Multistage Stochastic Integer Programming: Approximate Solution Methods and Applications

多阶段随机整数规划：近似解法及应用

• 批准号: RGPIN-2018-04984
• 负责人: Bodur, Merve
• 金额: $ 2.62万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=759630
• 关键词: Multistage; Stochastic; Integer; Programming; Approximate

Multistage stochastic programming (MSP) provides a modeling framework for sequential decision making under uncertainty. The majority of the application of mathematical programming assumes deterministic data. However, real world problems almost always include some uncertain parameters (e.g., in a portfolio optimization problem, the returns of different assets are highly uncertain at the time of investment). It has been traditionally difficult to predict such uncertainties with a high accuracy, but now with the existence of substantial historical records and advances in data analytics, we can accurately model uncertainty. The ability to exploit available data made it possible to incorporate uncertainty into mathematical models, which is the case in stochastic programming. Moreover, in many applications, the planning horizon has multiple decision stages and the uncertainty is revealed gradually over time. Therefore, MSP is a viable modeling approach. MSP has numerous applications in areas like energy, finance, and scheduling. However, MSP models are notoriously hard to solve in general, and existing solution approaches frequently fail to solve real-life size problems. Motivated by its application potential and limitations of the state-of-the-art solution methods, this program aims to make fundamental algorithmic and theoretical contributions to MSP (especially with integer variables), and extend its applications in a variety of areas.Theme 1 of the program will focus on developing methods that can overcome modeling and algorithmic challenges in the class of MSP problems, especially the ones involving integer variables, and that can provide (provably) good feasible policies. The methodology will be mostly based on novel ways of using (linear) decision rules. In particular, new decision rules will be developed for MSP models with integer variables. The tractability of the proposed methods and the quality of the obtained solutions will be analyzed. The results will significantly advance the state-of-the-art in stochastic programming.Theme 2 of the program will explore diverse applications of MSP such as operating room scheduling, power systems and portfolio optimization. Novel MSP models will be proposed for certain important problems in these areas, and the value of such models over deterministic and two-stage stochastic programming models will be investigated. The results will provide valuable planning, scheduling and operational tools for decision makers.

多阶段随机规划（MSP）为不确定性下的顺序决策提供了一个建模框架。数学规划的大部分应用都假设确定性数据。然而，现实世界的问题几乎总是包含一些不确定的参数（例如，在投资组合优化问题中，不同资产的回报在投资时具有高度不确定性）。传统上很难高精度地预测此类不确定性，但现在随着大量历史记录的存在和数据分析的进步，我们可以准确地对不确定性进行建模。利用可用数据的能力使得将不确定性纳入数学模型成为可能，随机规划就是这种情况。此外，在许多应用中，规划范围具有多个决策阶段，并且随着时间的推移，不确定性逐渐显现出来。因此，MSP是一种可行的建模方法。 MSP 在能源、金融和调度等领域有大量应用。然而，众所周知，MSP 模型一般来说很难解决，并且现有的解决方法经常无法解决现实生活中的尺寸问题。受其应用潜力和最先进解决方法的局限性的激励，该计划旨在为 MSP（特别是整数变量）做出基础算法和理论贡献，并将其应用扩展到各个领域。 主题 1该项目的重点是开发能够克服 MSP 问题类的建模和算法挑战的方法，特别是涉及整数变量的问题，并且能够提供（可证明）良好的可行策略。该方法将主要基于使用（线性）决策规则的新颖方法。特别是，将为具有整数变量的 MSP 模型开发新的决策规则。将分析所提出方法的易处理性和所获得解决方案的质量。结果将显着推进随机规划的最先进水平。该计划的主题 2 将探索 MSP 的多种应用，例如手术室调度、电力系统和投资组合优化。针对这些领域中的某些重要问题，我们将提出新的 MSP 模型，并将研究此类模型相对于确定性和两阶段随机规划模型的价值。结果将为决策者提供有价值的规划、调度和操作工具。