轨道列车时刻表问题研究综述

广泛的实践应用和复杂的计算挑战，使得轨道列车时刻表优化问题，多年来一直是交通运 输及运筹管理学界的热点研究问题。作为轨道交通运营规划的一个子阶段，列车时刻表向上与 线路规划(或开行方案)、向下与动车组调度融合，可以得到多个延伸的研究选题。在特定的时空 网络中，列车时刻表设计就是为每个列车确定一条无冲突的运行路径，使基于用户的度量指标如 乘客候车时间，或企业的度量指标如运营费用达到最优。对于没有列车越行和停站模式给定的 情况，通过整数变量可以完整地刻画列车时刻表模型，但如果考虑列车越行或列车停站决策，则 需要引入列车在车站出发顺序或停车决策的0-1变量。一般而言，列车时刻表问题的数学模型是 一类典型的大规模、多目标、强耦合的NP完全问题。算法设计是列车时刻表问题最为重要和困 难的部分。对于问题较简单或规模较小的情况，常用方法是对原有复杂问题进行适当简化和(或) 对难处理表达式进行合理修改，然后使用先进的计算架构和商用优化软件求解更新后模型。当 然，分支定界和动态规划这两类直接分解算法，是求解列车时刻表问题的重要方法。对于问题复 杂和规模庞大的情况，以拉格朗日和列生成为代表的对偶分解算法，则是求解列车时刻表问题的 最佳选择。未来，探讨列车时刻表与各种现实需要(如设施维修)，以及时变票价和客票分配等因 素之间的深度融合，是一个有价值的研究方向；其次，研究网络环境下列车时刻表问题，将是一个 非常有意义的研究选题；最后，应进一步设计集成了问题特点与现代优化技术的各类求解算法， 开发能够完全应用于实际运营的商用软件。

Spatial Feature of Mandatory Lane Changing and Its Impact on Traffic Flow at Diverging Area

To examine the vehicle following and lane- changing behaviors at multiple lane diverging area, this study classified the mandatory lane-changing behavior into aggressive and mild mandatory lane-changing behaviors. Based on the relation between the desire of lane-changing and vehicle position, this study quantified the transformation conditions of the aggressive and mild mandatory lane- changing behaviors. The rules of lanechanging behavior of diverging vehicle were proposed by optimizing the deceleration factor of car- following model. The car- following and lane-changing model for the multiple lane diverging area was then developed and the critical parameters were calibrated. The model was validated by the real data. The result shows that the spatial distribution of diverging vehicles at each lane have significant impact on the stability of traffic flow. When the leftmost lane has high density of diverging vehicles at, the middle two lanes would experience significant speed. The maximum reduction rate of vehicle speed was 51.4% , and takes longer time to restore the traffic flow stability. Based on the analysis of four different scenarios, the average speed could be significantly improved by reasonable spatial distribution of diverging vehicles.