University of Michigan
Due to the existence of information uncertainty in real-world problems, decision makers often need to balance risk and return outcomes even without knowing their exact decision criteria and preferences. This award supports fundamental research to develop new paradigms for decision making under uncertainty to currently existing approaches. The research will have applicability in a wide range of industry and science sectors. In particular, the intended applications to electric power grids and to transportation systems will promote synergy among different disciplines, and will advance the state-of-the-art techniques for analyzing a variety of the nation's critical infrastructures. The results will be disseminated through education, to improve students' learning in science and engineering, and promote the participation of underrepresented groups in research. The objective of this project is to develop new models and approaches, using chance-constrained programming and data-driven optimization approaches, for managing risk under ambiguous decision preferences and data uncertainty. The proposed research focuses on stochastic programs with probabilistic (chance) constraints formulated for guaranteeing the quality of service. Moreover, we consider adjustable risk parameters in related chance constraints and their effects on the overall objective value. Given known or ambiguous distributional information of the uncertainty, we study the corresponding data-informed or data-driven modeling paradigms for risk management. The scalability and efficacy of our computation approaches are built through convex representations and binarization techniques from data mining. The proposal also includes investigations of two related applications in optimal power flow operations and sensor deployment for monitoring transportation systems. We aim to demonstrate that (i) differentiating risk in multiple chance constraints effectively balances cost and reliability under uncertainty, and (ii) the selection of risk levels can be guided and improved by data-driven optimization approaches in problems with imperfect information.
Division of Civil, Mechanical and Manufacturing Innovation (CMMI)