以安全为导向的地铁过饱和线路跳站停车策略优化模型

陶乐风; 石俊刚; 杨静; 杨晓光

doi:10.3963/j.jssn.1674-4861.2022.03.006

以安全为导向的地铁过饱和线路跳站停车策略优化模型

doi: 10.3963/j.jssn.1674-4861.2022.03.006

1.
华东交通大学交通运输工程学院南昌 330013
2.
同济大学交通运输工程学院上海 201804

基金项目:

国家自然科学基金青年基金项目 71801093

江西省社会科学基金项目 21GL37D

详细信息

作者简介:
陶乐风(1996—)，硕士研究生. 研究方向：交通运输系统建模与优化. E-mail：1045586854@qq.com

通讯作者:
石俊刚(1986—)，博士，副教授.研究方向：交通运输系统建模与优化. E-mail：jgshi@ecjtu.edu.cn

中图分类号: U293.13
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出版历程
- 收稿日期: 2022-01-02
- 网络出版日期: 2022-07-25

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

1.
College of Transportation Engineering, East China Jiaotong University, Nanchang 330013, China
2.
College of Transportation Engineering, Tongji University, Shanghai 201804, China

摘要

摘要: 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%。
- 城市地铁 /
- 跳站停车策略 /
- 运营安全 /
- 可变邻域搜索(VNS) /
- 过饱和线路
Abstract: 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%.
- urban rail transit /
- skip-stop strategy /
- operational safety /
- variable neighborhood search (VNS) /
- oversaturated metro line

HTML全文

图 1 站站停与跳站停策略的说明

Figure 1. Illustration of the all-stop and skip-stop strategy

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图 2 乘客在k车站等待时间

Figure 2. The illustration of passenger waiting time at station k

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图 3 北京地铁八通线线路

Figure 3. Beijing Metro Batong Line Route

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图 4 不同情景下的停站策略与乘客等待数量

Figure 4. Stopping strategy and waiting passengers volume under different situations

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表 1 符号与索引

Table 1. Symbols and Indexes

符号与索引	定义	符号与索引	定义
S	车站集合，S={1, 2, …，\|S\|}	t_p	p组乘客到达站台的时间，∀p ∈ P
k, s	车站索引，∀k, s∈S	t_停	列车停留时间
I	列车集合，I={1, 2, …，\|I\|}	t_r	相邻2列车的最小安全追踪间隔
i, j	列车索引，∀i, j∈I	μ	乘客聚集风险系数
[0, T]	考虑的时间范围	t_s^y	到达s站时列车在区间内的总运行时间
p	乘客需求组索引，∀p∈P	N^max	车站最大连续不停站列车次数
p	乘客需求组集合，P = {1, 2, …\|P\|}	U_k	k站可容纳的等待乘客的安全数量
p	乘客需求组集合，P = {1, 2, …\|P\|}	H_k	k站可容纳的等待乘客的最大数量
o_p	p组乘客的始发站，∀p ∈ P	C	超员情况下列车最大承载容量
d_P	p组乘客的目的站，∀p∈P	M	1个较大的正数

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表 2 中间变量表

Table 2. Indirect variables

中间变量	定义	中间变量	定义
n_p	p组乘客的数量，∀p ∈ P	v_kⁱ	列车i从k站出发时的载客量，∀i ∈ I, k ∈ S
td_sⁱ	列车i在s站的出发时间，∀i ∈ I, s ∈ S	v_kⁱ	列车i从k站出发时的载客量，∀i ∈ I, k ∈ S
td_sⁱ	列车i在s站的到达时间，∀i ∈ I, s ∈ S	l_{k, s}ⁱ	在k站列车i出发时遗留的去往s站的乘客数量，∀i ∈ I, k ∈ S
w_kⁱ	在k站等待登上列车i的乘客数量，∀i ∈ I, k ∈ S	c_kⁱ	列车i在k站剩余的载客容量，∀i ∈ I, k ∈ S
w_k^{i, e}	在k站等待登上列车i的有效乘客数量，∀i ∈ I, k ∈ S	a_kⁱ	列车i在k站下车的乘客数量，∀i ∈ I, k ∈ S
w_{k, s}ⁱ	在k站等待登上列车i去往s站的乘客数量，∀i ∈ I, k ∈ S	w_k(t)	k站t时刻等待的乘客数量，k ∈ S, t ∈[0, T]
nb_kⁱ	在k站不会登上列车i的乘客数量，∀i ∈ I, k ∈ S	w_k	k站的乘客总等待时间，k ∈ S
b_kⁱ	在k站登上列车i的乘客数量，∀i ∈ I, k ∈ S	r_k(t)	k站t时刻乘客聚集的风险值，k ∈ S, t ∈[0, T]
b_{k, s}ⁱ	在k站登上列车i去往s站的乘客数量，∀i ∈ I, k ∈ S	r_k	k站的总风险值，k ∈ S

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表 3 求解参数

Table 3. Solving parameters

参数	符号	值
列车数量/列	\|I\|	42
车站数量/站	\|S\|	13
超员情况列车最大承载容量/人	C	1 860
停站时间/min	t_停	1
等待乘客的安全数量/人	U_k	2 000
等待乘客的最大数量/人	H_k	4 000
相邻列车最小安全间隔/min	t_r	2
车站最大连续不停站列车次数	N^max	3
目标权重	θ₁，θ₂	0.5
乘客积累风险系数	μ	2

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表 4 各车站跳站列车的编号和总次数

Table 4. Number and total number of skip-stop trains at each station

车站名称	跳站列车的编号	跳站列车总次数/列
土桥	-	0
临河里	1, 6, 13, 14, 16, 18, 23, 25, 30, 35, 37, 41	12
梨园	1, 5, 7, 9, 10, 12, 13, 16, 17, 19, 24, 25, 28, 32, 34, 36, 38, 40	18
九棵树	6, 15, 17, 18, 21, 22, 23, 26, 27, 31, 32, 39, 40, 41	14
果园	4, 7, 11, 12, 13, 15, 17, 18, 22, 23, 24, 26, 39	13
通州北苑	2, 8, 11, 12, 16, 18, 20, 21, 22, 24, 27, 29, 31, 32, 40	15
八里桥	3, 5, 8, 10, 11, 12, 17, 18, 21, 22, 26, 27, 30, 33, 35, 40	16
管庄	1, 6, 7, 10, 12, 14, 15, 19, 20, 21, 23, 24, 27, 29, 30, 33, 34, 39	18
双桥	9, 11, 13, 14, 18, 20, 21, 28, 30, 31, 33	11
传媒大学	1, 3, 8, 9, 14, 16, 19, 20, 22, 23, 25, 28, 29, 32, 35, 38	16
高碑店	11, 14, 15, 16, 19, 20, 21, 25, 26, 29, 31, 33, 37, 39	14
四惠东	1, 4, 9, 10, 12, 15, 17, 19, 23, 24, 31, 34, 37, 41	14
四惠	-	0

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表 5 站站停与跳停策略的求解结果

Table 5. Result of all-stop and skip-stop strategies solving

运营模式	目标函数	总等待时间/min	平均等待时间/min	风险值	最大等待乘客数量/人
跳站停	374 047.0	743 104	9.15	4 990	2 495
站站停	581 381.5	771 343	9.49	391 420	5 299

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表 6 车站最大列车连续不停策略

Table 6. Maximum continuous train strategy at the station

策略	连续不停站的车次数	总乘客等待时间/min	上游车站乘客平均等待时间/min	风险值
策略1	2	761 648	5.81	32 876
策略2	3	743 104	6.35	4 990

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表 7 权衡系数的取值

Table 7. The value of the trade-off coefficient

θ₁/θ₂	总乘客等待时间/min	最大等待乘客数量/人	风险值
0/1	774 395	2 084	694
0.2/0.8	771 283	2 163	1 394
0.4/0.6	760 624	2 456	1 778
0.6/0.4	735 768	2 531	8 634
0.8/0.2	723 816	2 724	30 300
1/0	710 960	2 881	52 682

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