Risk Averse Multistage Stochastic Integer Programming

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

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.