面向客流聚集风险防控的城轨列车实时调度模型与算法

In the post-pandemic era, the passenger volume of urban rail transit has rebounded rapidly and continues to increase. To address the problem of unexpectedly heavy passenger flows caused by train delays in urban rail transit, we propose a mathematical model and algorithm for real-time train rescheduling with station and carriage-congestion control. Based on the condition that the line operation is disrupted by abnormal disturbances, we propose a mixed-integer linear programming model, that minimizes line (station) congestion and considers carriage congestion as a model constraint for the real -time train rescheduling problem to jointly optimize the train stop – skipping strategy and train timetable. To improve the computational efficiency, we introduce a variable neighborhood search (VNS) algorithm to solve our model. First, based on the relaxation principle of linear programming, we design a heuristic rule to generate the initial solution of the model. Subsequently, we use the VNS algorithm to iteratively search for the near-optimal solution, which is also the final solution of our mathematical model, in the neighborhood of the initial solution. A numerical experiment based on the operation data of the Yizhuang line of the Beijing Metro is performed. The simulation results indicate that, compared with the benchmark, i.e., the train timetable under the standard non-skip strategy (the train stops at every station), the final solution of our model reduces the line congestion and maximum section passenger flow by 67.56% and 38.28%, respectively, within approximately 1 min of computing time, thus satisfying the real-time requirement. The experiment results verify that our model and proposed algorithm can reduce station congestion and balance the section distribution of passenger flow; hence, they are advantageous for solving the problem of abrupt heavy passenger flows caused by train delays to control the spread of epidemics.