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

Pornpimon Boriwan, Matthias Ehrgott, Daishi Kuroiwa and Narin Petrot
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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

Sustainability, 2020, vol. 12, issue 18, 1-21

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.

Keywords: uncertain multi-objective optimization; robustness concept; minmax robustness; lexicographic tolerable robust; water resources management planning (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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