The goal of this subproject is to develop algorithmic fundamentals for the efficient treatment of switching decisions in gas networks. In particular, this involves the modelling and algorithmics of the switching operations in compressor stations, since these pose a significant source of modelling and runtime complexity.
The set of feasible operating points of a compressor station is, in general, non-convex, in some circumstances even non-connected. However, it can be well approximated by the union of convex polyhedra. Hence, the treatment of such structures in MIPs and MINLPs will be the main focus of research in this subproject. While being motivated by the optimization of gas networks, the methods to be developed will be relevant for many applications of MIPs and MINLPs.
Known techniques for modelling unions of polyhedra as the feasible set of a MIP rely on the inequality description of the underlying polyhedra. In contrast to this, another approach adapted to the geometric properties of the overall set can be considered. More precisely, the goal is to find and analyze a hierarchical description of a non-convex set that provides an as good as possible polyhedral relaxation on each level. This hierarchy can then be used by suitable branching strategies in the branch-and-bound procedure for solving MINLPs.
In the long term, this subproject of SFB/TRR 154 is aiming at the development of real-time methods for obtaining combinatorial decisions. Furthermore, since the transient control of gas networks requires the successive solving of many similar MIPs/MINLPs, reoptimization techniques come into view that use known information from previous optimization problems in order to reduce running time. For these, a detailed analysis of the problem structure and a deeper understanding of the complex MIP/MINLP solving process will be an essential topic of research.
A poster to A04 can be found here.