The spatiotemporal imbalance of passenger flows is a prominent characteristic of urban rail transit systems. To match the provided transportation capacity with passenger distribution, this study considers an integer linear programming model to optimize train operation on a Y-type line, including the train timetable, rolling stock circulation plan and virtual coupling/uncoupling strategy that enables trains to switch between different compositions or configurations during operations. To enhance solution efficiency, certain integer decision variables in the model are relaxed to be continuous, and it is proved that this does not affect the optimal value of the model. To account for the dynamic nature of passenger flows, a “prediction + optimization” method with the rolling optimization framework, which utilizes real-time predicted passenger flow data to enable train operations to be performed and adjusted in response, is proposed. Three variants of the proposed model are embedded to meet the real-time requirements of operations. Numerical experiments verify the effectiveness and applicability of our proposed approach, with real-world data from Shanghai Metro Line 5. The computational results demonstrate that our method performs well under operation scenarios with both normal and abnormal passenger flows. Compared to fixed train composition, virtual coupling can perform much better in both peak and off-peak periods.

中文翻译：

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Y型地铁线上虚拟耦合运行的实时列车时刻表


客流时空不平衡是城市轨道交通系统的突出特点。为了使所提供的运输能力与乘客分布相匹配，本研究考虑采用整数线性规划模型来优化 Y 型线路上的列车运行，包括列车时刻表、机车车辆流通计划以及使列车能够在之间切换的虚拟耦合/解耦合策略。操作过程中的不同成分或配置。为了提高求解效率，模型中某些整数决策变量被放宽为连续的，并且证明这并不影响模型的最优值。针对客流的动态特性，提出了一种采用滚动优化框架的“预测+优化”方法，利用实时预测的客流数据来执行和调整列车运行。嵌入了所提出模型的三个变体以满足操作的实时要求。数值实验利用上海地铁5号线的真实数据验证了我们提出的方法的有效性和适用性。计算结果表明我们的方法在正常和异常客流的运营场景下都表现良好。与固定列车编组相比，虚拟耦合无论在高峰期还是非高峰期都能表现得更好。