基于动态规划的列车节能运行两阶段优化方法

针对地铁列车多站间节能运行优化问题，提出将列车节能驾驶优化过程和时刻表优化过程结合的两阶段优化方法，分别求解两优化过程的全局最优解，从而获取列车在多站间运行的最优操纵策略. 首先考虑节能和节时两个目标，构建列车节能驾驶多目标优化模型，结合动态规划多阶段寻优思路，建立一系列包含多个过程指标及约束的子阶段求解模型，逆序求解后获取列车站间运行最优操纵策略的Pareto前沿；其次建立时刻表优化模型，基于动态规划方法，调用各站间Pareto前沿，搜索站间运行时间最优分配方案；最后以北京地铁亦庄线为例，验证两阶段优化方法的有效性和高效性. 试验结果表明，与最速操纵策略相比，经过两个阶段优化后的列车牵引能耗分别降低了53.87%和54.69%，两阶段优化过程分别用时258.90 s和0.08 s. 

Two-Stage Optimization Method of Train Energy-Efficient Operation Based on Dynamic Programming

Focusing on the problem of train energy-efficient operation between multi-sections in urban rail transit, a two-stage optimization method was proposed by integrating the processes of energy-efficient driving optimization and timetable optimization. To obtain the optimum train driving strategy between multi-sections, each process was solved with global optimum solutions, respectively. First, to realize energy saving and time saving, a multi-objective energy-efficient driving model was constructed. Utilizing the multistage-based dynamic programming searching approach, a series of sub-stage models that contain multiple objects and constrains were constructed. The Pareto front of the optimum driving strategy was generated by inverse order method. Then, a timetable optimization model was constructed, in which the Pareto front of sections was applied, and the optimum running time allocation of multi-sections was searched by dynamic programming approach. A case study of Yizhuang urban rail line in Beijing was conducted to verify the effectiveness and efficiency of the two-stage optimization method. Compared with the flat-out running strategy, the optimization of two stages resulted in 53.87% and 54.69% energy saving improvement respectively; the calculation time of two process was 258.90 s and 0.08 s respectively.