We study combinatorial structures in large-scale mixed-integer (nonlinear) programming problems arising in gas network optimization. We propose a preprocessing strategy exploiting the observation that a large part of the combinatorial complexity arises in certain subnetworks. Our approach analyzes these subnetworks and the combinatorial structure of the flows within these subnetworks in order to provide alternative models with a stronger combinatorial structure that can be exploited by off-the-shelve solvers. In particular, we consider the modeling of operation modes for complex compressor stations (i.e., ones with several in- or outlets) in gas networks. We propose a refined model that allows to precompute tighter bounds for each operation mode and a number of model variants based on the refined model exploiting these tighter bounds. We provide a procedure to obtain the refined model from the input data for the original model. This procedure is based on a nontrivial reduction of the graph representing the gas flow through the compressor station in an operation mode. We evaluate our model variants on reference benchmark data, showing that they reduce the average running time between 10% for easy instances and 46% for hard instances. Moreover, for three of four considered networks, the average number of search tree nodes is at least halved, showing the effectivity of our model variants to guide the solver’s search.

我们研究天然气网络优化中出现的大规模混合整数（非线性）规划问题中的组合结构。我们提出了一种预处理策略，利用观察到的组合复杂性的很大一部分出现在某些子网络中。我们的方法分析这些子网络和这些子网络内流的组合结构，以提供具有更强组合结构的替代模型，可供现成的求解器利用。特别是，我们考虑了气体网络中复杂压缩机站（即具有多个入口或出口的压缩机站）的运行模式建模。我们提出了一个改进的模型，该模型允许为每种操作模式预先计算更严格的边界，以及基于利用这些更严格边界的改进模型的许多模型变体。我们提供了从原始模型的输入数据中获取精炼模型的程序。该过程基于表示在操作模式下通过压缩机站的气体流量的图表的非平凡缩减。我们在参考基准数据上评估了我们的模型变体，表明它们将简单实例的平均运行时间减少了 10%，而困难实例的平均运行时间减少了 46%。此外，对于四个考虑的网络中的三个，搜索树节点的平均数量至少减半，这表明我们的模型变体指导求解器搜索的有效性。我们在参考基准数据上评估了我们的模型变体，表明它们将简单实例的平均运行时间减少了 10%，而困难实例的平均运行时间减少了 46%。此外，对于四个考虑的网络中的三个，搜索树节点的平均数量至少减半，这表明我们的模型变体指导求解器搜索的有效性。我们在参考基准数据上评估了我们的模型变体，表明它们将简单实例的平均运行时间减少了 10%，而困难实例的平均运行时间减少了 46%。此外，对于四个考虑的网络中的三个，搜索树节点的平均数量至少减半，这表明我们的模型变体指导求解器搜索的有效性。