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Convex reformulations for solving a nonlinear network design problem

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Abstract

We consider a nonlinear nonconvex network design problem that arises, for example, in natural gas or water transmission networks. Given is such a network with active and passive components, that is, valves, compressors, control valves (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes in the network. The active elements are associated with costs when used. Besides flow conservation constraints in the nodes, the flow must fulfill nonlinear nonconvex pressure loss constraints on the arcs subject to potential values (i.e., pressure levels) in both end nodes of each arc. The problem is to compute a cost minimal setting of the active components and numerical values for the flow and node potentials. We examine different (convex) relaxations for a subproblem of the design problem and benefit from them within a branch-and-bound approach. We compare different approaches based on nonlinear optimization numerically on a set of test instances.

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Acknowledgments

We are grateful to Open Grid Europe GmbH (OGE, Essen/Germany) for supporting our work. The second coauthor conducted parts of this research under a Konrad-Zuse-Fellowship. We thank two anonymous referees for their various helpful comments on our manuscript.

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Authors and Affiliations

  1. Zuse Institute Berlin, Takustr. 7, 14195, Berlin, Germany

    Jesco Humpola

  2. Helmut Schmidt University/University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043, Hamburg, Germany

    Armin Fügenschuh

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  1. Jesco Humpola
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  2. Armin Fügenschuh
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Correspondence to Armin Fügenschuh.

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Humpola, J., Fügenschuh, A. Convex reformulations for solving a nonlinear network design problem. Comput Optim Appl 62, 717–759 (2015). https://doi.org/10.1007/s10589-015-9756-2

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