Improved optimization models for potential-driven network flow problems via ASTS orientations
(2019)
The class of potential-driven network flow problems provides important models for a range of infrastructure networks. For real-world applications, they need to be combined with integer models for switching certain network elements, giving rise to hard-to-solve MINLPs. We observe that on large-scale real-world meshed networks the relaxations usu-
ally employed are rather weak due to cycles in the network. To address this situation, we introduce the concept of ASTS orientations, a generalization of bipolar orientations, as a combinatorial relaxation of feasible solutions of potential-driven flow problems, study their structure, and
show how they can be used to strengthen existing relaxations and thus provide improved optimization models. Our computational results indicate that ASTS orientations can be used to derive much stronger bounds on the flow variables than existing bound tightening methods. We also
show that our proposed model extensions yield significant performance improvements for an existing state-of-the-art MILP model for large-scale gas networks.
In commodity transport networks such as natural gas, hydrogen and water networks, flows arise from nonlinear potential differences between the nodes, which can be represented by so-called “potential-driven” network models. When operators of these networks face increasing demand or the need to handle more diverse transport situations, they regularly seek to expand the capacity of their network by building new pipelines parallel to existing ones (“looping”). The paper introduces a new mixed-integer non-linear programming (MINLP) model and a new non-linear programming (NLP) model and compares these with existing models for the looping problem and related problems in the literature, both theoretically and experimentally. On this basis, we give recommendations about the circumstances under which a certain model should be used. In particular, it turns out that one of our novel models outperforms the existing models.
Moreover, the paper is the first to include the practically relevant option that a particular pipeline may be looped several times.
We discuss drift-diffusion models for charge-carrier transport in organic semiconductor de- vices. The crucial feature in organic materials is the energetic disorder due to random alignment of molecules and the hopping transport of carriers between adjacent energetic sites. The for- mer leads to so-called Gauss-Fermi statistics, which describe the occupation of energy levels by electrons and holes. The latter gives rise to complicated mobility models with a strongly nonlin- ear dependence on temperature, density of carriers, and electric field strength. We present the state-of-the-art modeling of the transport processes and provide a first existence result for the stationary drift-diffusion model taking all of the peculiarities of organic materials into account. The existence proof is based on Schauder’s fixed-point theorem. Finally, we discuss the numerical discretization of the model using finite-volume methods and a generalized Scharfetter-Gummel scheme for the Gauss-Fermi statistics.
This paper deals with the analysis of an instationary drift-diffusion model for organic semicon- ductor devices including Gauss–Fermi statistics and application-specific mobility functions. The charge transport in organic materials is realized by hopping of carriers between adjacent ener- getic sites and is described by complicated mobility laws with a strong nonlinear dependence on temperature, carrier densities and the electric field strength.
To prove the existence of global weak solutions, we consider a problem with (for small den- sities) regularized state equations on any arbitrarily chosen finite time interval. We ensure its solvability by time discretization and passage to the time-continuous limit. Positive lower a priori estimates for the densities of its solutions that are independent of the regularization level en- sure the existence of solutions to the original problem. Furthermore, we derive for these solutions global positive lower and upper bounds strictly below the density of transport states for the densi- ties. The estimates rely on Moser iteration techniques.