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Evolving the best known approximation to the Q function

Published:07 July 2012Publication History

ABSTRACT

The Gaussian Q-function is the integral of the tail of the Gaussian distribution; as such, it is important across a vast range of fields requiring stochastic analysis. No elementary closed form is possible, so a number of approximations have been proposed. We use a Genetic Programming (GP) system, Tree Adjoining Grammar Guided GP (TAG3P) with local search operators to evolve approximations of the Q-function in the form given by Benitez [1]. We found more accurate approximations than any previously published. This confirms the practical importance of local search in TAG3P.

References

  1. M. Benitez and F. Casadevall. Versatile, accurate, and analytically tractable approximation for the gaussian q-function. IEEE Transactions on Communications, 59(4):917--922, 2011.Google ScholarGoogle ScholarCross RefCross Ref
  2. P. Borjesson and C. Sundberg. Simple approximations of the error function q(x) for communications applications. IEEE Transactions on Communications, 27:639--643, 1979.Google ScholarGoogle ScholarCross RefCross Ref
  3. Y. Chan and N. Beaulieu. A simple polynomial approximation to the gaussian q-function and its application. IEEE Communications Letters, 12:124--126, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. M. Chiani, D. Dardari, and M. K. Simon. New exponential bounds and approximations for the computation of error probability in fading channels. IEEE Transactions on Wireless Communications, 2(4):840--845, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. N. X. Hoai. A Flexible Representation for Genetic Programming from Natural Language Processing. PhD thesis, Australian Defence force Academy, University of New South Wales, Australia, 2004.Google ScholarGoogle Scholar
  6. N. X. Hoai, R. I. McKay, and H. A. Abbass. Tree adjoining grammars, language bias, and genetic programming. In Genetic Programming, Proceedings of EuroGP'2003, volume 2610 of LNCS, pages 335--344. Springer-Verlag, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. N. X. Hoai, R. I. B. McKay, and D. Essam. Representation and structural difficulty in genetic programming. IEEE Transactions on Evolutionary Computation, 10(2):157--166, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. T. H. Hoang, N. X. Hoai, R. I. B. McKay, and D. Essam. The importance pf local search: A grammar based approach to environmental time series modelling. In T. Yu, R. L. Riolo, and B. Worzel, editors, Genetic Programming Theory and Practice III, volume 9 of Genetic Programming, chapter 11. Springer-Verlag, 2005.Google ScholarGoogle Scholar
  9. T. H. Hoang, R. B. McKay, D. Essam, and N. X. Hoai. On synergistic interactions between evolution, development and layered learning. IEEE Transactions on Evolutionary Computation, 15(3):287--312, June 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. A. Joshi, L. Levy, and M. Takahashi. Tree adjunct grammars. Journal of Computer and System Sciences, 10(1):136--163, 1975. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. A. Joshi and Y. Schabes. Tree-adjoining grammars. Handbook of formal languages, 3:69--124, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. A. Karagiannidis and A. Lioumpas. An improved approximation for the gaussian q-function. IEEE Communication Letters, 11:644--646, 2007.Google ScholarGoogle ScholarCross RefCross Ref
  13. J. Koza. Genetic Programming: On the Programming of Computers by Natural Selection. MIT Press, MA, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. J. R. Koza. Human-competitive results produced by genetic programming. Genetic Programming and Evolvable Machines, 11(3/4):251--284, 2010. Tenth Anniversary Issue: Progress in Genetic Programming and Evolvable Machines. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. S. Mahler, D. Robilliard, and C. Fonlupt. Tarpeian bloat control and generalization accuracy. In Genetic Programming, 8th European Conference, volume 3447 of LNCS. Springer-Velag, 2005. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. E. Murphy, M. O'Neill, and A. Brabazon. Examining mutation landscapes in grammar based genetic programming. In Proceedings of the 14th European Conference on Genetic Programming, EuroGP 2011, volume 6621 of LNCS, pages 130--141. Springer Verlag, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. D. N. Phong, N. Q. Uy, N. X. Hoai, and R. I. B. McKay. Evolving approximations for the gaussian q-function by genetic programming with semantic based crossover. In Congress on Evolutionary Computation, page To Appear. IEEE, IEEE Press, June 2012.Google ScholarGoogle Scholar
  18. R. Poli. A simple but theoretically-motivated method to control bloat in genetic programming. In Genetic Programming, 6th European Conference, volume 2610 of LNCS, pages 204--217. Springer-Verlag, 2003. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. R. Poli, W. Langdon, and N. McPhee. A Field Guide to Genetic Programming. http://lulu.com, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. M. Rosenlicht. Liouville's theorem on functions with elementary integrals. Pac. J Math., 24(1):153--161, 1968.Google ScholarGoogle ScholarCross RefCross Ref
  21. M. Simon. Probability Distributions Involving Gaussian Random Variables: A Handbook for Engineers and Scientists. Kluwer Academics, 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. M. Simon and M. Alouini. Digital Communications Over Fading Channels: A Unified Approach to Performance Analysis. Wiley and Sons, 2000.Google ScholarGoogle Scholar

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          cover image ACM Conferences
          GECCO '12: Proceedings of the 14th annual conference on Genetic and evolutionary computation
          July 2012
          1396 pages
          ISBN:9781450311779
          DOI:10.1145/2330163

          Copyright © 2012 ACM

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          Publication History

          • Published: 7 July 2012

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