Discrete Optimization Problems with Interval Data: Pareto Set of Solutions or Set of Weak Solutions?


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Abstract

For optimization problems with interval uncertainty, traditionally researchers have considered definitions based on element-wise optimality: a feasible solution is a strong solution if it optimizes the objective function f(x, c) for all possible values of the parameters c within the given intervals c, and it is a weak solution if it optimizes the objective function f(x, c) for some values cc. In our previous papers, we introduced the alternative approach based on the idea of Pareto optimality.In this paper, we analyze the relation between these two concepts of optimality, and provide arguments in favor of the Pareto approach.

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