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Approximating Combinatorial Optimization Problems with Uncertain Costs and the OWA Criterion

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Operations Research Proceedings 2012

Part of the book series: Operations Research Proceedings ((ORP))

Abstract

In this paper a class combinatorial optimization problems with uncertain costs is discussed. This uncertainty is modeled by specifying a scenario set containing K distinct cost vectors. In order to choose a solution the Ordered Weighted Averaging aggregation operator (OWA) is used. For most classical problems, for example network problems, minimizing OWA is NP-hard even for two scenarios. In this paper some positive and negative approximation results for the problem are shown.

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References

  1. Aissi, H., Bazgan, C., Vanderpooten, D.: General approximation schemes for minmax (regret) versions of some (pseudo-)polynomial problems. Discrete Optim. 7, 136–148 (2010)

    Article  Google Scholar 

  2. Averbakh, I.: On the complexity of a class of combinatorial optimization problems with uncertainty. Math Program. 90, 263–272 (2001)

    Article  Google Scholar 

  3. Kasperski, A., Zieliński, P.: On the approximability of minmax (regret) network optimization problems. Inf. Process. Lett. 109, 262–266 (2009)

    Article  Google Scholar 

  4. Kasperski, A., Zieliński, P.: A randomized algorithm for the min-max selecting items problem with uncertain weights. Ann. Oper. Res. 172, 221–230 (2009)

    Article  Google Scholar 

  5. Kohli, R., Krishnamurti, R., Mirchandani, P.: The minimum satisfiability problem. SIAM J. Discrete Math. 7, 275–283 (1994)

    Article  Google Scholar 

  6. Kouvelis, P., Yu, G.: Robust Discrete Optimization and its applications. Kluwer Academic Publishers, Dordrecht (1997)

    Google Scholar 

  7. Mittal, S., Schulz, A.S.: A general framework for designing approximation schemes for combinatorial optimization problems with many objectives combined into one. In: APPROX-RANDOM 2008, Lecture Notes in Computer Science, vol. 5171, pp. 179–192. Springer-Verlag (2008)

    Google Scholar 

  8. Papadimitriou, C.H., Yannakakis, M.: On the Approximability of Trade-offs and Optimal Access of Web Sources. In: FOCS 2000, pp. 86–92 (2000)

    Google Scholar 

  9. Yager, R.R.: On Ordered Weighted Averaging Aggregation Operators in Multi-Criteria Decision Making. IEEE Trans. Syst. Man Cybern. 18, 183–190 (1988)

    Article  Google Scholar 

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Acknowledgments

The work was partially supported by Polish Committee for Scientific Research, grant N N206 492938.

Author information

Authors and Affiliations

  1. Institute of Industrial Engineering and Management, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 , Wrocław, Poland

    Adam Kasperski

  2. Faculty of Fundamental Problems of Technology, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 , Wrocław, Poland

    Paweł Zieliński

Authors
  1. Adam Kasperski
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  2. Paweł Zieliński
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Corresponding author

Correspondence to Adam Kasperski .

Editor information

Editors and Affiliations

  1. Institute of Production Management, Leibniz Universität Hannover, Hannover, Germany

    Stefan Helber

  2. Institute for Information Systems Resear, Leibniz Universität Hannover, Hannover, Germany

    Michael Breitner

  3. Institute for Banking and Finance, Leibniz Universität Hannover, Hannover, Germany

    Daniel Rösch

  4. Institute of Production Management, Leibniz Universität Hannover, Hannover, Germany

    Cornelia Schön

  5. Institute for Risk and Insurance, Leibniz Universität Hannover, Hannover, Germany

    Johann-Matthias Graf von der Schulenburg

  6. Institute of Statistics, Leibniz Universität Hannover, Hannover, Germany

    Philipp Sibbertsen

  7. Institute of Applied Mathematics, Leibniz Universität Hannover, Hannover, Germany

    Marc Steinbach

  8. Institute of Probability and Statistics, Leibniz Universität Hannover, Hannover, Germany

    Stefan Weber

  9. Institute of Production Management, Leibniz Universität Hannover, Hannover, Germany

    Anja Wolter

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Kasperski, A., Zieliński, P. (2014). Approximating Combinatorial Optimization Problems with Uncertain Costs and the OWA Criterion. In: Helber, S., et al. Operations Research Proceedings 2012. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-00795-3_21

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