Robust Optimization in discrete Optimization – Taking decisions under uncertainty

Prof. Christina Büsing presents her current research in the HDS-LEE / SSD Seminar Series: Robust Optimization in discrete Optimization – Taking decisions under uncertainty.

Discrete optimization is one of the most important methods for making good decisions in logistics, production or healthcare. Often, decisions have to be made in which future prices or fluctuations in demand play an important role. Robust optimization is an approach to integrate these uncertainties into the decision-making process. Here, a solution is sought that remains admissible under all considered uncertainties and whose maximum occurring costs are minimal.

One of the best-known and most frequently used approaches of robust optimization is the modelling of uncertainties through so-called budget uncertainties. This is due to the very intuitive construction of the uncertainty sets and the existence of a compact robust reformulation for (mixed-integer) linear programs. However, despite its compactness, the reformulation performs poorly in solving robust integer problems due to its weak linear relaxation.

In this talk, we will start with some applications for an robust optimization approach. I will then present several theoretical results to obtain a customized Branch & Bound algorithm for robust optimization problems with budget uncertainties. Finally, we will show in a computational study that our current approaches outperform all known algorithms and that using robustness helps to improve taking decision in uncertain settings.