15.05.2017

Montag, 15. Mai 2017, 16.15 Uhr, Seminarraum II

Prof. Dr. Frauke Liers
Lehrstuhl für Wirtschaftsmathematik
Department Mathematik
Universität Erlangen-Nürnberg

Robust Mathematical Optimization Methods and Their Applications in Air Traffic Management

Real applications often face uncertainty in the input parameters. One way of protecting against such uncertainties is to apply and to develop methodologies from robust optimization. The latter takes these uncertainties into account already in the mathematical model. Then, the task is to determine solutions that are feasible for all considered realizations of the uncertain parameters, and among them one with best guaranteed solution value. In this talk, we will give an overview over such robust optimization reformulations, approaches, and algorithms. We then develop models and solution approaches for efficient planning of runway utilization under uncertainty. We evaluate them with respect to algorithmic tractability and conservatism of the resulting robust solutions. The derivation of very flexible recoverable robustness approaches leads to NP-hard optimization problems in which two-stage (robust) b-matchings with knapsack constraints need to be determined. In order to solve these tasks, we develop mixed-integer reformulations of the corresponding optimization tasks such that the number of integer variables is drastically reduced. This talk is based on joint work with Norbert Fürstenau (DLR Braunschweig), Lena Hupp, Manu Kapolke, Alexander Martin (all FAU), and Robert Weismantel (ETH Zürich).