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Genetic Programming and Evolvable Machines

, Volume 8, Issue 2, pp 187–220 | Cite as

Introducing probabilistic adaptive mapping developmental genetic programming with redundant mappings

  • Garnett Wilson
  • Malcolm Heywood
Original Paper

Abstract

Developmental Genetic Programming (DGP) algorithms have explicitly required the search space for a problem to be divided into genotypes and corresponding phenotypes. The two search spaces are often connected with a genotype-phenotype mapping (GPM) intended to model the biological genetic code, where current implementations of this concept involve evolution of the mappings along with evolution of the genotype solutions. This work presents the Probabilistic Adaptive Mapping DGP (PAM DGP), a new developmental implementation that involves research contributions in the areas of GPMs and coevolution. The algorithm component of PAM DGP is demonstrated to overcome coevolutionary performance problems that are identified and empirically benchmarked against the latest competing algorithm that adapts similar GPMs. An adaptive redundant mapping encoding is then incorporated into PAM DGP for further performance enhancement. PAM DGP with two mapping types are compared to the competing Adaptive Mapping algorithm and Traditional GP in two medical classification domains, where PAM DGP with redundant encodings is found to provide superior fitness performance over the other algorithms through it’s ability to explicitly decrease the size of the function set during evolution.

Keywords

Developmental genetic programming Cooperative coevolution Genotype-phenotype mapping Neutrality Redundant representation 

Notes

Acknowledgments

The authors gratefully acknowledge the support of a NSERC PGS-B and Izaak Walton Killam scholarship (Garnett Wilson), and the CFI New Opportunities and NSERC research grants (Dr. M. Heywood).

References

  1. 1.
    Keller, R., Banzhaf, W.: The evolution of genetic code in genetic programming. In: Banzhaf, W., Daida, J., Eiben, A., Garzon, M., Honavar, V., Jakiela, M., Smith, R. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 1999), Orlando, Florida, pp. 1077–1082. Morgan Kaufman, San Francisco (1999)Google Scholar
  2. 2.
    Wilson, G., Heywood, M.: Probabilistic (Genotype) adaptive mapping combinations for developmental genetic programming. In: Proceedings of the 2006 IEEE Congress on Evolutionary Computation (CEC 2006), pp. 8667–8674. IEEE Press, Vancouver, Canada (2006)Google Scholar
  3. 3.
    Wilson, G., Heywood, M.: Probabilistic adaptive mapping developmental genetic programming (PAM DGP): a new developmental approach. In: Runarsson, T., Beyer, H.-G., Burke, E., Merelo-Guervos, J., Whitley, L., Yao, X. (eds.) Proceedings of the 9th International Conference on Parallel Problem Solving from Nature (PPSN IX), Reykjavik, Iceland, pp. 751–760. Springer-Verlag, Berlin (2006)CrossRefGoogle Scholar
  4. 4.
    Margetts, S.: Adaptive Genotype to Phenotype Mappings for Evolutionary Algorithms, Ph.D. thesis, School of Computer Science, Cardiff University, Wales, Great Britain (2001)Google Scholar
  5. 5.
    Margetts, S., Jones A.: Phlegmatic mappings for functional optimisation with genetic programming. In: Whitley, L., Goldberg, D., Cantu-Paz, E., Spector, L., Parmee, I., Beyer, H.-G. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2000), Las Vegas, Nevada, pp. 82–89. Morgan Kaufman (2000)Google Scholar
  6. 6.
    Margetts, S., Jones, A.: An adaptive mapping for developmental genetic programming. In: Miller, J., Tomassini, M., Lanzi, P., Ryan, C., Tettamanzi, A., Langdon, W. (eds.) Proceedings of the Fourth European Conference on Genetic Programming (EuroGP 2001), Lake Como, Italy, pp. 97–107. Springer Verlag, Berlin (2001)Google Scholar
  7. 7.
    Banzhaf, W.: Genotype-phenotype mapping and neutral variation. In: Davidor, Y., Schwefel, H.-P., Manner, R. (eds.) Parallel Problem Solving from Nature III, Jerusalem, Israel, pp. 322–332. Berlin, Springer-Verlag (1994)Google Scholar
  8. 8.
    Keller, R., Banzhaf, W.: Genetic programming using genotype-phenotype mapping from linear genomes in linear phenotypes. In: Koza, J., Goldberg, D., Fogel, D., Riolo, R. (eds.) Genetic Programming 1996: Proceedings of the First Annual Conference, Stanford, California, pp. 116–122. MIT Press, Cambridge, MA (1996)Google Scholar
  9. 9.
    Keller, R., Banzhaf, W.: Evolution of genetic code on a hard problem. In: Spector, L., Goodman, E., Wu, A., Langdon, W., Voigt, H.-M., Gen, M., Sen, S., Dorigo, M., Pezeshk, S., Garzon, M., Burke, E. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2001), San Francisco, California, pp. 50–56. Morgan Kaufman, San Francisco (2001)Google Scholar
  10. 10.
    O’Neill, M., Brabazon, A.: mGGA: The meta-grammar genetic algorithm. In: Kaijzer, M., Tettamanzi, A., Collet, P., Hemert, J., Tomassini, M. (eds.) Proceedings of the 8th European Conference on Genetic Programming (EuroGP 2005), Lausanne, Switzerland, pp. 311–320. Springer, Berlin (2005)Google Scholar
  11. 11.
    O’Neill, M., Ryan, C.: Grammatical evolution by grammatical evolution: the evolution of grammar and genetic code. In: Keijzer, M., O’Reilly, U.-M., Lucas, S., Costa, E., Soule, T. (eds.) Proceedings of the Seventh European Conference on Genetic Programming (EuroGP 2004), Coimbra, Portugal, pp. 138–149. Springer, Berlin (2004)Google Scholar
  12. 12.
    Freeland, S.: The darwinian genetic code: an adaptation for adapting? Gen. Program. Evol. Mach. 3(2), 113–127 (2002)MATHCrossRefGoogle Scholar
  13. 13.
    Wagner, G., Altenberg, L.: Perspectives: complex adaptations and the evolution of evolvability. Evolution 50(3), 967–976 (1996)CrossRefGoogle Scholar
  14. 14.
    Sella, G., Ardell, D.: The coevolution of genes and genetic codes: crick’s frozen accident revisted. J. Mol. Evol. 63(3), 297–313 (2006)CrossRefGoogle Scholar
  15. 15.
    Crick, F.: The origin of the genetic code. J. Mol. Biol. 38(3), 367–379 (1968)CrossRefGoogle Scholar
  16. 16.
    de Jong, E., Pollack, J.: Ideal evaluation from coevolution. Evol. Comput. 12(2), 159–192 (2004)CrossRefGoogle Scholar
  17. 17.
    Potter, M.: The design and analysis of a computational model of cooperative coevolution, Ph.D. thesis, Department of Computer Science, George Mason University, Fairfax, VA (1997)Google Scholar
  18. 18.
    Potter, M., De Jong, K.: Cooperative coevolution: an architecture for evolving coadapted subcomponents. Evol. Comput. 8(1), 1–29 (2000)CrossRefGoogle Scholar
  19. 19.
    Cliff, D., Miller, G.: Tracking the red queen: measurements of adaptive progress in co-evolutionary simulations. In: Moran, F., Moreno, A., Merelo, J., Chacon, P. (eds.) Advances in Artificial Life: Proceedings of the Third European Conference on Artificial Life (ECAL 95), Granada, Spain, pp. 200–218. Springer-Verlag, London (1995)Google Scholar
  20. 20.
    Wiegand, R., Potter, M.: Robustness in cooperative coevolution. In: Keijzer, M., Arnold, D., Babovic, V., Blum, C., Bosman, P., Butz, M., Coello, C., Dasgupta, D., Ficici, S., Foster, J., Hernandez-Aguirre, A., Hornby, G., Lipson, H., McMinn, P., Moore, J., Raidl, G., Rothlauf, F., Ryan, C., Thierens, D. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2006), Seattle, Washington, pp. 369–376. ACM Press, New York (2006)Google Scholar
  21. 21.
    Bucci, A., Pollack, J.: On identifying global optima in cooperative coevolution. In: Beyer, H.-G., O’Reilly, U.-M., Arnold, D., Banzhaf, W., Blum, C., Bonabeau, E., Cantu-Paz, E., Dasgupta, D., Deb, K., Foster, J., Jong, E.d., Lipson, H., Llora, X., Mancoridis, S., Pelikan, M., Raidl, G., Soule, T., Tyrrell, A., Watson, J.-P., Zitzler, E. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2005), Washington, DC, USA, pp. 539–544. ACM Press, New York (2005)CrossRefGoogle Scholar
  22. 22.
    Panait, L., Luke, S., Wiegand, R.: Biasing coevolutionary search for optimal multiagent behaviors. IEEE Trans. Evol. Comput. 10(6), 629–645 (2006)CrossRefGoogle Scholar
  23. 23.
    Panait, L., Wiegand, R., Luke, S.: A sensitivity analysis of a cooperative coevolutionary algorithm biased for optimization. In: Seattle, W.A., Deb, K., Poli, R., Banzhaf, W., Beyer, H.-G., Burke, E., Darwen, P., Dasgupta, D., Floreano, D., Foster, J., Harman, M., Holland, O., Lanzi, P., Spector, L., Tettamanzi, A., Thierens, D. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2004), Seattle, pp. 573–584. Springer, Berlin (2004)Google Scholar
  24. 24.
    Gathercole, C., Ross, P.: An adverse interaction between crossover and restricted tree depth in genetic programming. In: Koza, J., Goldberg, D., Fogel, D., Riolo, R. (eds.) Genetic Programming 1996: Proceedings of the First Annual Conference, Stanford, California, pp. 291–296. MIT Press, Cambridge, MA (1996)Google Scholar
  25. 25.
    Langdon, W., Poli, R.: An analysis of the MAX problem in genetic programming. In: Koza, J., Deb, K., Dorigo, M., Fogel, D., Garzon, M., Iba, H., Riolo, R. (eds.) Genetic Programming 1997: Proceedings of the Second Annual Conference, Stanford, California, pp. 222–230. Morgan Kaufman (1997)Google Scholar
  26. 26.
    Di Caro, G., Dorigo, M.: AntNet: distributed stigmergetic control for communication networks. J. Artif. Intell. Res. 9, 317–365 (1998)MATHGoogle Scholar
  27. 27.
    Kimura, M.: Evolutionary rate at the molecular level. Nature 217, 624–626 (1968)CrossRefGoogle Scholar
  28. 28.
    Wilson, G.: Probabilistic Adaptive Mapping Developmental Genetic Programming, Ph.D. thesis, Faculty of Computer Science, Dalhousie University, Halifax, NS, Canada (2007)Google Scholar
  29. 29.
    Newman, D., Hettich, S., Blake, C., Merz C.: UCI Repository of machine learning databases [http://www.ics.uci.edu/∼mlearn/MLRepository.html], University of California, Department of Information and Computer Science, Irvine, CA (1998)
  30. 30.
    Detrano, R., Janosi, A., Steinbrunn, W., Pfisterer, M., Schmid, J., Sandhu, S., Guppy, K., Lee, S., Froelicher, V.: International application of a new probability algorithm for the diagnosis of coronary artery disease. Am. J. Cardiol. 64, 304–310 (1989)CrossRefGoogle Scholar
  31. 31.
    Wolberg, W., Mangasarian, O.: Multisurface method of pattern separation for medical diagnosis applied to breast cytology. Proceedings of the National Academy of Sciences, USA, vol. 87, pp. 9193–9196 (1990)Google Scholar
  32. 32.
    Brameier, M., Banzhaf, W.: A comparison of linear genetic programming and neural networks in medical data mining. IEEE Trans. Evol. Comput. 5(1), 17–26 (2001)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Faculty of Computer ScienceDalhousie UniversityHalifaxCanada

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