摘要
In the conventional robust optimization(RO)context,the uncertainty is regarded as residing in a predetermined and fixed uncertainty set.In many applications,however,uncertainties are affected by decisions,making the current RO framework inapplicable.This paper investigates a class of two-stage RO problems that involve decision-dependent uncertainties.We introduce a class of polyhedral uncertainty sets whose right-hand-side vector has a dependency on the here-and-now decisions and seek to derive the exact optimal wait-and-see decisions for the second-stage problem.A novel iterative algorithm based on the Benders dual decomposition is proposed where advanced optimality cuts and feasibility cuts are designed to incorporate the uncertainty-decision coupling.The computational tractability,robust feasibility and optimality,and convergence performance of the proposed algorithm are guaranteed with theoretical proof.Four motivating application examples that feature the decision-dependent uncertainties are provided.Finally,the proposed solution methodology is verified by conducting case studies on the pre-disaster highway investment problem.
基金
This work was supported by the Joint Research Fund in Smart Grid under cooperative agreement between the National Natural Science Foundation of China(NSFC)and State Grid Corporation of China(U1966601).
