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arXiv · 2503.22327

Valid Cuts for the Design of Potential-based Flow Networks

Pascal Börner·Max Klimm·Annette Lutz·Marc E. Pfetsch·Martin Skutella·Lea Strubberg
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Abstract

The construction of a cost minimal network for flows obeying physical laws is an important problem for the design of electricity, water, hydrogen, and natural gas infrastructures. We formulate this problem as a mixed-integer non-linear program with potential-based flows. The non-convexity of the constraints stemming from the potential-based flow model together with the binary variables indicating the decision to build a connection make these programs challenging to solve. We develop a novel class of valid inequalities on the fractional relaxations of the binary variables. Further, we show that this class of inequalities can be separated in polynomial time for solutions to a fractional relaxation. This makes it possible to incorporate these inequalities into a branch-and-cut framework. The advantage of these inequalities is lastly demonstrated in a computational study on the design of real-world gas transport networks.

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Pascal Börner, Max Klimm, Annette Lutz, Marc E. Pfetsch, Martin Skutella, Lea Strubberg. 2025-03-28. Valid Cuts for the Design of Potential-based Flow Networks. https://arxiv.org/abs/2503.22327

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