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.

翻译：构建满足物理定律的成本最小化流网络是电力、水力、氢能与天然气基础设施设计中的重要问题。我们将该问题建模为基于势能流的混合整数非线性规划。源于势能流模型的约束非凸性，以及表示连接建设决策的二元变量，使得此类规划问题求解极具挑战性。我们针对二元变量的分数松弛提出了一类新颖的有效不等式。进一步证明，对于分数松弛解，该类不等式可在多项式时间内被分离。这使得将这些不等式纳入分支割平面框架成为可能。最后，通过对实际天然气输送网络设计的计算研究，验证了该类不等式的优势。