Optimization tasks that involve discrete decisions are ubiquitous in mathematics, industry, and buisness. Examples include the planning of transportation systems, e.g., public transport or gas transportation. Here, one has to choose among a set of discrete options, i.e., to select a certain integral number of objects (e.g., busses, frequencies, etc.) or to turn certain options on/off (e.g., to close a valve). These problems are modelled as mathematical optimization problems. Typically such problems become large in practice and are inherently hard to solve. Thus, array of techniques is needed in order to be able to sucessfully handle them.

The research group Discrete Optimization develops methods, algorithms, and software to deal with such discrete optimization problems. In particular, methods from integer and combinatorial optimization are developed.

Our research group is engaged, among others, in the following projects:

• DFG Collaborative Research Center SFB 666 "Integral sheet metal design with higher order bifurcations - Development, Production, Evaluation"
• DFG Collaborative Research Center SFB 805 "Control of Uncertainties in Load-Carrying Structures in Mechanical Engineering"
• DFG project "SPEAR - Sparse Exact and Approximate Recovery"
• BMWi funded project on "Gas Transport Optimization"

The research group Discrete Optimization had been previously formed by Alexander Martin. Detailed and updated information of their work can be found on their website in Erlangen. There remains a strong collaboration.