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.
Highlights
Water is an essential resource for all life on the planet
Before we are going to the approach of lexicographic tolerable robust solution, let us recall the important definition of ordering the values nonincreasingly which will be used throughout this work
There may occur the situation that some decision makers are not satisfied with the solution found by the lexicographic tolerable robust solution concept
Summary
Water is an essential resource for all life on the planet. one of the biggest concerns for our water-based resources in the future is the sustainability of the current and future water resources allocation, see [1]. As water becomes more scarce in the future, the importance of how it is managed grows vastly in this research area. Finding a balance between what is needed by humans and what is needed in the environment is an important step in the sustainability of water resources. The goals of water resource planning usually involve balancing water demands and available water resources, whereas many other objectives need to be achieved, depending on the particular water system structures. Due to conflicts between multiple goal requirements, multiple criteria decision-making techniques are useful tools to explore different management options. To handle these kind of water resources management planning, many researchers adopted the techniques of multi-objective optimization to solve the problem. One may see more details in [2,3,4,5,6]
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