Bilevel optimization is a rather young but very active sub-field of mathematical optimization. The main reason is that bilevel optimization problems can serve as a powerful tool for modeling hierarchical decision-making processes, which arise in various real-world applications such as in critical infrastructure defense, transportation, or energy. However, the nested structure of bilevel problems makes them intrinsically hard to solve—even if all parameters of the problem are exactly known. Further challenges arise if problems under uncertainty are considered.

In this talk, we begin with a brief introduction to the key concepts of bilevel optimization, covering the structure, characteristics, and commonly used reformulations of these problems. We then explore how techniques from robust optimization can be used to tackle bilevel problems under uncertainty. In particular, we highlight that the sources of uncertainty in bilevel optimization are much richer compared to classic, i.e., single-level, problems since not only the problem data but also the (observation of the) decisions of the two players can be subject to uncertainty.

Finally, we discuss recent algorithmic advances for solving mixed-integer linear bilevel problems with a binary lower level and a Gamma-robust treatment of lower-level objective uncertainty. To solve these Gamma-robust bilevel problems, we present an exact and problem-tailored branch-and-cut approach as well as a heuristic framework. The latter relies on solving a linear number of deterministic bilevel problems so that no problem-specific tailoring is required.