We present a solution algorithm for problems from steady-state gas transport optimization. Due to nonlinear and nonconvex physics and engineering models as well as discrete controllability of active network devices, these problems lead to hard nonconvex mixed-integer nonlinear optimization models. The proposed method is based on mixed-integer linear techniques using piecewise linear relaxations of the nonlinearities and a tailored alternating direction method. In addition to most other publications in the field of gas transport optimization, we do not only consider pressure and flow as main physical quantities but further incorporate heat power supplies and demands as well as a mixing model for different gas qualities. We demonstrate the capabilities of our method on Germany's largest transport networks and hereby present numerical results on the largest instances that were ever reported in the literature for this problem class.
Technical report, (a) Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Discrete Optimization, Cauerstraße 11, 91058 Erlangen, Germany; (b) Energie Campus Nürnberg, Fürther Straße 250, 90429 Nürnberg, Germany. November 2014.