关于在分布鲁棒性模糊中纳入决策依赖的相关性研究
On the Relevance of Incorporating Decision Dependence in Distributional Ambiguity
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- Clemson University（克莱姆森大学）
- Northwestern University（西北大学）
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中文总结 AI 辅助
本文研究决策依赖模糊集在分布鲁棒优化中的价值，通过两阶段随机混合整数规划建模，提出割平面算法，实验表明可显著降低失望度与样本外成本，但计算代价更高。
中文摘要 AI 辅助
大多数关于具有决策依赖模糊集的分布鲁棒优化（DRO）的现有研究都集中在这一类问题所带来的计算和理论挑战上。在本文中，我们采用建模与计算相结合的视角，来理解建模保真度、解质量和计算工作量之间的权衡，特别是与使用决策独立模糊集的DRO模型进行比较。受联合定价-库存报童问题（需求依赖于价格）和设施选址问题（需求依赖于位置）等代表性应用的启发，我们考虑了一个具有（非）凸连续补偿的两阶段随机混合整数规划。在假设有限样本空间的情况下，我们用多面体模糊集对决策依赖的分布模糊性进行建模，并将问题重构为非凸混合整数非线性规划。为了高效求解重构问题，我们提出了基于分解的割平面算法。我们在基准实例上的实验表明，决策依赖模糊集显著降低了报童问题的决策后失望度和设施选址问题的样本外成本，平均分别降低高达65%和7%；从而相对于决策独立的DRO减轻了优化者的诅咒。然而，这种改进是以增加计算工作量为代价的，对于中大型报童实例，绝对运行时间比在2到25之间，对于设施选址实例在2到12之间。
英文摘要
Most existing studies on distributionally robust optimization (DRO) with a decision-dependent ambiguity set focus on the computational and theoretical challenges posed by this class of problems. In this paper, we adopt a combined modeling and computational perspective to understand the trade-offs between modeling fidelity, solution quality, and computational effort, particularly in comparison with DRO models using decision-independent ambiguity sets. Motivated by representative applications in joint pricing-stocking newsvendor problems with price-dependent demand and facility location problems with location-dependent demand, we consider a two-stage stochastic mixed-integer program with (non)convex continuous recourse. Assuming a finite sample space, we model the decision-dependent distributional ambiguity with a polyhedral ambiguity set and reformulate the problem as a nonconvex mixed-integer nonlinear program. To efficiently solve the reformulations, we propose decomposition-based cutting-plane algorithms. Our experiments on benchmark instances indicate that a decision-dependent ambiguity set substantially reduces the postdecision disappointment for the newsvendor and out-of-sample cost for the facility location problems, up to 65% and 7% on average, respectively; thereby mitigating the optimizer's curse relative to a decision-independent DRO. However, this improvement is achieved at the expense of increased computational effort, with the absolute runtime ratio falling between 2 and 25 for medium- to large-sized newsvendor instances and between 2 and 12 for facility location instances.
