基于虚拟编组的城轨列车时刻表优化方法

李岩; 巩亮; 许得杰; 潘星; 胡晨皓

doi:10.3963/j.jssn.1674-4861.2024.03.008

基于虚拟编组的城轨列车时刻表优化方法

doi: 10.3963/j.jssn.1674-4861.2024.03.008

兰州交通大学交通运输学院兰州 730070

基金项目:

国家自然科学基金项目 72261025

甘肃省高等学校创新基金项目 2021B-103

甘肃省教育厅双一流重大科研项目 GSSYLXM-04

详细信息

作者简介:
李岩（1997—），硕士研究生. 研究方向：轨道交通运行图优化. E-mail: liyan19970618@126.com

通讯作者:
许得杰（1986—），博士，副教授. 研究方向：轨道交通运输组织优化、交通网络配流. E-mail: xudejie126@126.com

中图分类号: U292.4
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出版历程
- 收稿日期: 2023-08-18
- 网络出版日期: 2024-10-21

A Timetable Optimization Method for Urban Train Transit Based on Virtual Coupling

School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China

摘要

摘要: 针对高峰时段城市轨道交通客流与运力不匹配问题，考虑城市轨道交通客流时空分布特征、交通过饱和状态和车场车底数量限制，提出了基于虚拟编组的城轨列车时刻表优化方法。构造动态客流累计需求函数，预测不同时段客流量；考虑乘客需求、发车间隔、运行时间、车底数量、车底接续等约束条件，以列车在首站的发车时刻和各车次的编组方案为决策变量，以乘客平均等待时间与列车走行里程最小化为优化目标，建立了基于虚拟编组的城轨列车时刻表优化模型。针对原问题包含大量耦合约束条件，利用拉格朗日松弛算法将耦合性约束吸收至目标函数，将原问题分解为2个独立路径的子问题，降低问题的复杂度；再利用商业求解器求解子问题的下界解，并设计启发式算法求解子问题的上界可行解，得到原问题解的上下界。以上海地铁某线路为算例进行验证，结果表明：在高峰时段，所提动态客流累计需求函数与客流实际到达规律拟合度较高；固定编组模式下，非均匀发车时刻表相比于均匀发车时刻表，可降低24.15%的乘客平均等待时间和51.73%的滞留乘客等待时间；而所提虚拟编组列车时刻表相比于固定编组模式下非均匀发车时刻表，不仅可减少0.33%的列车运行里程，还可进一步减少16.95%的乘客平均等待时间和6.03%的滞留乘客等待时间。
- 城市交通 /
- 城市轨道交通 /
- 列车时刻表 /
- 拉格朗日松弛算法 /
- 动态客流需求 /
- 虚拟编组
Abstract: To solve the mismatch between train capacity and demand during peak hours, a timetable optimization method for urban train transit based on virtual coupling technical is proposed, incorporating spatiotemporal characteristics of passenger flow, oversaturation of trains during peak hours, and the limitation of the number of rolling stocks. A dynamic passenger flow cumulative demand (PFCD) function is proposed to pedict the passenger flow at different hours. Then, the schedule optimization model for urban rail transit based on the virtual coupling is established, in which, the departure time of trains at the first station and the marshaling scheme of each train are decision variables and the average waiting time (AWT) of passengers and the train travel mileage (TTM) are minimized under constraints such as passenger demand in different hours, departure interval, running time, number of rolling stocks, rolling stock circulation, etc. Lagrangian relaxation is introduced to reduce the complexity of the problem by absorbing the coupling constraints into the objective, and the original problem is decomposed into two independent subproblems. By using a commercial solver and the designed heuristic algorithm, the lower bound and upper bound of the problems are found. A metro line in Shanghai Metro is employed for demonstration, and the results show that: ① the proposed dynamic PFCD function fits the arrival pattern of passengers well during the peak hours; ② compared with the uniform departure schedule, the non-uniform departure (non-UD) schedule under the fixed train composition (FTC) mode can reduce the AWT of passengers by 24.15% and the waiting time of stranded passengers by 51.73%; ③ compared with the non-UD schedule under the FTC mode, the train timetable based on virtual coupling can reduce not only the train running kilometers by 0.33% but also the AWT of passengers and the waiting time of stranded passengers by 16.95% and 6.03%, respectively.
- public transit /
- urban rail transits /
- train timetable /
- Lagrangian relaxation algorithm /
- dynamic passenger flow demand /
- virtual coupling

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图 1 双向轨道交通线路

Figure 1. Two-way rail lines

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图 2 折返站解编列车示意图

Figure 2. Schematic diagram of unmarshalling trains at the turn-back station

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图 3 折返站重联列车示意图

Figure 3. Schematic diagram of reconnecting trains at the turn-back station

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图 4 折返站大小编组列车动态接续过程

Figure 4. Dynamic connection process of large and small marshalling trains in turn-back station

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图 5 总客流数据分时统计

Figure 5. Time-sharing statistics of total passenger flow data

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图 6 车站1—车站13累计客流需求拟合和实际曲线比较

Figure 6. Station 1-station 13 cumulative passenger flow demand fitting and actual curve comparison

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图 7 拉格朗日松弛算法迭代过程

Figure 7. Lagrangian relaxation algorithm iterative process

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图 8 虚拟编组模式下最优列车时刻表

Figure 8. Optimal train timetable in virtual coupling mode

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图 9 车底平均利用率变化趋势

Figure 9. Variation trend of average utilization rate of rolling stock

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表 1 符号说明

Table 1. Symbol description

符号	含义
i, j	车站的索引
m /座	单条路径上的车站总数
S	车站的集合，S = {1 2 m}
f	路径索引，f = 1为上行、f = 2为下行
k	列车车次的索引
N_f /列	在所研究时段内路径f上的总运行车次
n_f /辆	在所研究时段内路径f上的可用车底数量
K_f	路径f上列车车次的集合，K_f = {1, 2, 3, … ,N_f }
d_ij^f (t)	路径f上t时刻从i站到j站的累计需求函数
T_{k, f}ⁱ /min	决策变量，路径f上第k车次在第i站的发车时刻
T /min	总的研究时间
h_min /min	最小发车间隔
h_max /min	最大发车间隔
tz /min	折返时间
ty_iⁱ⁺¹ /min	列车从i站到i + 1站的运行时间
tw_i /min	列车在i站的停站时间
α_{k, f}ⁱ /人	路径f上第i站能乘上第k车次的乘客数
q_f^ij /人	路径f上从第i站到第j站的乘客数
Q_fⁱ /人	路径f上第i站的总上车乘客数
p_{k, f}ⁱ /人	路径f上第k车次在第i站的下车乘客数
A_{k, f}ⁱ /人	路径f上第k车次在第i - 1站出发时的在车乘客数
φ_{k, f}ⁱ /人	路径f上第i站未能乘上第k车次的滞留乘客数
D /（人/辆）	列车定员
L /km	单向线路总长度
Ω /次	选代次数
c_f^k /辆	决策变量，路径f上第k车次的列车编组数量
c_min/辆	最小编组数量
c_max/辆	最大编组数量

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表 2 上行方向站间距及运行时间

Table 2. The station spacing and running time in the upward direction

区间编号	长度/km	运行时间/min	区间编号	长度/km	运行时间/min
1	1.9	3	7	2.3	4
2	2.0	3	8	2.9	5
3	1.9	3	9	2.4	4
4	1.8	3	10	4	6
5	1.3	2	11	2.3	4
6	2.1	3	12	1.6	2

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表 3 上行方向列车停站时间

Table 3. The dwell time of upward direction train

车站编号	时间/min	车站编号	时间/min
1	1	8	0.7
2	0.5	9	0.5
3	0.3	10	0.3
4	0.5	11	0.8
5	0.4	12	0.6
6	0.6	13	1
7	0.4

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表 4 各车次编组情况

Table 4. The grouping of each train

车次编号	上行编组辆数/辆	下行编组辆数/辆	车次编号	上行编组辆数/辆	下行编组辆数/辆
1	4	4	26	8	5
2	4	4	27	8	5
3	4	4	28	8	5
4	4	4	29	8	6
5	4	4	30	8	5
6	4	4	31	8	7
7	4	4	32	8	8
8	4	4	33	8	6
9	4	4	34	8	8
10	4	4	35	8	8
11	4	4	36	8	8
12	4	4	37	8	8
13	4	7	38	6	8
14	5	5	39	7	8
15	4	4	40	5	8
16	4	5	41	8	8
17	8	4	42	8	7
18	4	5	43	8	7
19	5	4	44	8	5
20	7	4	45	8	8
21	8	4	46	6	6
22	8	4	47	8	6
23	8	5	48	6	5
24	8	4	49	8	8
25	8	5	50	8	8

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表 5 各运营模式下的运行指标

Table 5. Running indices under various operating modes

运营模式	乘客平均等待时间/min	dis₁ /%	列车走行里程数/km	dis₂ /%	车底平均利用率/%	dis₃ /%	滞留乘客等待时间/min	dis₄ /%
模式1	16.824 6	24.15	15 900	0.00	0.819 7	-11.02	9 173 639.11	51.73
模式2	13.552 3		15 900		0.921 2		6 046 122.36
模式3	11.255 7	-16.95	15 847	-0.33	0.934 5	1.44	5 681 252.90	-6.03

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表 6 不同权重系数的最优目标值

Table 6. Optimal target values for different weights

案例	σ₁	σ₂	目标函数值	平均等待时间/min	列车走行里程数/km
1	0.000 1	0.999 9	12.78	11.190 2	15 953.0
2	0.001	0.999	27.69	12.572 6	15 131.5
3	0.01	0.99	156.38	14.753 2	14 177.5

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