Matrix Analysis of Genetic Programming Mutation

  • Andrew J. Parkes
  • Ender Özcan
  • Matthew R. Hyde
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7244)

Abstract

Heuristic policies for combinatorial optimisation problems can be found by using Genetic programming (GP) to evolve a mathematical function over variables given by the current state of the problem, and whose value is used to determine action choices (such as preferred assignments or branches). If all variables have finite discrete domains, then the expressions can be converted to an equivalent lookup table or ‘decision matrix’. Spaces of such matrices often have natural distance metrics (after conversion to a standard form). As a case study, and to support the understanding of GP as a meta-heuristic, we extend previous bin-packing work and compare the distances between matrices from before and after a GP-driven mutation. We find that GP mutations often correspond to large moves within the space of decision matrices. This strengthens evidence that the role of mutations within GP might be somewhat different than their role within Genetic Algorithms.

Keywords

Genetic programming Genotype-phenotype mapping 

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References

  1. 1.
    Allen, S., Burke, E.K., Hyde, M.R., Kendall, G.: Evolving reusable 3D packing heuristics with genetic programming. In: Proceedings of the ACM Genetic and Evolutionary Computation Conference (GECCO 2009), Montreal, Canada, pp. 931–938 (July 2009)Google Scholar
  2. 2.
    Burke, E.K., Gustafson, S., Kendall, G.: Diversity in genetic programming: an analysis of measures and correlation with fitness. IEEE Transactions on Evolutionary Computation 8(1), 47–62 (2004)CrossRefGoogle Scholar
  3. 3.
    Burke, E.K., Hyde, M.R., Kendall, G.: Providing a memory mechanism to enhance the evolutionary design of heuristics. In: Proceedings of the IEEE World Congress on Computational Intelligence (WCCI 2010), Spain, pp. 3883–3890 (July 2010)Google Scholar
  4. 4.
    Burke, E.K., Hyde, M., Kendall, G., Ochoa, G., Özcan, E., Woodward, J.: Exploring Hyper-heuristic Methodologies with Genetic Programming. In: Mumford, C.L., Jain, L.C. (eds.) Computational Intelligence. ISRL, vol. 1, pp. 177–201. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  5. 5.
    Burke, E.K., Hyde, M.R., Kendall, G.: Evolving Bin Packing Heuristics with Genetic Programming. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 860–869. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Burke, E.K., Hyde, M.R., Kendall, G., Woodward, J.: Automatic heuristic generation with genetic programming: Evolving a jack-of-all-trades or a master of one. In: Proceedings of the 9th ACM Genetic and Evolutionary Computation Conference (GECCO 2007), London, UK, pp. 1559–1565 (July 2007)Google Scholar
  7. 7.
    Burke, E.K., Hyde, M.R., Kendall, G., Woodward, J.: The scalability of evolved on line bin packing heuristics. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2007), Singapore, pp. 2530–2537 (September 2007)Google Scholar
  8. 8.
    Burke, E.K., Hyde, M.R., Kendall, G., Woodward, J.: A genetic programming hyper-heuristic approach for evolving two dimensional strip packing heuristics. IEEE Transactions on Evolutionary Computation 14(6), 942–958 (2010)CrossRefGoogle Scholar
  9. 9.
    Ekárt, A., Németh, S.Z.: A Metric for Genetic Programs and Fitness Sharing. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., Fogarty, T.C. (eds.) EuroGP 2000. LNCS, vol. 1802, pp. 259–270. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. 10.
    Fukunaga, A.S.: Automated discovery of local search heuristics for satisfiability testing. Evolutionary Computation 16(1), 31–61 (2008)Google Scholar
  11. 11.
    Geiger, C.D., Uzsoy, R., Aytug, H.: Rapid modeling and discovery of priority dispatching rules: An autonomous learning approach. Journal of Scheduling 9(1), 7–34 (2006)MATHCrossRefGoogle Scholar
  12. 12.
    Gittins, J.C.: Bandit processes and dynamic allocation indices. Journal of the Royal Statistical Society. Series B (Methodological) 41(2), 148–177 (1979)MathSciNetMATHGoogle Scholar
  13. 13.
    Gustafson, S., Vanneschi, L.: Crossover-based tree distance in genetic programming. IEEE Transactions on Evolutionary Computation 12(4), 506–524 (2008)CrossRefGoogle Scholar
  14. 14.
    Martello, S., Toth, P.: Lower bounds and reduction procedures for the bin packing problem. Discrete Applied Mathematics 28(1), 59–70 (1990)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    McPhee, N.F., Miller, J.D.: Accurate replication in genetic programming. In: Eshelman, L. (ed.) Genetic Algorithms: Proceedings of the Sixth International Conference (ICGA 1995), July 15-19, pp. 303–309. Morgan Kaufmann, Pittsburgh (1995)Google Scholar
  16. 16.
    Özcan, E., Parkes, A.J.: Policy matrix evolution for generation of heuristics. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, GECCO 2011, pp. 2011–2018. ACM, New York (2011)CrossRefGoogle Scholar
  17. 17.
    Poli, R., Langdon, W.B., McPhee, N.F.: A field guide to genetic programming. lulu.com, freely available at (2008), http://www.gp-field-guide.org.uk
  18. 18.
    Soule, T., Foster, J.A.: Removal bias: a new cause of code growth in tree based evolutionary programming. In: 1998 IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, USA, May 5-9, pp. 781–786 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrew J. Parkes
    • 1
  • Ender Özcan
    • 1
  • Matthew R. Hyde
    • 1
  1. 1.School of Computer ScienceThe University of NottinghamNottinghamUnited Kingdom (UK)

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