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Robust Discrete Optimization Problems with the WOWA Criterion

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Book cover Operations Research Proceedings 2014

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

Abstract

In this paper a class of combinatorial optimization problems with uncertain costs is discussed. The uncertainty is modeled by specifying a discrete scenario set containing all possible vectors of the costs which may occur. In order to choose a solution the Weighted Ordered Weighted Averaging aggregation operator (WOWA) is used. The WOWA operator allows decision makers to take both their attitude towards the risk and subjective probabilities for scenarios into account. The complexity of the problem is described and an approximation algorithm with some guaranteed worst case ratio is constructed.

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References

  1. Aissi, H., Bazgan, C., Vanderpooten, D.: General approximation schemes for minmax (regret) versions of some (pseudo-)polynomial problems. Discret. 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. Grabish, M.: Owa operators and nonadditive integrals. In: Kacprzyk, J., Yager, R.R., Beliakov, G. (eds.) Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice. Studies in Fuzziness and Soft Computing, vol. 265, pp. 3–15. Springer, Berlin (2011)

    Chapter  Google Scholar 

  4. Kasperski, A., Kurpisz, A., Zieliński, P.: Approximating the min-max (regret) selecting items problem. Inf. Process. Lett. 113, 23–29 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

  6. Kasperski, A., Zieliński, P.: Combinatorial optimization problems with uncertain costs and the OWA criterion. Theor. Comput. Sci. 565, 102–112 (2015)

    Article  Google Scholar 

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

    Book  Google Scholar 

  8. Luce, R.D., Raiffa, H.: Games and Decisions: Introduction and Critical Survey. Dover Publications Inc., New York (1957)

    Google Scholar 

  9. Ogryczak, W., Śliwiński, T.: On efficient WOWA optimization for decision support under risk. Int. J. Approx. Reason. 50, 915–928 (2009)

    Article  Google Scholar 

  10. Parmigiani, G., Inoue, L.Y.: Decision theory. Principles and Approaches, Wiley (2009)

    Google Scholar 

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

    Article  Google Scholar 

  12. 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 second author is partially supported by the National Center for Science (Narodowe Centrum Nauki), grant 2013/09/B/ST6/01525.

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Authors and Affiliations

  1. Department of Operations Research, Wrocław University of Technology, Wrocław, Poland

    Adam Kasperski

  2. Department of Computer Science (W11/K2), Wrocław University of Technology, Wrocław, Poland

    Paweł Zieliński

Authors
  1. Adam Kasperski
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  2. Paweł Zieliński
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Corresponding authors

Correspondence to Adam Kasperski or Paweł Zieliński .

Editor information

Editors and Affiliations

  1. Operations Research, RWTH Aachen University, Aachen, Germany

    Marco Lübbecke

  2. Lehrstuhl II für Mathematik, RWTH Aachen University, Aachen, Germany

    Arie Koster

  3. RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Peter Letmathe

  4. E.ON Energy Research Center, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Reinhard Madlener

  5. Management Science, RWTH Aachen University, Aachen, Nordrhein-Westfalen, Germany

    Britta Peis

  6. Chair of Operations Management, RWTH Aachen University, Aachen, Germany

    Grit Walther

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Kasperski, A., Zieliński, P. (2016). Robust Discrete Optimization Problems with the WOWA Criterion. In: Lübbecke, M., Koster, A., Letmathe, P., Madlener, R., Peis, B., Walther, G. (eds) Operations Research Proceedings 2014. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-28697-6_38

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