Having just arrived in Poznan, I’m much looking forward to the exciting talks we will see during the coming days.
My own talk (TC 47) will be on a recent paper on “Variable-Sized Uncertainty and Inverse Problems in Robust Optimization”. The idea is that we do not know the uncertainty set exactly, but only its shape. If the uncertainty size is zero, the nominal solutions is also an optimal “robust” solution. How does this change when the uncertainty increases?
In the first kind of problem we consider, robust optimisation with variable-sized uncertainty, we try to find a smallest set of robust solutions that contains an optimal solution for every possible uncertainty set. In the second kind of problem, inverse robust optimisation, we only consider how much uncertainty can or must be added such that the nominal solution is not an optimal solution for the robust problem anymore.
This is the abstract:
In robust optimization, the general aim is to find a solution that performs well over a set of possible parameter outcomes, the so-called uncertainty set. In this paper, we assume that the uncertainty size is not fixed, and instead aim at finding a set of robust solutions that covers all possible uncertainty set outcomes. We refer to these problems as robust optimization with variable-sized uncertainty. We discuss how to construct smallest possible sets of min-max robust solutions and give bounds on their size.
A special case of this perspective is to analyze for which uncertainty sets a nominal solution ceases to be a robust solution, which amounts to an inverse robust optimization problem. We consider this problem with a min-max regret objective and present mixed-integer linear programming formulations that can be applied to construct suitable uncertainty sets.
Results on both variable-sized uncertainty and inverse problems are further supported with experimental data.
Other talks in the session are given by Andre Chassein (Approximation of Ellipsoids Using Bounded Uncertainty Sets), Krzysztof Postek (Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information), and Mikita Hradovich (The Robust Recoverable Spanning Tree Problem with Interval Costs). So do come and enjoy!