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Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs

Author

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  • Goberna, M.A.
  • Jeyakumar, V.
  • Li, G.
  • Vicente-Pérez, J.

Abstract

This paper deals with uncertain multi-objective convex programming problems, where the data of the objective function or the constraints or both are allowed to be uncertain within specified uncertainty sets. We present sufficient conditions for the existence of highly robust weakly efficient solutions, that is, robust feasible solutions which are weakly efficient for any possible instance of the objective function within a specified uncertainty set. This is done by way of estimating the radius of highly robust weak efficiency under linearly distributed uncertainty of the objective functions. In the particular case of robust quadratic multi-objective programs, we show that these sufficient conditions can be expressed in terms of the original data of the problem, extending and improving the corresponding results in the literature for robust multi-objective linear programs under ball uncertainty.

Suggested Citation

  • Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2018. "Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs," European Journal of Operational Research, Elsevier, vol. 270(1), pages 40-50.
    • Handle: RePEc:eee:ejores:v:270:y:2018:i:1:p:40-50
    DOI: 10.1016/j.ejor.2018.03.018
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    References listed on IDEAS

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    1. Georgiev, Pando Gr. & Luc, Dinh The & Pardalos, Panos M., 2013. "Robust aspects of solutions in deterministic multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 229(1), pages 29-36.
    2. Gabriel R. Bitran, 1980. "Linear Multiple Objective Problems with Interval Coefficients," Management Science, INFORMS, vol. 26(7), pages 694-706, July.
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    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. Goberna, M.A. & Guerra-Vazquez, F. & Todorov, M.I., 2016. "Constraint qualifications in convex vector semi-infinite optimization," European Journal of Operational Research, Elsevier, vol. 249(1), pages 32-40.
    7. 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.
    8. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
    9. 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.
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    Cited by:

    1. 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.
    2. Engau, Alexander & Sigler, Devon, 2020. "Pareto solutions in multicriteria optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 357-368.
    3. Yue Zhou-Kangas & Kaisa Miettinen, 2019. "Decision making in multiobjective optimization problems under uncertainty: balancing between robustness and quality," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(2), pages 391-413, June.
    4. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.
    5. Yunqiang Xue & Lin Cheng & Haoran Jiang & Jun Guo & Hongzhi Guan, 2023. "The Optimization of Bus Departure Time Based on Uncertainty Theory—Taking No. 207 Bus Line of Nanchang City, China, as an Example," Sustainability, MDPI, vol. 15(8), pages 1-18, April.
    6. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2022. "The radius of robust feasibility of uncertain mathematical programs: A Survey and recent developments," European Journal of Operational Research, Elsevier, vol. 296(3), pages 749-763.

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