Column-and-constraint generation approach to partition-based risk-averse two-stage stochastic programs

IF 4.5 3区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Jongheon Lee, Kyungsik Lee
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引用次数: 0

Abstract

Typically, two-stage stochastic programs have been modeled and solved based on the finite support assumption, but the large number of scenarios makes it hard to solve, and there also are potential risks of inaccurate estimation of underlying distribution. In this paper, to mitigate the drawbacks, we present a novel risk-averse two-stage stochastic program with finite support, which we call partition-based risk-averse two-stage stochastic program. In the program, a set of scenarios is partitioned into several groups, and the second-stage cost is defined as the expectation of risk levels for all of the groups. In particular, the conditional value-at-risk is considered as a risk measure for each group, and so the risk level of the model is affected by a quantile parameter or a partition of a given set of scenarios. In order to solve the model exactly for a given partition, a column-and-constraint generation algorithm is proposed. In addition, a scenario partitioning algorithm to enable the risk level of the model to be close to a given target is devised, and partitioning schemes for combining it with the proposed column-and-constraint generation algorithm are proposed. Extensive numerical experiments were performed that demonstrated the effectiveness of the proposed partitioning schemes and the efficiency of the proposed solution approach.

基于分区的风险规避两阶段随机规划的列约束生成方法
通常情况下,两阶段随机规划的建模和求解都是基于有限支持假设,但由于情景数量多,求解难度大,而且存在对底层分布估计不准确的潜在风险。为了解决这一问题,本文提出了一种新的具有有限支持度的风险规避两阶段随机规划,我们称之为基于分区的风险规避两阶段随机规划。在该方案中,一组场景被划分为几个组,第二阶段成本被定义为所有组的风险水平的期望。特别是,条件风险值被视为每个组的风险度量,因此模型的风险水平受到分位数参数或给定场景集的分区的影响。为了精确求解给定分区的模型,提出了一种列约束生成算法。此外,设计了一种使模型的风险等级接近给定目标的场景划分算法,并提出了将其与所提出的列约束生成算法相结合的划分方案。大量的数值实验证明了所提出的划分方案的有效性和所提出的求解方法的效率。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Annals of Operations Research
Annals of Operations Research 管理科学-运筹学与管理科学
CiteScore
7.90
自引率
16.70%
发文量
596
审稿时长
8.4 months
期刊介绍: The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications. In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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