand L. B. Booker (eds.), Morgan Kaufmann: San Francisco, CA, 1991, pp. 143-150.

    Google Scholar 

  21. B. S. Mulloy, R. L. Riolo, and R. S. Savit, “Dynamics of genetic programming and chaotic time series prediction,” in Genetic Programming 1996: Proc. First Annual Conf., Stanford University, CA, J. R. Koza, D. E. Goldberg, D. E. Fogel, and R. L. Riolo (eds.), The MIT Press: Cambridge, MA, 1996, pp. 166-174.

    Google Scholar 

  22. R. H. Myers, Classical and Modern Regression with Applications, PWS-Kent Publ., Duxbury Press: CA, 1990.

    Google Scholar 

  23. N. I. Nikolaev and H. Iba, “Regularization approach to inductive genetic programmimg,” IEEE Trans. Evolutionary Comput., 2001.

  24. P. Nordin and W. Banzhaf, “Programmatic compression of images and sound,” in Genetic Programming 1996: Proc. First Annual Conf., Stanford University, CA, J. R. Koza, D. E. Goldberg, D. E. Fogel and R. L. Riolo (eds.), The MIT Press: Cambridge, MA, 1996, pp. 345-350.

    Google Scholar 

  25. R. Poli, “Genetic programming for image analysis,” in Genetic Programming 1996: Proc. First Annual Conf., Stanford University, CA, J. R. Koza, D. E. Goldberg, D. E. Fogel and R. L. Riolo (eds.), The MIT Press: Cambridge, MA, 1996, pp. 363-368.

    Google Scholar 

  26. W. H. Press, B. P. Flannery, S. A. Teukolski, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed., Cambridge University Press: Cambridge, UK, 1992.

    Google Scholar 

  27. K. Rodriguez-Vazquez, C. M. Fonseca, and P. J. Fleming, “An evolutionary approach to nonlinear polynomial system identification,” in Proc. 11th IFAC Symp. System Identification, 1997, pp. 2395-2400.

  28. W. A. Tackett and A. Carmi, “The donut problem: scalability and generalization in genetic programming,” in Advances in Genetic Programming, K. E. Kinnear, Jr. (ed.), The MIT Press: Cambridge, MA, 1994, pp. 143-176.

    Google Scholar 

  29. G. Wahba, Spline Models for Observational Data, CBMS-NSF Regional Conf. Series 59, SIAM Press: Philadelphia, 1990.

    Google Scholar 

  30. H. C. Yau and M. T. Manry, “Iterative improvement of a nearest neighbor classifier,” Neural Networks vol. 4(4), pp. 517-524, 1991.

    Google Scholar 

  31. B.-T. Zhang, P. Ohm, and H. Mühlenbein, “Evolutionary induction of sparse neural trees,” Evolutionary Comput. vol. 5(2), pp. 213-236, 1997.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nikolaev, N.I., Iba, H. Accelerated Genetic Programming of Polynomials. Genetic Programming and Evolvable Machines 2, 231–257 (2001). https://doi.org/10.1023/A:1011949326249

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011949326249

Keywords

Navigation