论文标题
具有固定追索权的两阶段随机程序的广义自适应分区方法
Generalized Adaptive Partition-based Method for Two-Stage Stochastic Programs with Fixed Recourse
论文作者
论文摘要
当不确定性空间可以具有离散或连续分布时，我们提出了一种解决两阶段随机问题的方法。给定不确定性空间的分区，该方法被解决以解决分区的每个元素（不确定性空间的子区域）的一个方案。固定第一阶段变量，我们为每个元素制定了第二阶段子问题，并从这些问题的双重问题中利用信息，我们提供了分区必须满足以获得最佳解决方案的条件。这些条件提供了有关如何完善分区的指导，并迭代地融入了最佳解决方案。计算实验的结果表明该方法如何自动完善问题区域中不确定性空间的分区。我们的算法是Song＆Luedtke（2015）提出的基于自适应分区的方法的概括，用于离散分布，将其适用性扩展到更一般的情况。
We present a method to solve two-stage stochastic problems with fixed recourse when the uncertainty space can have either discrete or continuous distributions. Given a partition of the uncertainty space, the method is addressed to solve a discrete problem with one scenario for each element of the partition (sub-regions of the uncertainty space). Fixing first stage variables, we formulate a second stage subproblem for each element, and exploiting information from the dual of these problems, we provide conditions that the partition must satisfy to obtain the optimal solution. These conditions provide guidance on how to refine the partition, converging iteratively to the optimal solution. Results from computational experiments show how the method automatically refines the partition of the uncertainty space in the regions of interest for the problem. Our algorithm is a generalization of the adaptive partition-based method presented by Song & Luedtke (2015) for discrete distributions, extending its applicability to more general cases.
