Potential-based flows constitute a basic model to represent physical behavior in networks. Under natural assumptions, the flow in such networks must be acyclic. The goal of this article is to exploit this property for the solution of corresponding optimization problems. To this end, we introduce several combinatorial models for acyclic flows, based on binary variables for flow directions. We compare these models and introduce a particular model that tries to capture acyclicity together with the supply/demand behavior. We analyze properties of this model, including variable fixing rules. Our computational results show that the usage of the corresponding constraints speeds up solution times by about a factor of 3 on average and a speed-up of a factor of almost 5 for the time to prove optimality.

中文翻译：

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基于势流的组合非循环模型

基于电位的流构成了表示网络中物理行为的基本模型。在自然假设下，此类网络中的流必须是非循环的。本文的目标是利用这个特性来解决相应的优化问题。为此，我们基于流向的二元变量为非循环流引入了几种组合模型。我们比较了这些模型并引入了一个特定模型，该模型试图将非周期性与供需行为一起捕获。我们分析了这个模型的属性，包括变量固定规则。我们的计算结果表明，使用相应的约束将求解时间平均加快了大约 3 倍，并且在证明最优性的时间上加快了近 5 倍。