散度测度下可实践的鲁棒随机优化
Practicable Robust Stochastic Optimization under Divergence Measures
AI总结：
本文针对基于 f-散度模糊集的两阶段鲁棒随机优化提出新的散度函数，在保持建模灵活性的同时显著提升混合整数情形下的数值可实践性，并通过巴西人道主义选址-分配案例验证了其在公平性与鲁棒性上的优势。
摘要：
我们致力于在模糊集由 f-散度半径构造时，为两阶段鲁棒随机优化（RSO）模型提供可实践的近似。这些模型在数值上具有不同程度的挑战性，具体取决于所选择的 f-散度函数。当第一阶段决策为混合整数时，数值挑战更加突出。在本文中，我们提出了新的散度函数，能够产生可实践的鲁棒对应模型，同时在建模多样化的模糊厌恶方面保持灵活性。我们的函数所产生的鲁棒对应模型在数值难度上与其名义问题相当。我们还提出了利用我们的散度来模拟现有 f-散度而不影响可实践性的方法。我们在巴西人道主义行动的一个现实选址-分配模型中实现了我们的模型。我们的人道主义模型优化了效果-公平权衡，该权衡由一个新的效用函数和基尼平均差系数定义。通过案例研究，我们展示了：1）与现有 f-散度相比，采用我们提出的散度函数后 RSO 对应模型的可实践性显著提高；2）我们的新目标函数所强制实现的更高人道主义响应公平性；3）当考虑模糊性时，所得计划对概率估计变化的更强鲁棒性。
英文摘要：
We seek to provide practicable approximations of the two-stage robust stochastic optimization (RSO) model when its ambiguity set is constructed with an f-divergence radius. These models are known to be numerically challenging to various degrees, depending on the choice of the f-divergence function. The numerical challenges are even more pronounced under mixed-integer first-stage decisions. In this paper, we propose novel divergence functions that produce practicable robust counterparts, while maintaining versatility in modeling diverse ambiguity aversions. Our functions yield robust counterparts that have comparable numerical difficulties to their nominal problems. We also propose ways to use our divergences to mimic existing f-divergences without affecting the practicability. We implement our models in a realistic location-allocation model for humanitarian operations in Brazil. Our humanitarian model optimizes an effectiveness-equity trade-off, defined with a new utility function and a Gini mean difference coefficient. With the case study, we showcase 1) the significant improvement in practicability of the RSO counterparts with our proposed divergence functions compared to existing f-divergences, 2) the greater equity of humanitarian response that our new objective function enforces and 3) the greater robustness to variations in probability estimations of the resulting plans when ambiguity is considered.
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