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On highly robust efficient solutions to uncertain multiobjective linear programs

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  • Dranichak, Garrett M.
  • Wiecek, Margaret M.

Abstract

Decision making in the presence of uncertainty and multiple conflicting objectives is a real-life issue in many areas of human activity. To address this type of problem, we study highly robust (weakly) efficient solutions to uncertain multiobjective linear programs (UMOLPs) with objective-wise uncertainty in the objective function coefficients. We develop properties of the highly robust efficient set, characterize highly robust (weakly) efficient solutions using the cone of improving directions associated with the UMOLP, derive several upper and lower bound sets on the highly robust (weakly) efficient set, and present a robust counterpart for a class of UMOLPs. As various results rely on the acuteness of the cone of improving directions, we also propose methods to verify this property.

Suggested Citation

  • Dranichak, Garrett M. & Wiecek, Margaret M., 2019. "On highly robust efficient solutions to uncertain multiobjective linear programs," European Journal of Operational Research, Elsevier, vol. 273(1), pages 20-30.
    • Handle: RePEc:eee:ejores:v:273:y:2019:i:1:p:20-30
    DOI: 10.1016/j.ejor.2018.07.035
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    References listed on IDEAS

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    1. Gabriel R. Bitran, 1980. "Linear Multiple Objective Problems with Interval Coefficients," Management Science, INFORMS, vol. 26(7), pages 694-706, July.
    2. S. Rivaz & M. A. Yaghoobi & M. Hladík, 2016. "Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 237-253, September.
    3. Alexander Engau & Margaret M. Wiecek, 2008. "Interactive Coordination of Objective Decompositions in Multiobjective Programming," Management Science, INFORMS, vol. 54(7), pages 1350-1363, July.
    4. Oliveira, Carla & Antunes, Carlos Henggeler, 2007. "Multiple objective linear programming models with interval coefficients - an illustrated overview," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1434-1463, September.
    5. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2015. "Robust solutions to multi-objective linear programs with uncertain data," European Journal of Operational Research, Elsevier, vol. 242(3), pages 730-743.
    6. Ehrgott, Matthias & Ide, Jonas & Schöbel, Anita, 2014. "Minmax robustness for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 17-31.
    7. Harold P. Benson, 1985. "Multiple Objective Linear Programming with Parametric Criteria Coefficients," Management Science, INFORMS, vol. 31(4), pages 461-474, April.
    8. Kuhn, K. & Raith, A. & Schmidt, M. & Schöbel, A., 2016. "Bi-objective robust optimisation," European Journal of Operational Research, Elsevier, vol. 252(2), pages 418-431.
    9. Nguyen Thoai, 2012. "Criteria and dimension reduction of linear multiple criteria optimization problems," Journal of Global Optimization, Springer, vol. 52(3), pages 499-508, March.
    10. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    11. Hunt, Brian J. & Wiecek, Margaret M. & Hughes, Colleen S., 2010. "Relative importance of criteria in multiobjective programming: A cone-based approach," European Journal of Operational Research, Elsevier, vol. 207(2), pages 936-945, December.
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    Cited by:

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    2. Schöbel, Anita & Zhou-Kangas, Yue, 2021. "The price of multiobjective robustness: Analyzing solution sets to uncertain multiobjective problems," European Journal of Operational Research, Elsevier, vol. 291(2), pages 782-793.
    3. Groetzner, Patrick & Werner, Ralf, 2022. "Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 101-115.
    4. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    5. Yao, Zhaosheng & Wang, Zhiyuan & Ran, Lun, 2023. "Smart charging and discharging of electric vehicles based on multi-objective robust optimization in smart cities," Applied Energy, Elsevier, vol. 343(C).

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