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Robust aspects of solutions in deterministic multiple objective linear programming

Author

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  • Georgiev, Pando Gr.
  • Luc, Dinh The
  • Pardalos, Panos M.

Abstract

We study questions of robustness of linear multiple objective problems in the sense of post-optimal analysis, that is, we study conditions under which a given efficient solution remains efficient when the criteria/objective matrix undergoes some alterations. We consider addition or removal of certain criteria, convex combination with another criteria matrix, or small perturbations of its entries. We provide a necessary and sufficient condition for robustness in a verifiable form and give two formulae to compute the radius of robustness.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:1:p:29-36
    DOI: 10.1016/j.ejor.2013.02.037
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    References listed on IDEAS

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    1. Harold P. Benson, 1985. "Multiple Objective Linear Programming with Parametric Criteria Coefficients," Management Science, INFORMS, vol. 31(4), pages 461-474, April.
    2. Sitarz, Sebastian, 2008. "Postoptimal analysis in multicriteria linear programming," European Journal of Operational Research, Elsevier, vol. 191(1), pages 7-18, November.
    3. Sebastian Sitarz, 2011. "Sensitivity Analysis Of Weak Efficiency In Multiple Objective Linear Programming," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 28(04), pages 445-455.
    4. Sebastian Sitarz, 2010. "Standard sensitivity analysis and additive tolerance approach in MOLP," Annals of Operations Research, Springer, vol. 181(1), pages 219-232, December.
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    Cited by:

    1. Gabriele Eichfelder & Corinna Krüger & Anita Schöbel, 2017. "Decision uncertainty in multiobjective optimization," Journal of Global Optimization, Springer, vol. 69(2), pages 485-510, October.
    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. Botte, Marco & Schöbel, Anita, 2019. "Dominance for multi-objective robust optimization concepts," European Journal of Operational Research, Elsevier, vol. 273(2), pages 430-440.
    4. T. D. Chuong & V. H. Mak-Hau & J. Yearwood & R. Dazeley & M.-T. Nguyen & T. Cao, 2022. "Robust Pareto solutions for convex quadratic multiobjective optimization problems under data uncertainty," Annals of Operations Research, Springer, vol. 319(2), pages 1533-1564, December.
    5. 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.
    6. Morteza Rahimi & Majid Soleimani-damaneh, 2020. "Characterization of Norm-Based Robust Solutions in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 554-573, May.
    7. Sanaz Sadeghi & S. Morteza Mirdehghan, 2018. "Stability of Local Efficiency in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 591-613, August.
    8. Morteza Rahimi & Majid Soleimani-damaneh, 2023. "Aubin property for solution set in multi-objective programming," Journal of Global Optimization, Springer, vol. 85(2), pages 441-460, February.
    9. Thai Doan Chuong, 2022. "Second-order cone programming relaxations for a class of multiobjective convex polynomial problems," Annals of Operations Research, Springer, vol. 311(2), pages 1017-1033, April.
    10. 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.
    11. 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.
    12. Morteza Rahimi & Majid Soleimani-damaneh, 2018. "Robustness in Deterministic Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 137-162, October.

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