MIP-based Alternating Direction Methods for High-Detail Stationary Gas Transport MINLPs

MIP-based Alternating Direction Methods for High-Detail Stationary Gas Transport MINLPs


The goal of this project is to develop problem-tailored alternating direction methods (ADMs) for highly detailed stationary gas transport models. The theoretical and practical achievements should be used to solve mixed-integer nonlinear models incorporating mixing models for specific gas quality parameters and, especially, highly detailed models of compressor stations (see, e.g., Schmidt et al. 2015).

In recent years, significant advances in the algorithmic optimization of mixed-integer nonlinear and non convex models of stationary gas transport have been made (see, e.g., Koch et al. 2015 or Pfetsch et al. 2015). These advances are mainly based on the decoupling of discrete and nonlinear aspects of the models.

The discrete aspects are typically addressed by using mixed-integer linear (MILP) approaches that are capable of handling switching decisions of the active network elements (like valves, control valves, and compressor stations) as well as of handling approximating formulations of nonlinear functions via piecewise linear modeling techniques. The advances of the last years in this area made it possible to solve MILP models of networks of national scale in a reasonable time limit (see, e.g., Geißler et al. 2013, Geißler et al. 2012, or Domschke et al 2010).

On the other hand, highly detailed nonlinear models (NLPs) have been developed for the description of gas flows in pipes and for the description of compressor stations including compressor drives. These models can also be solved efficiently.

The coupling of these two approaches has been mainly realized by a single-stage approach that does not incorporate a reasonable feedback loop between the MILP and NLP models. To be more specific, the MILP models yield discrete controls of the active network elements together with an approximation of the resulting physical gas flow. These outcomes are then fixed and serve as input for the highly detailed NLP models that are then able to validate the physical and technical feasibility of the given discrete controls. After a positive validation this yields a feasible solution of the underlying highly detailed mixed-integer nonlinear model. Unfortunately, there are only a few strategies of how to proceed if this is not the case.

The strategy of this project is the coupling of the MILP and NLP models by using ADMs. However, in order to use these kinds of methods it is necessary to reformulate the underlying MINLP model in an appropriate way.

People involved

Björn Geißler
Antonio Morsi
Lars Schewe
Martin Schmidt


For further details about this project please contact Lars Schewe (lars.schewe[at]

Supported by

Deutsche Forschungsgemeinschaft, Sonderforschungsbereich/Transregio 154


Solving power-constrained gas transportation problems using an MIP-based alternating direction method. Björn Geißler, Antonio Morsi, Lars Schewe, and Martin Schmidt. In Computers & Chemical Engineering, 2015, Vol. 82, pages 303-317. DOI: 10.1016/j.compchemeng.2015.07.005. Preprint (11/2014): Optimization Online.