Skip to main content
SpringerLink
Log in

Complexity Measures for Multi-objective Symbolic Regression

  • Conference paper
  • First Online:
Book cover Computer Aided Systems Theory – EUROCAST 2015 (EUROCAST 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9520))

Included in the following conference series:

Abstract

Multi-objective symbolic regression has the advantage that while the accuracy of the learned models is maximized, the complexity is automatically adapted and need not be specified a-priori. The result of the optimization is not a single solution anymore, but a whole Pareto-front describing the trade-off between accuracy and complexity.

In this contribution we study which complexity measures are most appropriately used in symbolic regression when performing multi- objective optimization with NSGA-II. Furthermore, we present a novel complexity measure that includes semantic information based on the function symbols occurring in the models and test its effects on several benchmark datasets. Results comparing multiple complexity measures are presented in terms of the achieved accuracy and model length to illustrate how the search direction of the algorithm is affected.

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and 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

References

  1. Affenzeller, M., Winkler, S., Kronberger, G., Kommenda, M., Burlacu, B., Wagner, S.: Gaining deeper insights in symbolic regression. In: Riolo, R., Moore, J.H., Kotanchek, M. (eds.) Genetic Programming Theory and Practice XI. Genetic and Evolutionary Computation, pp. 175–190. Springer, New York (2014)

    Chapter  Google Scholar 

  2. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  3. 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 

  4. Friedman, J.H.: Multivariate adaptive regression splines. Ann. Stat. 19, 1–67 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  5. Keijzer, M., Foster, J.: Crossover bias in genetic programming. In: Ebner, M., O’Neill, M., Ekárt, A., Vanneschi, L., Esparcia-Alcázar, A.I. (eds.) EuroGP 2007. LNCS, vol. 4445, pp. 33–44. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

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

    MATH  Google Scholar 

  7. Luke, S.: Issues in scaling genetic programming: breeding strategies, tree generation, and code bloat. Ph.D. thesis, Dept. of Computer Science. University of Maryland, College Park (2000)

    Google Scholar 

  8. Luke, S., Panait, L., et al.: Lexicographic parsimony pressure. In: GECCO 2002: Proceedings of the Genetic and Evolutionary Computation Conference, vol. 2, pp. 829–836 (2002)

    Google Scholar 

  9. Poli, R.: Covariant tarpeian method for bloat control in genetic programming. In: Riolo, R., McConaghy, T., Vladislavleva, E. (eds.) Genetic Programming Theory and Practice VIII 8, pp. 71–90. Springer, New York (2010)

    Google Scholar 

  10. Poli, R., Langdon, W.B., McPhee, N.F.: A field guide to genetic programming (2008). http://lulu.com

  11. Silva, S., Costa, E.: Dynamic limits for bloat control in genetic programming and a review of past and current bloat theories. Genet. Program Evolvable Mach. 10(2), 141–179 (2009)

    Article  MathSciNet  Google Scholar 

  12. Smits, G.F., Kotanchek, M.: Pareto-front exploitation in symbolic regression. In: O’Reilly, U.-M., et al. (eds.) Genetic Programming Theory and Practice II, pp. 283–299. Springer, New York (2005)

    Chapter  Google Scholar 

  13. Vanneschi, L., Castelli, M., Silva, S.: Measuring bloat, overfitting and functional complexity in genetic programming. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, pp. 877–884. ACM (2010)

    Google Scholar 

  14. Vladislavleva, E.J., Smits, G.F., Den Hertog, D.: Order of nonlinearity as a complexity measure for models generated by symbolic regression via pareto genetic programming. IEEE Trans. Evol. Comput. 13(2), 333–349 (2009)

    Article  Google Scholar 

  15. White, D.R., McDermott, J., Castelli, M., Manzoni, L., Goldman, B.W., Kronberger, G., Jaskowski, W., O’Reilly, U.M., Luke, S.: Better GP benchmarks: community survey results and proposals. Genet. Program Evolvable Mach. 14(1), 3–29 (2013)

    Article  Google Scholar 

Download references

Acknowledgments

The work described in this paper was done within the COMET Project Heuristic Optimization in Production and Logistics (HOPL), #843532 funded by the Austrian Research Promotion Agency (FFG).

Author information

Authors and Affiliations

  1. Heuristic and Evolutionary Algorithms Laboratory, School of Informatics, Communications and Media, University of Applied Sciences Upper Austria, Softwarepark 11, 4232, Hagenberg, Austria

    Michael Kommenda, Andreas Beham, Michael Affenzeller & Gabriel Kronberger

  2. Institute for Formal Models and Verification, Johannes Kepler University Linz, Altenbergerstr. 69, 4040, Linz, Austria

    Michael Kommenda, Andreas Beham & Michael Affenzeller

Authors
  1. Michael Kommenda
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Beham
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Michael Affenzeller
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gabriel Kronberger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Michael Kommenda .

Editor information

Editors and Affiliations

  1. de Gran Canaria, Universidad de las Palmas de Gran Canari, Las Palmas de Gran Canaria, Spain

    Roberto Moreno-Díaz

  2. Johannes Kepler University Linz, Linz, Austria

    Franz Pichler

  3. de Gran Canaria, Universidad de las Palmas de Gran Canari, Las Palmas de Gran Canaria, Spain

    Alexis Quesada-Arencibia

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Kommenda, M., Beham, A., Affenzeller, M., Kronberger, G. (2015). Complexity Measures for Multi-objective Symbolic Regression. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2015. EUROCAST 2015. Lecture Notes in Computer Science(), vol 9520. Springer, Cham. https://doi.org/10.1007/978-3-319-27340-2_51

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27340-2_51

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27339-6

  • Online ISBN: 978-3-319-27340-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation