流量加油选址问题模型的强度分析及循环路径扩展
The Strength of Flow Refueling Location Problem Formulations and an Extension to Cyclic Routing
AI总结：
针对偏差FRLP模型，研究比较了两种典型模型的LP松弛强度，证明其一界更紧；放宽往返同路径假设提出循环FRLP，扩展模型并设计分支切割算法，实验显示其在加州网络实例中设施需求减少30%。
摘要：
流量加油选址问题（FRLP）是一种用于确定有限续航里程车辆（如氢燃料电池车和电动车）最优加油站位置的典型模型。其一个显著扩展——偏差FRLP，考虑了驾驶员可能偏离偏好路线去加油或充电的情况。尽管针对该扩展的多种数学规划模型求解技术已被深入探索，但这些模型之间的关系和强度缺乏理论洞察。在本研究中，针对偏差扩展，我们研究了文献中两种突出的FRLP模型，并从线性规划（LP）松弛的角度比较了它们的强度。我们证明，其中一种模型的LP松弛产生的界至少与另一种模型的界一样紧，这可能解释了其观测到的优越性能。基于这些洞察，我们解决了FRLP中一个常见的建模假设：要求驾驶员在往返行程中使用相同路径。具体而言，我们放宽了这一假设，引入了循环FRLP，其中驾驶员在每个方向上可使用不同路径。我们展示了现有模型如何自然扩展以适应此设置，并描述了一种分支切割算法来求解该问题。我们提供了数值实验，突出了这种非对称路径规划的优势。例如，在基于加州网络的实例中，循环FRLP服务所有需求所用的设施比原始FRLP少30%。
英文摘要：
The Flow Refueling Location Problem (FRLP) is a stylized model for determining the optimal placement of refueling stations for vehicles with limited travel ranges, such as hydrogen fuel cell vehicles and electric vehicles. A notable extension, the deviation FRLP, accounts for the possibility that drivers may deviate from their preferred routes to refuel or recharge. While solution techniques based on various mathematical programming formulations have been thoroughly explored for this extension, there is a lack of theoretical insights into the relationships and strengths of these formulations. In this work, for the deviation extension, we study two prominent FRLP formulations from the literature and compare their strengths in terms of linear programming (LP) relaxations. We show that the LP relaxation of one formulation yields a bound that is at least as tight as that of the other, which may explain its observed superior performance. Building on these insights, we address a common modeling assumption in the FRLP that requires drivers to use the same paths for their outbound and inbound trips. Specifically, we relax this assumption and introduce the cyclic FRLP, where drivers may use different paths in each direction. We show how existing formulations can be naturally extended to accommodate this setting and describe a branch-and-cut algorithm to solve the problem. We provide numerical experiments highlighting the benefits of such asymmetric routing. For example, in an instance based on the Californian network, the cyclic FRLP serves all demands using 30% fewer facilities than the original FRLP.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
