Two-stage distributionally robust optimization is a recent optimization technique to handle uncertainty that is less conservative than robust optimization and more flexible than stochastic programming. The probability distribution of the uncertain parameters is not known but is assumed to belong to an ambiguity set. The size of certain types of ambiguity sets - such as several discrepancy-based ambiguity sets - is defined by a single parameter that makes it possible to control the degree of conservatism of the underlying optimization problem. Finding the values to assign to this parameter is a very relevant research topic. Hence, in this paper, we propose an exact and several heuristic methods for determining the control parameter values leading to all the relevant first-stage solutions. Our algorithmic approach resembles the ϵ−constrained method used to generate the Pareto front of a bi-objective problem. To demonstrate the applicability and efficacy of the proposed approaches, we conduct experiments on three different problems: scheduling, berth allocation, and facility location. The results obtained indicate that the proposed approaches provide sets of first-stage solutions very close to the optimal in a reasonable time.

中文翻译：

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两阶段分布稳健优化问题的 Pareto 前沿

两阶段分布稳健优化是一种最新的优化技术，用于处理不确定性，它比稳健优化更保守，比随机规划更灵活。不确定参数的概率分布是未知的，但假定属于模糊集。某些类型的模糊集（例如几个基于差异的模糊集）的大小由单个参数定义，该参数可以控制基础优化问题的保守程度。查找要分配给此参数的值是一个非常相关的研究主题。因此，在本文中，我们提出了一种精确的几种启发式方法来确定导致所有相关第一阶段解决方案的控制参数值。我们的算法方法类似于用于生成双目标问题的帕累托前沿的 ε 约束方法。为了证明所提出的方法的适用性和有效性，我们对三个不同的问题进行了实验：调度、泊位分配和设施位置。获得的结果表明，所提出的方法在合理的时间内提供了非常接近最优的第一阶段解集。