Advertisement

The Best Things Don’t Always Come in Small Packages: Constant Creation in Grammatical Evolution

  • R. Muhammad Atif Azad
  • Conor Ryan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8599)

Abstract

This paper evaluates the performance of various methods to constant creation in Grammatical Evolution (GE), and validates the results against those from Genetic Programming (GP). Constant creation in GE is an important issue due to the disruptive nature of ripple crossover, which can radically remap multiple terminals in an individual, and we investigate if more compact methods, which are more similar to the GP style of constant creation (Ephemeral Random Constants (ERCs), perform better.

The results are surprising. The GE methods all perform significantly better than GP on unseen test data, and we demonstrate that the standard GE approach of digit concatenation does not produce individuals that are any larger than those from methods which are designed to use less genetic material.

Keywords

Grammatical Evolution Constants Symbolic Regression Genetic Programming Digit Concatenation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Mitchell, T.M.: Machine learning. McGraw Hill, New York (1996)zbMATHGoogle Scholar
  2. 2.
    Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)zbMATHGoogle Scholar
  3. 3.
    Keijzer, M.: Improving symbolic regression with interval arithmetic and linear scaling. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 70–82. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Topchy, A., Punch, W.F.: Faster genetic programming based on local gradient search of numeric leaf values. In: Spector, et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2001), July 7-11, pp. 155–162. Morgan Kaufmann, San Francisco (2001)Google Scholar
  5. 5.
    McKay, B., Willis, M., Searson, D., Montague, G.: Non-linear continuum regression using genetic programming. In: Banzhaf, et al. (eds.) Proceedings of GECCO 1999, Orlando, Florida, USA, July 13-17, vol. 2, pp. 1106–1111. Morgan Kaufmann (1999)Google Scholar
  6. 6.
    Ryan, C., Keijzer, M.: An analysis of diversity of constants of genetic programming. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 404–413. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Evett, M., Fernandez, T.: Numeric mutation improves the discovery of numeric constants in genetic programming. In: Koza, et al. (eds.) Genetic Programming 1998: Proceedings of the Third Annual Conference, University of Wisconsin, Madison, Wisconsin, July 22-25, pp. 66–71. Morgan Kaufmann (1998)Google Scholar
  8. 8.
    O’Neill, M., Ryan, C.: Grammatical Evolution: Evolutionary Automatic Programming in a Arbitrary Language. Genetic programming, vol. 4. Kluwer Academic Publishers (2003)Google Scholar
  9. 9.
    Byrne, J., O’Neill, M., Hemberg, E., Brabazon, A.: Analysis of constant creation techniques on the binomial-3 problem with grammatical evolution. In: Tyrrell, et al. (eds.) 2009 IEEE Congress on Evolutionary Computation, Trondheim, Norway, May 18-21, pp. 568–573. IEEE Computational Intelligence Society, IEEE Press (2009)Google Scholar
  10. 10.
    O’Neill, M., Ryan, C., Keijzer, M., Cattolico, M.: Crossover in grammatical evolution. Genetic Programming and Evolvable Machines 4(1), 67–93 (2003)CrossRefzbMATHGoogle Scholar
  11. 11.
    Dempsey, I., O’Neill, M., Brabazon, A.: Constant creation in grammatical evolution. International Journal of Innovative Comput. and Applic. 1(1), 23–38 (2007)CrossRefGoogle Scholar
  12. 12.
    Augusto, D.A., Barbosa, H.J.C., Barreto, A.M.S., Bernardino, H.S.: Evolving numerical constants in grammatical evolution with the ephemeral constant method. In: Antunes, L., Pinto, H.S. (eds.) EPIA 2011. LNCS, vol. 7026, pp. 110–124. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Augusto, D.A., Barbosa, H.J.C., Barreto, A.M.S., Bernardino, H.S.: A new approach for generating numerical constants in grammatical evolution. In: Krasnogor, et al. (eds.) GECCO 2011: Proceedings of the 13th Annual Conference Companion on GECCO, Dublin, Ireland, July 12-16, pp. 193–194. ACM (2011)Google Scholar
  14. 14.
    Daida, J.M., Bertram, R.R., Stanhope, S.A., Khoo, J.C., Chaudhary, S.A., Chaudhri, O.A., Polito II, J.A.: What makes a problem GP-hard? Analysis of a tunably difficult problem in genetic programming. Genetic Programming and Evolvable Machines 2(2), 165–191 (2001)CrossRefzbMATHGoogle Scholar
  15. 15.
    Nicolau, M., Slattery, D.: libGE - Grammatical Evolution Library (2006)Google Scholar
  16. 16.
    Ryan, C., Azad, R.M.A.: Sensible initialisation in grammatical evolution. In: Barry, A.M. (ed.) GECCO 2003: Proceedings of the Bird of a Feather Workshops, Genetic and Evolutionary Computation Conference, Chigaco, pp. 142–145. AAAI (July 2003)Google Scholar
  17. 17.
    Vladislavleva, E.J., Smits, G.F., den Hertog, D.: Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming. IEEE Trans. on Evolutionary Computation 13(2), 333–349 (2009)CrossRefGoogle Scholar
  18. 18.
    Keijzer, M., Babovic, V.: Genetic programming, ensemble methods and the bias/variance tradeoff - introductory investigations. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., Fogarty, T.C. (eds.) EuroGP 2000. LNCS, vol. 1802, pp. 76–90. Springer, Heidelberg (2000)Google Scholar
  19. 19.
    Poli, R.: A simple but theoretically-motivated method to control bloat in genetic programming. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 204–217. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  20. 20.
    Costelloe, D., Ryan, C.: On improving generalisation in genetic programming. In: Vanneschi, L., Gustafson, S., Moraglio, A., De Falco, I., Ebner, M. (eds.) EuroGP 2009. LNCS, vol. 5481, pp. 61–72. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  21. 21.
    Banzhaf, W., Nordin, P., Keller, R.E., Francone, F.D.: Genetic Programming – An Introduction; On the Automatic Evolution of Computer Programs and its Applications. Morgan Kaufmann, San Francisco (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • R. Muhammad Atif Azad
    • 1
  • Conor Ryan
    • 1
  1. 1.CSIS DepartmentUniversity of LimerickIreland

Personalised recommendations