以安全为导向的地铁过饱和线路跳站停车策略优化模型

为缓解高峰时段地铁过饱和线路的客流极端拥挤情况，从安全角度出发，以降低线路客流聚集风险和乘客总等待时间为目的，研究了地铁跳站停车策略优化问题。考虑随时间变化的动态客流需求，通过构建列车跳停、追踪运行、乘客动态加载等约束，推算出跳站停车策略下各车站乘客的动态聚集人数，并设计了独特的客流聚集风险评估函数。在传统只考虑乘客等待时间的列车跳停策略优化模型的基础上，将客流聚集风险纳入到模型的目标函数中，构建了以安全为导向的地铁跳站停车策略优化模型。考虑到模型的非线性特性，设计了适用于问题的可变邻域搜索算法(VNS)，提出了3类邻域新解的产生方式，并设置违反约束的惩罚函数，以提高求解效率。以北京地铁八通线为例，对其早高峰和部分平峰时段(07:00—10:40)下行方向42趟开行列车的停站策略进行了优化实验。结果表明:所提出的模型可在5 min内求解出高质量的列车跳停方案，能有效缓解极端拥堵，提升客运服务质量。对比发现，相对于传统站站停策略，列车跳停策略下，车站最大等待人数由5 299人减少到2 495人，客流聚集风险降低了98.7%。在客运服务水平方面，乘客的平均等待时间由9.49 min降低到9.15 min，降低了3.6%。 

A Safety-oriented Optimization Model for Train Skip-stop Strategy of Oversaturated Metro Lines

In order to alleviate the extreme congestion of oversaturated passenger flow of metro lines during peak hours, an optimization problem of skip-stop strategy for metro trains is studied from the respective of safety, which aims to minimize both risk of passenger congestion and their waiting time. Due to varying passenger demands over time, the number of waiting passengers under the train skip-stop strategy is estimated at each station by considering multiple constraints, including skip-stop operation, train tracking, and dynamic loading of passengers, and a specific evaluation function is formulated to measure the risk of passenger congestion. Based on an optimization method for the traditional train skip-stop strategy only considering passenger waiting time, a safety-oriented optimization model is proposed by integrating risk of passenger congestion into its objective function. Due to nonlinear characteristics of the proposed model, a variable neighborhood search algorithm (VNS) is designed to improve computation efficiency, where three types of novel neighborhood solutions are presented, and a penalty function is set for constraint violations. Taking Beijing Batong metro line as a case study, the proposed optimization model for train skip-stop strategy is tested for the downstream direction with 42 operating trains during morning peak hours and a part of off-peak hours (from 07:00 to 10:40 am). The experiment results show that the proposed algorithm can find high-quality train skip-stop schemes within 5 min, which can significantly relieve passenger congestion and improve service quality. Compared with the scenario where trains stop at all stations, the maximum number of waiting passengers with the train skip-stop strategy decreases from 5 299 to 2 495 over all the stations, and the risk of passenger congestion is reduced by 98.7%. At the same time, the average passenger waiting time decreases from 9.49 min to 9.15 min, reduced by 3.6%.