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The Lexicographic Tolerable Robustness Concept for Uncertain Multi-Objective Optimization Problems: A Study on Water Resources Management

Author

Listed:
  • Pornpimon Boriwan

    (Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand)

  • Matthias Ehrgott

    (Department of Management Science, Lancaster University Management School, Lancaster LA1 4YX, UK)

  • Daishi Kuroiwa

    (Department of Mathematics, Faculty of Science and Engineering, Shimane University, Shimane 690-0823, Japan)

  • Narin Petrot

    (Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
    Center of Excellence in Nonlinear Analysis and Optimization, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand)

Abstract

In this study, we introduce a robust solution concept for uncertain multi-objective optimization problems called the lexicographic tolerable robust solution. This approach is advantageous for the practical implementation of problems in which the solution should satisfy priority levels in the objective function and the worst performance vector of the solution obtained by the proposed concept is close to a reference point of the considered problem, within an acceptable tolerance threshold. Important properties of the solution sets of this introduced concept as well as an algorithm for finding such solutions are presented and discussed. We provide the implementation of the proposed lexicographic tolerable robust solution to improve understanding for practitioners by relying on the data of the water resources master plan for Serbia from Simonovic, 2009. Moreover, we are also concerned with the method of updating a desirable solution for fitting with the preferences when compromising of the multiple groups of decision makers is needed.

Suggested Citation

  • Pornpimon Boriwan & Matthias Ehrgott & Daishi Kuroiwa & Narin Petrot, 2020. "The Lexicographic Tolerable Robustness Concept for Uncertain Multi-Objective Optimization Problems: A Study on Water Resources Management," Sustainability, MDPI, vol. 12(18), pages 1-21, September.
    • Handle: RePEc:gam:jsusta:v:12:y:2020:i:18:p:7582-:d:413513
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    References listed on IDEAS

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    6. Lizhen Shao & Matthias Ehrgott, 2008. "Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 257-276, October.
    7. Bokrantz, Rasmus & Fredriksson, Albin, 2017. "Necessary and sufficient conditions for Pareto efficiency in robust multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 262(2), pages 682-692.
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    Cited by:

    1. Pornpimon Boriwan & Thanathorn Phoka & Narin Petrot, 2022. "The Lightly Robust Max-Ordering Solution Concept for Uncertain Multiobjective Optimization Problems: An Ambulance Location Problem with Unavailability," Sustainability, MDPI, vol. 14(12), pages 1-18, June.

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