Skip to main content
SpringerLink
Log in

On the Non-uniform Redundancy in Grammatical Evolution

  • Conference paper
  • First Online:
Parallel Problem Solving from Nature – PPSN XIV (PPSN 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9921))

Included in the following conference series:

Abstract

This paper investigates the redundancy of representation in grammatical evolution (GE) for binary trees. We analyze the entire GE solution space by creating all binary genotypes of predefined length and map them to phenotype trees, which are then characterized by their size, depth and shape. We find that the GE representation is strongly non-uniformly redundant. There are huge differences in the number of genotypes that encode one particular phenotype. Thus, it is difficult for GE to solve problems where the optimal tree solutions are underrepresented. In general, the GE mapping process is biased towards short tree structures, which implies high GE performance if the optimal solution requires small programs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Caruana, R.A., Schaffer, J.D.: Representation and hidden bias: Gray vs. Binary coding for genetic algorithms. In: Proceedings of the Fifth International Conference on Machine Learning, pp. 153–161. Morgan Kaufmann (1988)

    Google Scholar 

  2. Daida, J.M.: Limits to expression in genetic programming: lattice-aggregate modeling. In: CEC 2002, pp. 273–278. IEEE Press, NJ, USA (2002)

    Google Scholar 

  3. Daida, J.M., Hilss, A.M.: Identifying structural mechanisms in standard genetic programming. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 1639–1651. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  4. Daida, J.M., Li, H., Tang, R., Hilss, A.M.: What makes a problem GP-Hard? validating a hypothesis of structural causes. In: Cantú-Paz, E., et al. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 1665–1677. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  5. Dignum, S., Poli, R.: Operator equalisation and bloat free GP. In: O’Neill, M., Vanneschi, L., Gustafson, S., Esparcia Alcázar, A.I., De Falco, I., Della Cioppa, A., Tarantino, E. (eds.) EuroGP 2008. LNCS, vol. 4971, pp. 110–121. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. 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 

  7. Harper, R.: GE, explosive grammars and the lasting legacy of bad initialisation. In: CEC 2010, pp. 1–8. IEEE Press (2010)

    Google Scholar 

  8. Hemberg, E., McPhee, N., O’Neill, M., Brabazon, A.: Pre-, In- and postfix grammars for symbolic regression in grammatical evolution. In: IEEE Workshop and Summer School on Evolutionary Computing, pp. 18–22 (2008)

    Google Scholar 

  9. Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)

    MATH  Google Scholar 

  10. Langdon, W., Poli, R.: Foundations of Genetic Programming. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  11. Montes de Oca, M.A.: Exposing a bias toward short-length numbers in grammatical evolution. In: O’Neill, M., Vanneschi, L., Gustafson, S., Esparcia Alcázar, A.I., De Falco, I., Della Cioppa, A., Tarantino, E. (eds.) EuroGP 2008. LNCS, vol. 4971, pp. 278–288. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  12. O’Neill, M., Ryan, C.: Genetic code degeneracy: implications for grammatical evolution and beyond. In: Floreano, D., Nicoud, J.D., Mondada, F. (eds.) Advances in Artificial Life. LNCS, vol. 1674, pp. 149–153. Springer, Berlin (1999)

    Chapter  Google Scholar 

  13. O’Neill, M., Brabazon, A., Nicolau, M., Garraghy, S.M., Keenan, P.: \(\pi \) grammatical evolution. In: Deb, K., Tari, Z. (eds.) GECCO 2004. LNCS, vol. 3103, pp. 617–629. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  14. O’Neill, M., Ryan, C.: Grammatical Evolution: Evolutionary Automatic Programming in an Arbitrary Language. Kluwer Academic Publishers, Norwell (2003)

    Book  MATH  Google Scholar 

  15. O’Neill, M., Ryan, C., Keijzer, M., Cattolico, M.: Crossover in grammatical evolution. Genet. Program. Evolvable Mach. 4(1), 67–93 (2003)

    Article  MATH  Google Scholar 

  16. Rothlauf, F.: Representations for Genetic and Evolutionary Algorithms, 2nd edn. Springer, Berlin (2006)

    MATH  Google Scholar 

  17. Rothlauf, F.: Design of Modern Heuristics. Springer, Heidelberg (2011)

    Book  MATH  Google Scholar 

  18. Rothlauf, F., Goldberg, D.E.: Redundant representations in evolutionary computation. Evol. Comput. 11(4), 381–415 (2003)

    Article  Google Scholar 

  19. Ryan, C., Collins, J.J., O’Neill, M.: Grammatical evolution: evolving programs for an arbitrary language. In: Banzhaf, W., Poli, R., Schoenauer, M., Fogarty, T.C. (eds.) EuroGP 1998. LNCS, vol. 1391, pp. 83–95. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  20. Thorhauer, A., Rothlauf, F.: Structural difficulty in grammatical evolution versus genetic programming. In: GECCO 2013, pp. 997–1004. ACM (2013)

    Google Scholar 

  21. Whigham, P.A.: Grammatically-based genetic programming. In: Proceedings of the Workshop on Genetic Programming: From Theory to Real-World Applications, pp. 33–41. Morgan Kaufmann, San Mateo (1995)

    Google Scholar 

  22. Whigham, P.A.: Search bias, language bias and genetic programming. In: Proceedings of the First Annual Conference on Genetic Programming 1996, pp. 230–237. MIT Press, CA, USA (1996)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Mainz, Mainz, Germany

    Ann Thorhauer

Authors
  1. Ann Thorhauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ann Thorhauer .

Editor information

Editors and Affiliations

  1. University of Manchester, Manchester, United Kingdom

    Julia Handl

  2. Edinburgh Napier University, Edinburgh, United Kingdom

    Emma Hart

  3. Aston University, Birmingham, United Kingdom

    Peter R. Lewis

  4. University of Manchester, Manchester, United Kingdom

    Manuel López-Ibáñez

  5. University of Stirling, Stirling, United Kingdom

    Gabriela Ochoa

  6. Edinburgh Napier University, Edinburgh, United Kingdom

    Ben Paechter

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing AG

About this paper

Cite this paper

Thorhauer, A. (2016). On the Non-uniform Redundancy in Grammatical Evolution. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45823-6_27

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45822-9

  • Online ISBN: 978-3-319-45823-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation