BCAM Scientific Seminar: On Distributionally Robust Optimization For Multistage Multiscale Mixed Interger Linear Problems Under Uncertaintly

LOCATION: Maryam Mirzakhani Seminar Room at BCAM and Online

ABSTRASCT:
Distributionally robust optimization (DRO) is motivated as a counterpart of the usually unknown underlying probability distribution (PD) frequently followed by the uncertainty in dynamic mathematical optimization problems. In this talk we present the main features of a project based on a DRO approach for solving multistage multiscale problems under uncertainty, where it is represented in a finite set of scenarios for the realization of the strategic and operational parameters in the related ambiguity sets. The aim of the project is threefold. First, introducing an approach for generating a disjoint scenario set, by appropriately perturbing the cumulative distribution functions that result from projecting in modeler-driven PDs the so-named Nominal Distribution (ND) of the immediate successor node (ISN) set of each node in the multistage scenario tree. The resulting strategic and operational ambiguity sets are prioritized by using the Wasserstein distance of each ambiguity set member to the ND for each ISN and stage sets. Second, building a distributionally robust mixed integer linear optimization modeling paradigm that considers the strategic ambiguity subset for each ISN set and the operational one for each stage in the multistage multiscale environment. The goal is to minimize the overall expected DRO solution value in the scenarios subject to the constraint system for each ambiguity set member. And third, given the intrinsic problem´s difficulty and the huge model´s dimensions in realistic applications, it is not practical to seek an optimal solution, so, a matheuristic algorithm so-named SFR3 (it stands for Scenario variables Fixing and constraints and variables' integrality iteratively Randomizing Relaxation Reduction) is considered for problem solving, where the solution quality is guaranteed. A supply network design problem is taken as a pilot case to validate the proposal, and provisional computational experience is reported.

Link to the session here