Development of Strong Algorithms and Applications of Complex Two-stage Robust Optimization and Related ModelsWang, Wei (2023) Development of Strong Algorithms and Applications of Complex Two-stage Robust Optimization and Related Models. Doctoral Dissertation, University of Pittsburgh. (Unpublished)
AbstractTwo-stage robust optimization (2-S RO) is a powerful modeling tool for dealing with uncertainty while achieving reliable solutions. Current solution methods focus on those with decision independent or continuous decision dependent uncertainty (DDU) set and continuous recourse problem. The lack of algorithms for general 2-S RO to handle mixed integer DDU set and/or recourse problem significantly restricts its applicability. In this dissertation, we first extend the latest algorithm, i.e., parametric column-and-constraint generation (C&CG) method, in two directions. One is to solve 2-S RO with mixed integer DDU set, and the other is to deal with mixed integer recourse and DDU set (by a nested implementation of C&CG). For both scenarios, our new algorithm development derives exact solutions in finite iterations. Note that mixed integer recourse is rather common in applications, but nested C&CG is difficult to implement and may be demanding on computation resources. Hence, we develop a series of approximation methods for this type of problems. All the approaches, adopting C&CG framework, are easy to apply and report both lower and upper bounds for evaluating the quality of solutions. Finally, we investigate some power system applications with more complex 2-S RO structures. Structural property-based approximation strategies and exact approaches are presented, which enable the development of tailored C\&CG methods for those sophisticated power grid operational models. Share
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