Linear and Nonlinear Integer Optimization
Integer programming deals with optimization problems where goods or decisions are indivisible. Many problems can efficiently be formulated by a linear objective function and linear constraints. In some applications, however, non-linear and discrete components interact in complex systems.
Many problems in telecommunications, traffic, or chip design can be formulated as so-called linear mixed integer programs (MIPs). But precisely because this method is so versatile, the demand for better and better solvers is constantly growing. We develop and improve fundamental algorithms in order to be able to solve MIPs in a generic way, independent of special problem structures.
Non-linear mixed integer programs (MINLPs) arise in applications such as revenue (= price x demand) optimization in public transport, the design and the operation of gas, water, and sewer networks, in which not only flow volumes, but also pressure and similar quantitities play a role, or in ore blending problems in the mining industry. Such problems are even more difficult and less well studied than MIPs. We work on both, the design of techniques to exploit special structures to solve particular real-world instances and on the improvement of general solution algorithms.