TU CE GSC CE People at the Graduate School CE Principal Investigators Marc Pfetsch - Discrete Optimization

The research group Discrete Optimization develops methods, algorithms, and software to deal with such discrete optimization problems. Such optimization tasks that involve discrete decisions are ubiquitous in mathematics, industry, and business. 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, an array of techniques is needed in order to be able to sucessfully handle them. In particular, methods from integer and combinatorial optimization are investigated. This involves topics such as symmetry handling in integer programming. Here, we develop methods to handle symmetry, for instance, in assignment based models, thereby exploiting symmetry to speed up the solution process. Further research takes place in Compressed Sensing, where the goal is to find sparse solutions to underdetermined linear equation systems. This is an inherently (hard) discrete problem, and we analyze algorithms to solve this problem. Several projects together with industry and/or engineering sciences are underway, for instance, in gas transportation, optimization of sheet metal structures, and the control of uncertainty in truss structure systems. We are also involved in the development of the branch-and-cut-and-price framework SCIP. SCIP incorporates one of the fastest non-commercial integer programming solvers available and provides the infrastructure for many specialized algorithms developed in our group.

Technische Universität Darmstadt

Graduate School CE

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D-64293 Darmstadt

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