Data-Driven Distributionally Robust Stochastic Programming

数据驱动的分布式鲁棒随机规划

• 批准号: 1563504
• 负责人: Guzin Bayraksan
• 金额: $ 26.41万
• 依托单位: Ohio State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-01 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1563504&HistoricalAwards=false
• 关键词: Data; Driven; Distributionally; Robust; Stochastic

Stochastic programming aids in solving difficult problems with many unknown factors. It does so by relying on probability distributions to mathematically represent and predict uncertain events. However, probabilities of possible outcomes are rarely known in real life. Distributionally robust optimization aims to obtain solutions in the presence of such distributional uncertainties. There are a variety of ways to form distributionally robust stochastic programs. However, which type of model to use for which type of data, system, or decision maker is not well understood. This award supports research to have a deeper understanding of this fundamental question and to explore multi-period uncertainties. The project considers long-term water resources management problems that take various sources of input including climate data, hydrological simulations, expert opinions, and so forth. The results, if successful, will yield improved water management, benefitting the U.S. society and economy. The research findings will be incorporated into educational materials on stochastic optimization. The project will therefore contribute to educating students. The water application will be used to demonstrate the societal impact of our field and to attract women to engineering.To address the problem of effective modeling, the project will attempt a classification of models in a way that highlights how different sources of data and problem characteristics may require differing problem formulations. This research task will use probability theory, statistics, and risk theory to make recommendations. It will then utilize these results to improve modeling and data collection and devise sampling schemes. To address the problem of uncertainty revealed over time, the project will investigate data-driven multistage distributionally robust stochastic programs. This research task will examine how to translate multi-period uncertainties into the model and investigate the resulting model structure and properties. To effectively solve these models, decomposition-based solution methodologies will be explored. In addition, the project will examine the value of data and the effect of different scenarios on optimal solutions and values. Finally, the project will implement the modeling, algorithmic, and theoretical findings to solve real-world multi-period water allocation problems. If successful, the results are also applicable to other problems in energy, transportation, and finance with complex multi-period uncertainties.

随机规划有助于解决具有许多未知因素的困难问题。 它依靠概率分布来数学地表示和预测不确定事件。然而，在真实的生活中，可能结果的概率是很少知道的。分布鲁棒优化的目标是在存在这种分布不确定性的情况下获得解。有多种方法可以形成分布鲁棒随机规划。然而，对于哪种类型的数据、系统或决策者使用哪种类型的模型还没有很好的理解。该奖项支持研究更深入地了解这一基本问题，并探索多时期的不确定性。该项目考虑了长期的水资源管理问题，这些问题需要各种来源的投入，包括气候数据、水文模拟、专家意见等。如果成功，这些成果将改善水资源管理，造福美国社会和经济。研究结果将纳入随机优化的教材。 因此，该项目将有助于教育学生。水的应用将被用来展示我们的领域的社会影响，并吸引妇女到工程。为了解决有效建模的问题，该项目将尝试以一种突出不同的数据来源和问题特征可能需要不同的问题表述的方式对模型进行分类。本研究课题将运用概率论、统计学和风险理论提出建议。然后，它将利用这些结果来改进建模和数据收集，并制定抽样计划。 为了解决随着时间的推移所揭示的不确定性问题，该项目将研究数据驱动的多级分布鲁棒随机程序。本研究将探讨如何将多周期不确定性转化为模型，并研究由此产生的模型结构和特性。为了有效地解决这些模型，将探讨基于分解的解决方案方法。此外，该项目还将研究数据的价值以及不同情景对最佳解决方案和价值的影响。最后，该项目将实施建模、算法和理论发现，以解决现实世界的多时期水分配问题。 如果成功，结果也适用于能源，交通和金融等复杂的多期不确定性问题。