## Sufficient Pruning Conditions for MINLP in Gas Network Design

Please always quote using this URN: urn:nbn:de:0297-zib-53489
• One quarter of Europe’s energy demand is provided by natural gas distributed through a vast pipeline network covering the whole of Europe. At a cost of 1 million Euros per kilometer the extension of the European pipeline network is already a multi billion Euro business. Therefore, automatic planning tools that support the decision process are desired. We model the topology extension problem in gas networks by a mixed-integer nonlinear program (MINLP). This gives rise to a so-called active transmission problem, a continuous nonlinear non-convex feasibility problem which emerges from the MINLP model by ﬁxing all integral variables. In this article we offer novel sufficient conditions for proving the infeasibility of this active transmission problem. These conditions can be expressed in the form of a mixed-integer program (MILP), i.e., the infeasibility of a non-convex NLP can be certiﬁed by solving an MILP. These results provide an efficient bounding procedure in a branch-and-bound algorithm. Our computational results demonstrate a substantial speed-up for the necessary computations.

$Rev: 13581$