标题： 多趟准网络流模型用于垂直对齐优化 显示英文标题

标题： Multi-Haul Quasi Network Flow Model for Vertical Alignment Optimization

摘要： 道路设计的垂直对齐优化问题旨在生成一条新道路的垂直对齐，以最小成本满足安全和设计约束。 我们提出了一种新的模型，称为多趟准网络流（MH-QNF），用于垂直对齐优化，该模型提高了之前混合整数线性规划模型的准确性和可靠性。 我们评估了新模型与该领域两种最先进的模型：完整运输图（CTG）和准网络流（QNF）模型的性能。 数值结果表明，在1%的相对误差范围内，所提出的模型具有鲁棒性，并且比CTG模型解决的测试问题多93%以上，而QNF模型则没有解决任何问题。 此外，MH-QNF模型求解问题的速度大约是CTG模型的8倍。 显示英文摘要

摘要： The vertical alignment optimization problem for road design aims to generate a vertical alignment of a new road with a minimum cost, while satisfying safety and design constraints. We present a new model called multi-haul quasi network flow (MH-QNF) for vertical alignment optimization that improves the accuracy and reliability of previous mixed integer linear programming models. We evaluate the performance of the new model compared to two state-of-the-art models in the field: the complete transportation graph (CTG) and the quasi network flow (QNF) models. The numerical results show that, within a 1% relative error, the proposed model is robust and solves more than 93% of test problems compared to 82% for the CTG and none for the QNF. Moreover, the MH-QNF model solves the problems approximately 8 times faster than the CTG model.