Combination of Nonlinear and Linear Optimization of Transient Gas Networks

Authors:
Pia Domschke;Bjorn Geißler;Oliver Kolb;Jens Lang;Alexander Martin;Antonio Morsi
Affiliations:
Department of Mathematics, Technische Universität Darmstadt, 64289 Darmstadt, Germany;Department of Mathematics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany;Department of Mathematics, Technische Universität Darmstadt, 64289 Darmstadt, Germany;Department of Mathematics, Center of Smart Interfaces, and Graduate School Computational Engineering, Technische Universität Darmstadt, 64289 Darmstadt, Germany;Department of Mathematics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany;Department of Mathematics, Technische Universität Darmstadt, 64289 Darmstadt, Germany
Venue:
INFORMS Journal on Computing
Year:
2011

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Abstract

In this paper, we study the problem of technical transient gas network optimization, which can be considered a minimum cost flow problem with a nonlinear objective function and additional nonlinear constraints on the network arcs. Applying an implicit box scheme to the isothermal Euler equation, we derive a mixed-integer nonlinear program. This is solved by means of a combination of (i) a novel mixed-integer linear programming approach based on piecewise linearization and (ii) a classical sequential quadratic program applied for given combinatorial constraints. Numerical experiments show that better approximations to the optimal control problem can be obtained by using solutions of the sequential quadratic programming algorithm to improve the mixed-integer linear program. Moreover, iteratively applying these two techniques improves the results even further.