Skip to main content

Functional Dependency and Degeneracy: Detailed Analysis of the GAuGE System

  • Conference paper
Book cover Artificial Evolution (EA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2936))

Abstract

This paper explores the mapping process of the GAuGE system, a recently introduced position-independent genetic algorithm, that encodes both the positions and the values of individuals at the genotypic level. A mathematical formalisation of its mapping process is presented, and is used to characterise the functional dependency feature of the system. An analysis of the effect of degeneracy in this functional dependency is then performed, and a mathematical theorem is given, showing that the introduction of degeneracy reduces the position specification bias of individuals. Experimental results are given, that backup these findings.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bagley, J.D.: The behaviour of adaptive systems which employ genetic and correlation algorithms. Doctoral Dissertation, University of Michigan (1967)

    Google Scholar 

  2. Banzhaf, W.: Genotype-Phenotype-Mapping and Neutral Variation - A case study in Genetic Programming. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 322–332. Springer, Heidelberg (1994)

    Google Scholar 

  3. Bean, J.: Genetic Algorithms and Random Keys for Sequencing and Optimization. ORSA Journal on Computing 6(2), 154–160 (1994)

    MATH  Google Scholar 

  4. Goldberg, D.E., Korb, B., Deb, K.: Messy genetic algorithms: Motivation, analysis, and first results. Complex Systems 3, 493–530 (1989)

    MATH  MathSciNet  Google Scholar 

  5. Harik, G.: Learning Gene Linkage to Efficiently Solve Problems of Bounded Difficulty Using Genetic Algorithms. Doctoral Dissertation, University of Illinois (1997)

    Google Scholar 

  6. Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)

    Google Scholar 

  7. Kalos, M.H., Withlock, P.A.: Monte Carlo Methods, vol. 1. Wiley, Chichester (1986)

    Book  MATH  Google Scholar 

  8. Kimura, M.: The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge (1983)

    Book  Google Scholar 

  9. Nicolau, M., Ryan, C.: LINKGAUGE: Tackling hard deceptive problems with a new linkage learning genetic algorithm. In: Langdon, et al. (eds.) Proceedings of the Genetic and Evolutionary Computation Conference GECCO 2002, pp. 488–494. Morgan Kaufmann Publishers, San Francisco (2002)

    Google Scholar 

  10. Nicolau, M., Ryan, C.: How Functional Dependency Adapts to Salience Hierarchy in the GAuGE System. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 153–163. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  11. Oliver, I.M., Smith, D.J., Holland, J.R.C.: A Study of Permutation Crossover Operators on the Traveling Salesman Problem. In: Proceedings of the Second International Conference on Genetic Algorithms, pp. 224-230 (1987)

    Google Scholar 

  12. O’Neill, M., Ryan, C., Keijzer, M., Cattolico, M.: Crossover in Grammatical Evolution. Genetic Programming and Evolvable Machines 4(1), 67–93 (2003)

    Article  MATH  Google Scholar 

  13. O’Neill, M., Ryan, C.: Grammatical Evolution - Evolving programs in an arbitrary language. Kluwer Academic Publishers, Dordrecht (2003)

    Google Scholar 

  14. O’Neill, M., Ryan, C.: Grammatical Evolution. IEEE Transactions on Evolutionary Computation 5(4), 349–358 (2001)

    Article  Google Scholar 

  15. 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 

  16. Ryan, C., Nicolau, M., O’Neill, M.: Genetic Algorithms using Grammatical Evolution. In: Foster, J.A., Lutton, E., Miller, J., Ryan, C., Tettamanzi, A.G.B. (eds.) EuroGP 2002. LNCS, vol. 2278, pp. 278–287. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nicolau, M., Auger, A., Ryan, C. (2004). Functional Dependency and Degeneracy: Detailed Analysis of the GAuGE System. In: Liardet, P., Collet, P., Fonlupt, C., Lutton, E., Schoenauer, M. (eds) Artificial Evolution. EA 2003. Lecture Notes in Computer Science, vol 2936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24621-3_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-24621-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-21523-3

  • Online ISBN: 978-3-540-24621-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics