基于多编组的列车满载率均衡化方法研究

针对多编组均衡发车导致的大小编组列车利用率不均的问题，本文构建了轨道交通多编组列车开行方案双层规划模型.上层模型以大小编组发车频率为决策变量，乘客出行费用和企业运营成本最小为目标；下层模型以列车编组和发车间隔为决策变量，大小编组列车间的满载率均衡程度最大为目标，并设计嵌套遗传算法求解.算例分析表明：当列车编组和发车频率一定时，大小编组列车均衡发车时平均满载率相差 50%，非均衡发车时两者仅相差 0.8%，这说明非均衡发车模式可以有效提高列车满载率均衡性；大小编组列车均衡发车时，列车编组辆数不宜相差过大，非均衡发车时可以通过调整发车间隔的方法提高列车满载率的时空均衡性.

Optimization of Multi-group Train Operations for Transit Urban Rail with Even Load

Multi-group train operations is one important part of the network operation technologies. In order to solve the problem that the train with fewer vehicles is over oversaturated and the train with more vehicles has a lower load factor, a bi-level programming model is established considering the equilibrium of load factor between different trains. The constraints are policy headway, platform length, maximum load and fleet size. The upper-level model is an optimization model of train plan, which is used to determine the optimal frequencies of two types of trains. The lower-level model is an optimization model of equilibrium of load factor, which is to determine the optimal formation plans and departure interval. And a nested genetic algorithm is also proposed. The results indicate that when the train formation and frequency is fixed, the average load of the trains under the even headways is 50%, the difference is only 0.8% under the uneven headways. The number of vehicles of two kinds of trains has minor differences can improve the equilibrium of train load factor under even headways. Besides, adjusting the headways between different train formations under uneven headways can realize the equilibrium of load factor in time and space.