Advertisement

Allele Diffusion in Linear Genetic Programming and Variable-Length Genetic Algorithms with Subtree Crossover

  • Riccardo Poli
  • Jonathan E. Rowe
  • Christopher R. Stephens
  • Alden H. Wright
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2278)

Abstract

In this paper we study, theoretically, the search biases produced by GP subtree crossover when applied to linear representations, such as those used in linear GP or in variable length GAs. The study naturally leads to generalisations of Geiringer’s theorem and of the notion of linkage equilibrium, which, until now, were applicable only to fixed-length representations. This indicates the presence of a diffusion process by which, even in the absence of selective pressure and mutation, the alleles in a particular individual tend not just to be swapped with those of other individuals in the population, but also to diffuse within the representation of each individual. More precisely, crossover attempts to push the population towards distributions of primitives where each primitive is equally likely to be found in any position in any individual.

Keywords

Genetic Program Length Distribution Linear Genetic Program Terminal Locus Length Bias 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    L. B. Booker. Recombination distributions for genetic algorithms. In FOGA-92, Foundations of Genetic Algorithms, Vail, Colorado, 24–29 July 1992. http://booker@mitre.org.
  2. [2]
    L. B. Booker, D. B. Fogel, D. Whitley, P. J. Angeline, and A. E. Eiben. Recombination. In T. Bäck, D. B. Fogel, and T. Michalewicz, editors, Evolutionary Computation 1: Basic Algorithms and Operators, chapter 33. Institute of Physics Publishing, 2000.Google Scholar
  3. [3]
    H. Geiringer. On the probability theory of linkage in Mendelian heredity. Annals of Mathe-matical Statistics, 15(1):25–57, March 1944.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    J. Holland. Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, USA, 1975.Google Scholar
  5. [5]
    W. B. Langdon, T. Soule, R. Poli, and J. A. Foster. The evolution of size and shape. In L. Spector, W. B. Langdon, U.-M. O’Reilly, and P. J. Angeline, editors, Advances in Genetic Programming 3, chapter 8, pages 163–190. MIT Press, Cambridge, MA, USA, June 1999.Google Scholar
  6. [6]
    N. F. McPhee and J. D. Miller. Accurate replication in genetic programming. In L. Eshelman, editor, Genetic Algorithms: Proceedings of the Sixth International Conference (ICGA95), pages 303–309, Pittsburgh, PA, USA, 15–19 July 1995. Morgan Kaufmann.Google Scholar
  7. [7]
    N. F. McPhee and R. Poli. A schema theory analysis of the evolution of size in genetic programming with linear representations. In Genetic Programming, Proceedings of EuroGP 2001, LNCS, Milan, 18–20 Apr. 2001. Springer-Verlag.Google Scholar
  8. [8]
    N. F. McPhee, R. Poli, and J. E. Rowe. A schema theory analysis of mutation size biases in genetic programming with linear representations. In Proceedings of the 2001 Congress on Evolutionary Computation CEC 2001, Seoul, Korea, May 2001.Google Scholar
  9. [9]
    N. F. McPhee, R. Poli, and J. E. Rowe. A schema theory analysis of mutation size biases in genetic programming with linear representations. In Proceedings of the 2001 Congress on Evolutionary Computation CEC2001, pages 1078–1085, COEX, World Trade Center, 159 Samseong-dong, Gangnam-gu, Seoul, Korea, 27–30 May 2001. IEEE Press.Google Scholar
  10. [10]
    R. Poli. Exact schema theorem and effective fitness for GP with one-point crossover. In D. Whitley, D. Goldberg, E. Cantu-Paz, L. Spector, I. Parmee, and H.-G. Beyer, editors, Proceedings of the Genetic and Evolutionary Computation Conference, pages 469–476, Las Vegas, July 2000. Morgan Kaufmann.Google Scholar
  11. [11]
    R. Poli. Hyperschema theory for GP with one-point crossover, building blocks, and some new results in GA theory. In R. Poli, W. Banzhaf, and et al., editors, Genetic Programming, Proceedings of EuroGP 2000. Springer-Verlag, 15-16 Apr. 2000.Google Scholar
  12. [12]
    R. Poli. Exact schema theory for genetic programming and variable-length genetic algo-rithms with one-point crossover. Genetic Programming and Evolvable Machines, 2(2), 2001. Forthcoming.Google Scholar
  13. [13]
    R. Poli. General schema theory for genetic programming with subtree-swapping crossover. In Genetic Programming, Proceedings of EuroGP 2001, LNCS, Milan, 18-20 Apr. 2001. Springer-Verlag.Google Scholar
  14. [14]
    R. Poli and W. B. Langdon. On the search properties of different crossover operators in genetic programming. In J. R. Koza, W. Banzhaf, K. Chellapilla, K. Deb, M. Dorigo, D. B. Fogel, M. H. Garzon, D. E. Goldberg, H. Iba, and R. Riolo, editors, Genetic Programming 1998: Proceedings of the Third Annual Conference, pages 293–301, University of Wisconsin, Madison, Wisconsin, USA, 22–25 July 1998. Morgan Kaufmann.Google Scholar
  15. [15]
    R. Poli and W. B. Langdon. Schema theory for genetic programming with one-point crossover and point mutation. Evolutionary Computation, 6(3):231–252, 1998.CrossRefGoogle Scholar
  16. [16]
    R. Poli and N. F. McPhee. Exact GP schema theory for headless chicken crossover and subtree mutation. In Proceedings of the 2001 Congress on Evolutionary Computation CEC 2001, Seoul, Korea, May 2001.Google Scholar
  17. [17]
    R. Poli and N. F. McPhee. Exact schema theorems for GP with one-point and standard crossover operating on linear structures and their application to the study of the evolution of size. In Genetic Programming, Proceedings of EuroGP 2001, LNCS, Milan, 18–20 Apr. 2001. Springer-Verlag.Google Scholar
  18. [18]
    R. Poli and N. F. McPhee. Exact schema theory for GP and variable-length GAs with homol-ogous crossover. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), San Francisco, California, USA, 7–11 July 2001. Morgan Kaufmann.Google Scholar
  19. [19]
    M. Ridley. Evolution. Blackwell Scientific Publications, Boston, 1993.Google Scholar
  20. [20]
    J. E. Rowe and N. F. McPhee. The effects of crossover and mutation operators on variable length linear structures. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), San Francisco, California, USA, 7–11 July 2001. Morgan Kauf-mann.Google Scholar
  21. [21]
    T. Soule, J. A. Foster, and J. Dickinson. Code growth in genetic programming. In J. R. Koza, D. E. Goldberg, D. B. Fogel, and R. L. Riolo, editors, Genetic Programming 1996: Proceedings of the First Annual Conference, pages 215–223, Stanford University, CA, USA, 28–31 July 1996. MIT Press.Google Scholar
  22. [22]
    W. M. Spears. Limiting distributions for mutation and recombination. In W. M. Spears and W. Martin, editors, Proceedings of the Foundations of Genetic Algorithms Workshop (FOGA 6), Charlottesville, VA, USA, July 2000. In press.Google Scholar
  23. [23]
    C. R. Stephens. Some exact results from a coarse grained formulation of genetic dynamics. In L. Spector, E. D. Goodman, A. Wu, W. B. Langdon, H.-M. Voigt, M. Gen, S. Sen, M. Dorigo, S. Pezeshk, M.H. Garzon, and E. Burke, editors, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), pages 631–638, San Francisco, California, USA, 7–11 July 2001. Morgan Kaufmann.Google Scholar
  24. [24]
    C. R. Stephens and H. Waelbroeck. Effective degrees of freedom in genetic algorithms and the block hypothesis. In T. Bäck, editor, Proceedings of the Seventh International Conference on Genetic Algorithms (ICGA97), pages 34–40, East Lansing, 1997. Morgan Kaufmann.Google Scholar
  25. [25]
    C. R. Stephens and H. Waelbroeck. Schemata evolution and building blocks. Evolutionary Computation, 7(2):109–124, 1999.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Riccardo Poli
    • 1
  • Jonathan E. Rowe
    • 2
  • Christopher R. Stephens
    • 3
  • Alden H. Wright
    • 4
  1. 1.Department of Computer ScienceUniversity of EssexUK
  2. 2.School of Computer ScienceThe University of BirminghamUK
  3. 3.Instituto de Ciencias NuclearesUNAMMexico
  4. 4.Computer Science DepartmentUniversity of MontanaUSA

Personalised recommendations