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An Ecological Approach to Measuring Locality in Linear Genotype to Phenotype Maps

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7244))

Abstract

Recent research has considered the role of locality in GP representations. We use a modified statistical technique drawn from numerical ecology, the Mantel test, to measure the locality of integer-encoded GP. Weak locality is identified in a case study on Cartesian Genetic Programming (CGP), a directed acyclic graph representation. A method of varying syntactic program locality continuously through the application of a biased mutation operator is demonstrated. The impact of varying locality under the new measure is assessed over a randomly generated set of polynomial symbolic regression problems. We observe that enforcing higher levels of locality in CGP is associated with poorer performance on the problem set and discuss implications in the context of existing models of GP genotype-phenotype maps.

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References

  1. Rothlauf, F.: Representations for Genetic and Evolutionary Algorithms, pp. 33–96. Springer, Heidelberg (2006)

    Book  Google Scholar 

  2. Gottlieb, J.: Empirical Analysis of Locality, Heritability and Heuristic Bias in Evolutionary Algorithms: A Case Study for the Multidimensional Knapsack Problem. Evolutionary Computation 43, 441–475 (2004)

    Google Scholar 

  3. Gen, M., Cheng, R.: Genetic Algorithms and Engineering Optimisation. John Wiley and Sons, Inc. (2000)

    Google Scholar 

  4. Rothlauf, F., Goldberg, D.E.: Pruefer Numbers and Genetic Algorithms: A Lesson on How the Low Locality of an Encoding Can Harm the Performance of GAs. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 395–404. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  5. Droste, S., Wiesmann, D.: On Representation and Genetic Operators in Evolutionary Algorithms. Technical report (SFB) 531: [249], Univ. of Dortmund (1998)

    Google Scholar 

  6. Galván-López, E., McDermott, J., Brabazon, A.: Defining locality as a problem difficulty measure in genetic programming. Genetic Programming and Evolvable Machines, 1–37 (2011)

    Google Scholar 

  7. Oltean, M., Grosnan, C., Diosan, L., Mihaila, C.: Genetic Programming with Linear Representation: A Survey. Int. J. on Artificial Intelligence Tools, 197–238 (2008)

    Google Scholar 

  8. Miller, J.F. (ed.): Cartesian Genetic Programming. Springer, Heidelberg (2011)

    MATH  Google Scholar 

  9. Rothlauf, F., Oetzel, M.: On the Locality of Grammatical Evolution. In: Collet, P., Tomassini, M., Ebner, M., Gustafson, S., Ekárt, A. (eds.) EuroGP 2006. LNCS, vol. 3905, pp. 320–330. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Fagan, D., O’Neill, M., Galván-López, E., Brabazon, A., McGarraghy, S.: An Analysis of Genotype-Phenotype Maps in Grammatical Evolution. In: Esparcia-Alcázar, A.I., Ekárt, A., Silva, S., Dignum, S., Uyar, A.Ş. (eds.) EuroGP 2010. LNCS, vol. 6021, pp. 62–73. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  11. Brameier, M.F., Banzhaf, W.: Linear Genetic Programming. Genetic and Evolutionary Computation. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  12. Mantel, N.: The detection of disease clustering and a generalized regression approach. Cancer Research 27, 209–220 (1967)

    Google Scholar 

  13. Dietz, E.J.: Permutation tests for association between two distance matrices. Systematic Zoology 32, 21–26 (1983)

    Article  Google Scholar 

  14. Oden, N.L., Sokal, R.R.: Directional autocorrelation: an extension of spatial correlograms to two dimensions. Systematic Biology 35, 608 (1986)

    Google Scholar 

  15. Legendre, P., Fortin, M.-J.: Spatial pattern and ecological analysis. Vegetatio 80, 107–138 (1989)

    Article  Google Scholar 

  16. Legendre, P., Lapointe, F.J., Cagrain, P.: Modeling brain evolution from behavior: a permutational regression approach. Evolution 48, 1487–1499 (1994)

    Article  Google Scholar 

  17. Lichstein, J.W.: Multiple regression on distance matrices: a multivariate spatial analysis tool. Plant Ecology 188, 117–131 (2006)

    Article  Google Scholar 

  18. Legendre, P., Fortin, M.-J.: Comparison of the Mantel test and alternative approaches for detecting complex multivariate relationships in the spatial analysis of genetic data. Molecular Ecology Resources, 831–844 (2010)

    Google Scholar 

  19. Chiam, S.C., Tan, K.C., Goh, C.K., Al Mamun, A.: Improving locality in binary representation via redundancy.. IEEE Trans. on Sys. Man. and Cybernetics (B) 38, 808–825 (2008)

    Article  Google Scholar 

  20. McDermott, J., Galván-Lopéz, E., O’Neill, M.: A Fine-Grained View of GP Locality with Binary Decision Diagrams as Ant Phenotypes. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 164–173. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  21. Krawiec, K.: Semantically Embedded Genetic Programming. In: Genetic and Evolutionary Computation Conference, Dublin, Ireland, pp. 1379–1386 (2011)

    Google Scholar 

  22. Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: Proc. of the 6th Int. Conference on Genetic Algorithms, vol. 129, pp. 184–192. Citeseer (1995)

    Google Scholar 

  23. Legendre, P., Legendre, L.: Numerical Ecology, 2nd edn. Developments in Environmental Modelling. Elsevier (1998)

    Google Scholar 

  24. Goslee, S.C., Urban, D.L.: The ecodist Package for Dissimilarity-based Analysis of Ecological Data. Journal Of Statistical Software 22 (2007)

    Google Scholar 

  25. Hien, N.T., Hoai, N.X.: A Brief Overview of Population Diversity Measures in Genetic Programming. In: 3rd Asian-Pacific Workshop on Genetic Programming, pp. 128–139 (2006)

    Google Scholar 

  26. Payne, A.J., Stepney, S.: Representation and Structural biases in CGP. In: IEEE Congress on Evolutionary Computation, vol. 8, pp. 1064–1071. IEEE (2009)

    Google Scholar 

  27. Vanneschi, L.: Theory and Practice for Efficient Genetic Programming. PhD thesis, Univ. of Lausanne (2004)

    Google Scholar 

  28. Keijzer, M.: Efficiently Representing Populations in Genetic Programming. In: Advances in Genetic Programming, vol. 2, pp. 259–278. MIT Press (1996)

    Google Scholar 

  29. Vanneschi, L.: Crossover-Based Tree Distance in Genetic Programming. IEEE Transactions on Evolutionary Computation 12, 506–524 (2008)

    Article  Google Scholar 

  30. Biernacki, P., Waldorf, D.: Snowball Sampling: Problems, Techniques and Chain-Referral Sampling. Socio. Methods And Research 10, 141–163 (1981)

    Google Scholar 

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Seaton, T., Miller, J.F., Clarke, T. (2012). An Ecological Approach to Measuring Locality in Linear Genotype to Phenotype Maps. In: Moraglio, A., Silva, S., Krawiec, K., Machado, P., Cotta, C. (eds) Genetic Programming. EuroGP 2012. Lecture Notes in Computer Science, vol 7244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29139-5_15

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  • DOI: https://doi.org/10.1007/978-3-642-29139-5_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29138-8

  • Online ISBN: 978-3-642-29139-5

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