Risk Averse Multistage Stochastic Integer Programming

多阶段随机规划是不确定条件下序列决策的一个重要框架，在许多应用中得到了广泛的应用。这种方法背后的数学模型构成了一类极具挑战性的优化问题。这些问题的解决策略已经有了非常重要的研究进展，但大部分都局限于风险中性设置和基本数学结构简单（凸）时。最近，在电力系统应用中，可再生能源的渗透所带来的波动性增加沿着与其结构的复杂性激励明确考虑风险和非凸结构在这个框架。 该项目旨在为风险规避多阶段随机规划做出基础理论和算法贡献，特别是用整数变量来建模非凸性，并研究其在能源领域的应用。如果成功，该项目的结果将为电力系统运营商提供有价值的规划和调度工具。这些发展还可能影响其他各种应用领域，包括制造业、金融和服务业。 该项目的成果将通过出版物和会议报告传播，并将在随机规划研究生课程中采用。该项目将通过支持博士生的研究来培养未来的学者和研究人员。该项目将开发基于抽样和动态规划的风险规避多级随机整数规划方法。支撑这种方法的理论和算法在风险中性和线性环境中得到了广泛的研究。在这个框架中的风险规避提出了至关重要的问题，从动态决策的角度来看，有意义的风险措施，并通过采样和动态规划的优化近似的角度来看，计算上有吸引力。简化整数决策引入了非凸性，需要新的分析和算法技术来解决。 该研究将集中在多级问题的假设下，stagewise独立的，或更一般的马尔可夫，结构的不确定数据过程和二进制状态变量，并利用由此产生的结构，开发可扩展的方法。特别是，该项目将调查（i）各种风险措施的建模和结构问题，（ii）基于抽样的方法来评估和优化风险规避目标，以及（iii）近似动态规划方法。

Multistage stochastic programming is well established as an important framework for sequential decision making under uncertainty in a variety of applications. The mathematical models underlying this approach constitute an extremely challenging class of optimization problems. There has been very significant research progress in solution strategies for these problems, but much of it has been restricted to the risk neutral setting and when the underlying mathematical structures are simple (convex). Recently, in power systems applications, the increasing volatility brought forth by the penetration of renewable energy sources along with their structural complexities motivate the explicit consideration of risk and non-convex structures in this framework. This project aims to make fundamental theoretical and algorithmic contributions to risk-averse multistage stochastic programming, especially with integer variables to model non-convexities, and investigate its applications in the energy sector. If successful, results from this project will provide valuable planning and scheduling tools for power system operators. The developments can also impact a variety of other application areas including manufacturing, finance and service. The results of this project will be disseminated through publications and conference presentations, and will be adopted in graduate courses on stochastic programming. The project will contribute to the training of future academics and researchers by supporting the research of doctoral students.The project will develop sampling and dynamic programming based approaches for risk-averse multistage stochastic integer programs. Theory and algorithms underpinning such approaches have been researched extensively in the risk neutral and linear setting. Incorporating risk aversion in this framework raises crucial questions regarding risk measures that make sense from the point of view of dynamic decisions, and are computationally attractive from the point of view of approximation via sampling and optimization via dynamic programming. Incorporating integer decisions introduces nonconvexities, and requires novel analysis and algorithmic techniques for their resolution. The research will focus on multistage problems under the assumption of stagewise independent, or more generally Markovian, structure of the uncertain data process and binary state variables, and exploit the resulting structure to develop scalable approaches. In particular, the project will investigate (i) modeling and structural issues for various risk measures, (ii) sampling based approaches for evaluating and optimizing risk-averse objectives, and (iii) approximate dynamic programming approaches.