Since its introduction in the early 2000s, robust optimization with budget uncertainty has received a lot of attention. This is due to the 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 when solving robust integer problems due to its weak linear relaxation.

To overcome the problems arising from the weak formulation, we propose a bilinear formulation for robust binary programming, which is as strong as theoretically possible. From this bilinear formulation, we derive strong linear formulations as well as structural properties for robust binary optimization problems, which we use within a tailored branch & bound algorithm.

We test our algorithm’s performance together with other approaches from the literature on a diverse set of “robustified” real-world instances from the MIPLIB 2017. Our computational study, which is the first to compare many sophisticated approaches on a broad set of instances, shows that our algorithm outperforms existing approaches by far. Furthermore, we show that the fundamental structural properties proven in this paper can be used to substantially improve the approaches from the literature.

This highlights the relevance of our findings, not only for the tested algorithms but also for future research on robust optimization. Part of the programme of the research training group UnRAVeL is a series of introductory lectures on the topics of "randomness" and "uncertainty" in UnRAVeL’s research thrusts: Algorithms and complexity, verification, logic and languages, and their application scenarios. The main aim is to

Dear all, this is a reminder for Christina Büsing's talk A Branch & Bound Algorithm for Robust Binary Optimization with Budget Uncertainty <https://www.unravel.rwth-aachen.de/cms/UnRAVeL/Das-Graduiertenkolleg/Aktuelle-Veranstaltungen/~tbahn/Ringvorlesung-/?lidx=1> taking place *today at 16:30* in room 5053.2 and on Zoom. Please find the details below. provide doctoral researchers as well as master students a broad overview of the subjects of UnRAVeL. Science undergoes continuous change and lives from the constant quest for novel and better results, which are presented at conferences and in journals. This year, 10 UnRAVeL professors will present some of their most recent research successes. Everyone interested, in particular doctoral researchers and master students, are invited to attend the UnRAVeL lecture series 2022 and engage in discussions with the researchers. The talks take place on Tuesdays, 16:30–18:00 in room 5053.2 in the ground floor of building E2. All events are hybrid. To join remotely, please use https://rwth.zoom.us/j/96003885007?pwd=aUczMVdVU0ZXVGtQUFpwQnJHQUFhUT09 / Meeting ID: 960 0388 5007 / Passcode: 273710 Please find a list of all upcoming talks on the UnRAVeL website <https://www.unravel.rwth-aachen.de/cms/UnRAVeL/Studium/~pzix/Ringvorlesung-Veranstaltung/?lidx=1> and below: * 21/06/2022 Sebastian Trimpe: Uncertainty Bounds for Gaussian Process Regression with Applications to Safe Control and Learning * 28/06/2022 Britta Peis: Stackelberg Network Pricing Games * 05/07/2022 Gerhard Lakemeyer: Tractable Reasoning in First-Order Knowledge Bases We are looking forward to seeing many of you in the UnRAVeL survey lecture "What's New in UnRAVeL?". Best regards, Andreas Klinger, Birgit Willms, and Tim Seppelt Logo