Skip to main content
SpringerLink
Log in

2-additive Choquet Optimal Solutions in Multiobjective Optimization Problems

  • Conference paper
Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2014)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 442))

Abstract

In this paper, we propose a sufficient condition for a solution to be optimal for a 2-additive Choquet integral in the context of multiobjective combinatorial optimization problems. A 2-additive Choquet optimal solution is a solution that optimizes at least one set of parameters of the 2-additive Choquet integral. We also present a method to generate 2-additive Choquet optimal solutions of multiobjective combinatorial optimization problems. The method is experimented on some Pareto fronts and the results are analyzed.

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 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. Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Berlin (2005)

    MATH  Google Scholar 

  2. Choquet, G.: Theory of capacities. Annales de l’Institut Fourier (5), 131–295 (1953)

    Google Scholar 

  3. Grabisch, M., Labreuche, C.: A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Annals OR 175(1), 247–286 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  4. Grabisch, M., Marichal, J.C., Mesiar, R., Pap, E.: Aggregation functions. Encyclopedia of Mathematics and its Applications, vol. 127. Cambridge University Press, Cambridge (2009)

    Book  MATH  Google Scholar 

  5. Yager, R.: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Systems, Man and Cybern. 18, 183–190 (1998)

    Article  MathSciNet  Google Scholar 

  6. Torra, V.: The weighted OWA operator. Int. J. Intell. Syst. (12), 153–166 (1997)

    Google Scholar 

  7. Grabisch, M.: k-order additive discrete fuzzy measures and their representation. Fuzzy Sets and Systems (92), 167–189 (1997)

    Google Scholar 

  8. Fouchal, H., Gandibleux, X., Lehuédé, F.: Preferred solutions computed with a label setting algorithm based on Choquet integral for multi-objective shortest paths. In: 2011 IEEE Symposium on Computational Intelligence in Multicriteria Decision-Making (MDCM), pp. 143–150. IEEE, Paris (2011)

    Chapter  Google Scholar 

  9. Galand, L., Perny, P., Spanjaard, O.: Choquet-based optimisation in multiobjective shortest path and spanning tree problems. European Journal of Operational Research 204(2), 303–315 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  10. Galand, L., Perny, P., Spanjaard, O.: A branch and bound algorithm for Choquet optimization in multicriteria problems. Proceedings Lecture Notes in Economics and Mathematical Systems 634, 355–365 (2011)

    Article  Google Scholar 

  11. Lust, T., Rolland, A.: Choquet optimal set in biobjective combinatorial optimization. Computers & Operations Research 40(10), 2260–2269 (2013)

    Article  MathSciNet  Google Scholar 

  12. Lust, T., Rolland, A.: On the computation of Choquet optimal solutions in multicriteria decision contexts. In: Ramanna, S., Lingras, P., Sombattheera, C., Krishna, A. (eds.) MIWAI 2013. LNCS, vol. 8271, pp. 131–142. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  13. Grabisch, M.: The application of fuzzy integrals in multicriteria decision making. European Journal of Operational Research 89, 445–456 (1996)

    Article  MATH  Google Scholar 

  14. Rota, G.C.: On the foundations of combinatorial theory I. Theory of Mobius functions. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2, 340–368 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  15. Chateauneuf, A., Jaffray, J.Y.: Some characterizations of lower probabilities and other monotone capacities through the use of mobius inversion. Mathematical Social Sciences 17(3), 263–283 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  16. Lust, T., Teghem, J.: The multiobjective multidimensional knapsack problem: a survey and a new approach. International Transactions in Operational Research 19(4), 495–520 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  17. Meyer, P., Pirlot, M.: On the expressiveness of the additive value function and the Choquet integral models. In: DA2PL 2012: from Multiple Criteria Decision Aid to Preference Learning, pp. 48–56 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sorbonne Universités, UPMC Univ Paris 06, LIP6-CNRS, Paris, France

    Thibaut Lust

  2. Université de Lyon, ERIC, France

    Antoine Rolland

Authors
  1. Thibaut Lust
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antoine Rolland
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University Montpellier 2, LIRMM - CNRS UMR 5506, 161, Rue Ada, 34392, Montpellier Cedex 5, France

    Anne Laurent

  2. LIRMM, UMR CNRS/Universite Montpellier II, 161 rue Ada, 34392, Montpellier cedex 5, France

    Olivier Strauss

  3. LIP6, UPMC Univ. Paris 06, CNRS UMR 7606, F-75005, Paris, France

    Bernadette Bouchon-Meunier

  4. Dept. of Information Systems, Iona College, 710 North Ave, 10801, New Rochelle, NY, USA

    Ronald R. Yager

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Lust, T., Rolland, A. (2014). 2-additive Choquet Optimal Solutions in Multiobjective Optimization Problems. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2014. Communications in Computer and Information Science, vol 442. Springer, Cham. https://doi.org/10.1007/978-3-319-08795-5_27

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08795-5_27

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08794-8

  • Online ISBN: 978-3-319-08795-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation