两阶段供应商问题的随机优化与学习
Stochastic Optimization and Learning for Two-Stage Supplier Problems
AI总结：
研究两阶段随机供应商聚类中预算随机性及非同质半径、拟阵和多背包约束问题，通过多项式场景算法与场景丢弃式 SAA 在黑盒分布下实现半径优化。
摘要：
本文主要关注带追索权的两阶段随机设置下基于半径的（供应商）聚类，其中模型的内在随机性以预算约束的形式出现。除了所有客户都必须位于距最近设施距离 $R$ 内的标准（同质）设置外，我们还给出了半径需求可能非同质（即每个客户各不相同）的更一般问题的结果。我们还探讨了对第一阶段决策施加额外约束的若干变体，特别是拟阵约束和多背包约束，并给出了这些设置下的结果。我们推导了最一般分布设置下的结果，在该设置中只能对底层分布进行黑盒访问。为实现这一点，我们首先开发了多项式场景设置下的算法；随后采用标准样本平均近似（SAA）方法的一种新颖的场景丢弃变体，该变体关键地利用了受限情形算法的性质。我们指出，对 SAA 方法的场景丢弃修改对于在半径上进行优化是必要的。
英文摘要：
The main focus of this paper is radius-based (supplier) clustering in the two-stage stochastic setting with recourse, where the inherent stochasticity of the model comes in the form of a budget constraint. In addition to the standard (homogeneous) setting where all clients must be within a distance $R$ of the nearest facility, we provide results for the more general problem where the radius demands may be inhomogeneous (i.e., different for each client). We also explore a number of variants where additional constraints are imposed on the first-stage decisions, specifically matroid and multi-knapsack constraints, and provide results for these settings. We derive results for the most general distributional setting, where there is only black-box access to the underlying distribution. To accomplish this, we first develop algorithms for the polynomial scenarios setting; we then employ a novel scenario-discarding variant of the standard Sample Average Approximation (SAA) method, which crucially exploits properties of the restricted-case algorithms. We note that the scenario-discarding modification to the SAA method is necessary in order to optimize over the radius.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
