Bilevel programming (BP) is a powerful mathematical framework for modeling hierarchical decision-making processes involving two players: a leader and a follower. In energy network design, for example, the leader aims to build a robust network that mitigates failures caused by the follower’s actions. A key characteristic of such applications is the presence of symmetries. For instance, a symmetric network naturally leads to symmetric failure scenarios, which are reflected in BP models. However, current BP software can neither detect nor exploit these symmetries. As a result, despite BP’s strong modeling capabilities, existing technology can only handle relatively small-scale problems.
InformationIn the SymBi project (Exploiting Symmetries for Faster Bilevel Optimization Algorithms), we address this limitation by developing a general mathematical theory of symmetries in BP and efficient algorithms for symmetry detection and exploitation. While the related field of mixed-integer programming (MIP) primarily uses symmetries to eliminate redundant parts of the solution space, SymBi goes further: it aims to enhance other components of BP solvers, such as cutting planes, to achieve a stronger coupling between leader and follower decisions.
We are seeking for a motivated and enthusiastic Postdoc (PD) researcher to join the Combinatorial Optimization group (https://www.tue.nl/en/research/research-groups/mathematics/statistics-probability-and-operations-research/combinatorial-optimization-1) under the supervision of dr. Christopher Hojny, assistant professor. The research activities of the PD will include
- defining a mathematically sound notion of symmetries for bilevel optimization problems,
- developing a novel theory for exploiting symmetries that is tailored for bilevel optimization problems, and
- implementing and testing the developed algorithms for solving benchmark problems.
Next to the research tasks, the PD will be asked to assist, for a small percentage of their time, with educational tasks (course support and supervision of students).
The SymBi project is a collaborative project between dr. Christopher Hojny (Eindhoven University of Technology) and prof. dr. Martin Schmidt (Trier University, Germany). Both groups will work closely together on the project to create synergies between the different expertise of the different groups. This synergy will not only yield a novel theoretical foundation for symmetries in BP but also advance state-of-the-art BP software—enabling researchers and practitioners in fields such as economics and engineering to solve complex problems significantly faster.