Valid Cuts for the Design of Potential-based Flow Networks
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.
Keywords
Cite
@article{arxiv.2503.22327,
title = {Valid Cuts for the Design of Potential-based Flow Networks},
author = {Pascal Börner and Max Klimm and Annette Lutz and Marc E. Pfetsch and Martin Skutella and Lea Strubberg},
journal= {arXiv preprint arXiv:2503.22327},
year = {2025}
}