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Minmax regret approach and optimality evaluation in combinatorial optimization problems with interval and fuzzy weights

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  • Kasperski, Adam
  • Zielinski, Pawel

Abstract

This paper deals with a general combinatorial optimization problem in which closed intervals and fuzzy intervals model uncertain element weights. The notion of a deviation interval is introduced, which allows us to characterize the optimality and the robustness of solutions and elements. The problem of computing deviation intervals is addressed and some new complexity results in this field are provided. Possibility theory is then applied to generalize a deviation interval and a solution concept to fuzzy ones.

Suggested Citation

  • Kasperski, Adam & Zielinski, Pawel, 2010. "Minmax regret approach and optimality evaluation in combinatorial optimization problems with interval and fuzzy weights," European Journal of Operational Research, Elsevier, vol. 200(3), pages 680-687, February.
    • Handle: RePEc:eee:ejores:v:200:y:2010:i:3:p:680-687
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    References listed on IDEAS

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    1. Chanas, Stefan & Zielinski, Pawel, 2002. "The computational complexity of the criticality problems in a network with interval activity times," European Journal of Operational Research, Elsevier, vol. 136(3), pages 541-550, February.
    2. Kasperski, Adam & Zielinski, Pawel, 2007. "On combinatorial optimization problems on matroids with uncertain weights," European Journal of Operational Research, Elsevier, vol. 177(2), pages 851-864, March.
    3. Averbakh, Igor & Lebedev, Vasilij, 2005. "On the complexity of minmax regret linear programming," European Journal of Operational Research, Elsevier, vol. 160(1), pages 227-231, January.
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    5. Dubois, Didier & Fargier, Helene & Fortemps, Philippe, 2003. "Fuzzy scheduling: Modelling flexible constraints vs. coping with incomplete knowledge," European Journal of Operational Research, Elsevier, vol. 147(2), pages 231-252, June.
    6. Dubois, Didier & Fargier, Helene & Galvagnon, Vincent, 2003. "On latest starting times and floats in activity networks with ill-known durations," European Journal of Operational Research, Elsevier, vol. 147(2), pages 266-280, June.
    7. Inuiguchi, Masahiro & Sakawa, Masatoshi, 1995. "Minimax regret solution to linear programming problems with an interval objective function," European Journal of Operational Research, Elsevier, vol. 86(3), pages 526-536, November.
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    Cited by:

    1. Nikulin, Y. & Karelkina, O. & Mäkelä, M.M., 2013. "On accuracy, robustness and tolerances in vector Boolean optimization," European Journal of Operational Research, Elsevier, vol. 224(3), pages 449-457.
    2. Marcin Siepak & Jerzy Józefczyk, 2014. "Solution algorithms for unrelated machines minmax regret scheduling problem with interval processing times and the total flow time criterion," Annals of Operations Research, Springer, vol. 222(1), pages 517-533, November.
    3. Chassein, André & Goerigk, Marc, 2018. "Compromise solutions for robust combinatorial optimization with variable-sized uncertainty," European Journal of Operational Research, Elsevier, vol. 269(2), pages 544-555.
    4. Schäfer, Luca E. & Dietz, Tobias & Barbati, Maria & Figueira, José Rui & Greco, Salvatore & Ruzika, Stefan, 2021. "The binary knapsack problem with qualitative levels," European Journal of Operational Research, Elsevier, vol. 289(2), pages 508-514.

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