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A Schema Theory Analysis of the Evolution of Size in Genetic Programming with Linear Representations

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Genetic Programming (EuroGP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2038))

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Abstract

In this paper we use the schema theory presented in [20] to better understand the changes in size distribution when using GP with standard crossover and linear structures. Applications of the theory to problems both with and without fitness suggest that standard crossover induces specific biases in the distributions of sizes,with a strong tendency to over sample small structures, and indicate the existence of strong redistribution effects that may be a major force in the early stages of a GP run. We also present two important theoretical results: An exact theory of bloat, and a general theory of how average size changes on flat landscapeswith glitches. The latter implies the surprising result that a single program glitch in an otherwise flat fitness landscape is sufficient to drive the average program size of an infinite population, which may have important implications for the control of code growth.

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References

  1. L. Altenberg. The evolution of evolvability in genetic programming. In K.E. Kinnear, Jr., editor, Advances in Genetic Programming, chapter 3, pages 47–74.MIT Press, 1994.

    Google Scholar 

  2. P.J. Angeline. Genetic programming and emergent intelligence. In K.E. Kinnear, Jr., editor, Advances in Genetic Programming, chapter 4, pages 75–98.MIT Press, 1994.

    Google Scholar 

  3. T. Blickle and L. Thiele. Genetic programming and redundancy. In J. Hopf, editor, Genetic Algorithms within the Framework of Evolutionary Computation (Workshop at KI-94, Saarbrücken), pages 33–38, Im Stadtwald, Building 44, D-66123 Saarbrücken, Germany, 1994. Max-Planck-Institut für Informatik (MPI-I-94-241).

    Google Scholar 

  4. R. Dawkins. The selfish gene. Oxford University Press, Oxford, 1976.

    Google Scholar 

  5. J.R. Koza. Genetic Programming:On the Programming of Computers byMeans of Natural Selection. MIT Press, Cambridge,MA, USA, 1992.

    Google Scholar 

  6. W.B. Langdon. Scaling of program tree fitness spaces. Evolutionary Computation, 7(4):399–428,Winter 1999.

    Article  Google Scholar 

  7. W.B. Langdon. Quadratic bloat in genetic programming. 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 (GECCO-2000), pages 451–458, Las Vegas, Nevada, USA, 10-12 July 2000.Morgan Kaufmann.

    Google Scholar 

  8. W.B. Langdon and W. Banzhaf. Genetic programming bloat without semantics. In M. Schoenauer, K. Deb, G. Rudolph, X. Yao, E. Lutton, J.J. Merelo, and H.-P. Schwefel, editors, Parallel Problem Solving from Nature-PPSN VI 6th International Conference, volume 1917 of LNCS, pages 201–210, Paris, France, Sept. 16-20 2000. Springer Verlag.

    Chapter  Google Scholar 

  9. W.B. Langdon and R. Poli. Fitness causes bloat. In P.K. Chawdhry, R. Roy, and R.K. Pant, editors, Soft Computing in Engineering Design and Manufacturing, pages 13–22. Springer-Verlag London, 23-27 June 1997.

    Google Scholar 

  10. W.B. Langdon and R. Poli. Why ants are hard. 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 193–201, University of Wisconsin, Madison, Wisconsin, USA, 22-25 July 1998. Morgan Kaufmann.

    Google Scholar 

  11. 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 

  12. N.F. McPhee. A note on the derivation of transmission probabilities for a flat fitness landscape and for the one-then-zeros problem. 2000. Unpublished; contact the author at http://www.mcphee@mrs.umn.edu for a copy.

  13. 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 

  14. N.F. McPhee, R. Poli, and J.E. Rowe. A schema theory analysis of mutation size biases in genetic programming with linear representations. Technical Report CSRP-00-24, University of Birmingham, School of Computer Science, December 2000.

    Google Scholar 

  15. P. Nordin and W. Banzhaf. Complexity compression and evolution. In L. Eshelman, editor, Genetic Algorithms: Proceedings of the Sixth International Conference (ICGA95), pages 310–317, Pittsburgh, PA, USA, 15-19 July 1995. Morgan Kaufmann.

    Google Scholar 

  16. 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 (GECCO-2000), pages 469–476, Las Vegas, Nevada, USA, 10-12 July 2000. Morgan Kaufmann.

    Google Scholar 

  17. 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 

  18. R. Poli and W.B. Langdon. A new schema theory for genetic programming with one-point crossover and point mutation. In J.R. Koza, K. Deb, M. Dorigo, D.B. Fogel, M. Garzon, H. Iba, and R.L. Riolo, editors, Genetic Programming 1997: Proceedings of the Second Annual Conference, pages 278–285, Stanford University, CA, USA, 13–16 July 1997.Morgan Kaufmann.

    Google Scholar 

  19. R. Poli and N.F. McPhee. Exact GP schema theory for headless chicken crossover and subtree mutation. Technical Report CSRP-00-23, University of Birmingham, School of Computer Science, December 2000.

    Google Scholar 

  20. 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 

  21. T. Soule. CodeGrowth in Genetic Programming. PhD thesis, University of Idaho, Moscow, Idaho, USA, 15May 1998.

    Google Scholar 

  22. T. Soule and J.A. Foster. Removal bias: a new cause of code growth in tree based evolutionary programming. In 1998 IEEE International Conference on Evolutionary Computation, pages 781–186,Anchorage, Alaska, USA, 5-9 May 1998. IEEE Press.

    Google Scholar 

  23. C.R. Stephens and H. Waelbroeck. Schemata evolution and building blocks. Evolutionary Computation, 7(2):109–124, 1999.

    Article  Google Scholar 

  24. B.-T. Zhang and H. Mühlenbein. Balancing accuracy and parsimony in genetic programming. Evolutionary Computation, 3(1):17–38, 1995.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Division of Science andMathematics, University of Minnesota Morris, Morris, MN, USA

    Nicholas Freitag McPhee

  2. School of Computer Science, The University of Birmingham, Birmingham, B15 2TT, UK

    Riccardo Poli

Authors
  1. Nicholas Freitag McPhee
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  2. Riccardo Poli
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Editor information

Editors and Affiliations

  1. School of Computer Science, University of Birmingham, Birmingham

    Julian Miller

  2. Computer Science Institute, University of Lausanne, Lausanne

    Marco Tomassini

  3. Dipartimento di Elettronica e Informazione, Politecnico di Milano, Italy

    Pier Luca Lanzi

  4. Computer Science and Information Systems, University of Limerick, Limerick

    Conor Ryan

  5. Dipartimento di Tecnologie dell’Informazione, Università degli Studi di Milano, Italy

    Andrea G. B. Tettamanzi

  6. Department of Computer Science, University College London, London

    William B. Langdon

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© 2001 Springer-Verlag Berlin Heidelberg

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Freitag McPhee, N., Poli, R. (2001). A Schema Theory Analysis of the Evolution of Size in Genetic Programming with Linear Representations. In: Miller, J., Tomassini, M., Lanzi, P.L., Ryan, C., Tettamanzi, A.G.B., Langdon, W.B. (eds) Genetic Programming. EuroGP 2001. Lecture Notes in Computer Science, vol 2038. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45355-5_10

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  • DOI: https://doi.org/10.1007/3-540-45355-5_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41899-3

  • Online ISBN: 978-3-540-45355-0

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