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A multi-commodity flow formulation for the generalized pooling problem

机译：广义合并问题的多商品流公式

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摘要

The pooling problem is an extension of the minimum cost network flow problem where the composition of the flow depends on the sources from which it originates. At each source, the composition is known. In all other nodes, the proportion of any component is given as a weighted average of its proportions in entering flow streams. The weights in this average are simply the arc flow. At the terminals of the network, there are bounds on the relative content of the various components. Such problems have strong relevance in e.g. planning models for oil refining, and in gas transportation models with quality constraints at the reception side. Although the pooling problem has bilinear constraints, much progress in solving a class of instances to global optimality has recently been made. Most of the approaches are however restricted to networks where all directed paths have length at most three, which means that there is no connection between pools. In this work, we generalize one of the most successful formulations of the pooling problem, and propose a multi-commodity flow formulation that makes no assumptions on the network topology. We prove that our formulation has stronger linear relaxation than previously suggested formulations, and demonstrate experimentally that it enables faster computation of the global optimum.
机译：合并问题是最小成本网络流问题的扩展，其中流的组成取决于流的来源。在每个来源，其组成都是已知的。在所有其他节点中，任何成分的比例均以其在进入流中的比例的加权平均值给出。该平均值中的权重仅是电弧流。在网络的终端，各个组件的相对内容都有界限。这些问题在例如炼油的规划模型，以及在接收方具有质量限制的天然气运输模型。尽管合并问题具有双线性约束，但是最近在解决一类实例到全局最优方面取得了很大进展。但是，大多数方法都限于所有定向路径的长度最多为3的网络，这意味着池之间没有连接。在这项工作中，我们概括了池化问题的最成功公式之一，并提出了一种多商品流公式，该公式不对网络拓扑进行任何假设。我们证明了我们的公式比以前建议的公式具有更强的线性松弛，并通过实验证明了它可以更快地计算全局最优值。

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