The optimization of energy networks, such as water or gas networks, is a key problem in energy supply and becomes more and more important in a transition to nuclear-free supply. Energy networks include continuous aspects such as the flow of water or gas in pipes as well as discrete aspects such as the switching of valves, pumps or compressors. From a mathematical point of view partial or at least ordinary differential equations are necessary to appropriately model the physics of these flows resulting even in simplified settings in non-linear non-convex constraints. These together with the switching components lead to mixed integer nonlinear optimization problems (MINLPs).
In this talk we look into the details of these MINLPs and address the question whether they are solvable by applying techniques from mixed integer programming. Computational results on real-world instances from gas and water supply will contribute to a positive answer, but will simultaneously give hints to future mathematical challenges.Shell Lectures Series are made possible through the generous support of the Shell Oil Company.