Our research group is concerned with both the theory and the practice of combinatorial optimisation.
Unfortunately, the modern tools and methods of combinatorial (or: discrete) optimisation are mostly unknown outside computing departments, so that many opportunities for better solutions and/or shorter solving times are wasted, especially by the widespread mistaken belief that (NP-)hard problems cannot be solved at all or can at best only be tackled by greedy algorithms or by other sub-optimal algorithms.
On the theoretical side, we address the following research issues:
- Global Constraints: specification and synthesis; reification; AUTOMATON, CUMULATIVE, and TREE constraints
- Constraint-Based Local Search: MiniZinc back-end; set variables and set constraints; specification of constraints via automata and monadic existential second-order logic; neighbourhood design; massive instance data
- Symmetry in Models and Search: detection and exploitation, in order to avoid exploring redundant parts of the search space
- Constraint-Based Modelling: string variables and constraints; relation variables; symmetry; the constraint-based modelling language ESRA
On the practical side, we apply combinatorial optimisation in hard real-world tasks:
- Air Traffic Management, with the European Organisation for the Safety of Air Navigation (EuroControl): airspace sectorisation; contingency planning; air-traffic complexity resolution in multi-sector planning
- Testing, Verification, and Analysis of Software: string variables and constraints; test-case generation
- Wireless Sensor Networks: network configuration
- Computational Biology: construction of phylogenetic super-trees
- Computational Finance: design of synthetic CDO squared portfolios