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ALOP-Colloquium with Frauke Liers, FAU Erlangen-Nürnberg
5. July 2021 / 16:00 - 17:00
On Monday, July 5, 2021 at 16:00 c.t. Prof. Dr. Frauke Liers with FAU Erlangen-Nuernberg will present her recent work at our colloquium. She will speak on the topic of
Data-Driven Robust Protection for Uncertain Optimization Problems
One way of protecting against uncertainties that occur in real-world applications is to apply and to develop methodologies from robust optimization that determine best possible robust solutions that are feasible regardless of how uncertainties manifest themselves within predefined uncertainty sets. However, it is often non-trivial to construct “suitable” uncertainty sets. In this talk, we present two methodologies in this area.
At first, we introduce a new iterative approach which uses scenario observations to learn more about the uncertainty over time, enabling us to improve our solutions. The goal is to incorporate new information when it arrives and to improve our solution without resolving the entire robust counterpart. We illustrate the effectiveness of our procedure by numerical experiments on mixed-integer optimization instances from popular benchmark libraries as well as on a practical network design problem. The proposed algorithm is able to solve the problem significantly faster than solving equivalent reformulations.
Subsequently, we show that robust protection can also be used for a robust safe approximation of joint chance constrained in DC Optimal Power Flow problems. We propose an approach that replaces probabilistic constraints by robust constraints where the task consists in constructing uncertainty sets from historical data using the scenario approach by Margellos et al. (IEEE Transactions on Automatic Control, 59 (2014)). The experimental tests demonstrate the effectiveness of this method and run times are very fast and lead to high-quality solutions.
The first part is joint with Kevin Aigner, Andreas Bärmann, Kristin Braun, Oskar Schneider, Sebastian Tschuppik (FAU Erlangen-Nürnberg), and Kartikey Sharma and Sebastian Pokutta (ZIB, Berlin). The second part is joint with Kevin Aigner, Jan-Patrick Clarner, and Alexander Martin (FAU Erlangen-Nürnberg, Germany).
This presentation will take place via ZOOM. A link will be e-mailed prior to the event.