轨道交通封站条件下应急疏散车辆路径优化

doi:10.3976/j.issn.1002-4026.2023.04.010

摘要/Abstract

摘要：

针对轨道交通封站条件下站外滞留乘客需要应急疏散的现实需求,设计了一种疏散服务模式,在保证滞留旅客有效疏散的前提下,允许线路沿途旅客搭乘以提高车辆的利用效率。以车辆运营成本和乘客时间成本之和最小为优化目标,建立应急疏散车辆路径优化模型,根据问题特点改进自适应大邻域搜索算法进行模型求解。最后,结合北京市城市交通数据,对应急疏散车辆进行路线设计并进行灵敏度分析,用算例验证了模型与算法的有效性。结果表明,相较于最短路径疏散方案,模型的优化结果节省了15.02%的乘客乘车时间,能够在保证乘客出行体验的前提下实现对站点滞留乘客的快速疏散,提升封站事件下轨道交通应急管理的精细化水平。

关键词: 城市轨道交通, 应急疏散, 车辆路径问题, 轨道交通封站, 自适应大邻域搜索算法

Abstract:

To address the problem of emergency evacuation of stranded passengers outside a rail station in case of its closure, this paper designs an evacuation route map, which allows passengers along the line to avail the emergency evacuation vehicles and facilitates the overall evacuation process. To minimize the total cost of vehicle operation and passenger time, this work proposes a route optimization model for emergency evacuation vehicles and improves the adaptive large neighborhood search algorithm to implement the model based on the characteristics of the problem. Finally, based on the urban traffic data of Beijing, we designed routes for emergency evacuation vehicles, analyzed their sensitivity, and verified the model and algorithm with specific examples. The results show that compared with the shortest route algorithm, the optimization results of the proposed model can reduce passengers' travelling time by 15.02%, allowing them to evacuate rapidly while ensuring their experience and improving emergency management systems in case of rail station closure.

Key words: urban rail transit, emergency evacuation, vehicle routing problem, rail station closure, adaptive large neighborhood search algorithm

中图分类号:

U491.12

张仪果, 屈云超, 尹浩东, 吴建军. 轨道交通封站条件下应急疏散车辆路径优化[J]. 山东科学, 2023, 36(4): 80-88.

ZHANG Yiguo, QU Yunchao, YIN Haodong, WU Jianjun. Route optimization for emergency evacuation vehicles in case of rail station closure[J]. Shandong Science, 2023, 36(4): 80-88.

图/表 9

表1

模型参数定义"

参数符号	参数定义
$n$	正常运营的轨道交通站点数
$d i j$	站点i和j间最短路距离; $i, j = 0,1, …, n,$ 其中 $0$ 为封站站点
$t i j$	站点i和j间行驶时间; $i, j = 0,1, …, n,$ 其中 $0$ 为封站站点
$Q$	疏散车辆最大载客数
$θ$	发车时车辆最低满载率
$T$	乘客接受的最长乘车时间
$t i$	站点 $i$ 停靠时间
$d i$	$i$ 站点下车总人数; $i = 1,2, …, n$
$p i$	$i$ 站点上车总人数; $i = 1,2, …, n$
$F c$	疏散车辆固定成本
$C d$	疏散车辆可变成本
$C t$	乘客单位时间成本
$v$	疏散车辆速度
$P m a x$	单条路径最大停靠次数

表1

表2

决策变量定义"

决策变量	变量定义
$x i j k$	0,1变量, $x i j k = 1$ 表示弧 $(i, j)$ 在车辆 $k$ 的路径上,否则为 $0$
$y i j k$	车辆 $k$ 在弧 $(i, j)$ 上时,车内累计上车总人数(包括站点 $i$ )
$z i j k$	车辆 $k$ 在弧 $(i, j)$ 上时,车内将要下车总人数(站点 $i$ 之后)
$n k$	第 $k$ 辆车停靠车站数

表2

图1

图2

表3

算法参数设置"

参数	意义	取值
$τ$	初始温度控制参数	0.05
$c$	冷却速率	0.95
$φ$	权重更新迭代次数	5
$n$	次优位置个数	5
$σ 1$	全局最优解评分	30
$σ 2$	当前最优解评分	20
$σ 3$	接受较差解评分	10
$ρ$	权重衰减系数	0.4
$θ -$	随机破坏程度上限	0.1
$θ -$	随机破坏程度下限	0.4
i_teration	算法迭代总次数	400

表3

图3

表4

表5

表6

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车辆序号	车辆行驶路由	车辆行驶距离/km	车辆行驶时间/h
1号车	3-7-11-12-8	14.7	0.90
2号车	4-0-2-18	18.1	0.92
3号车	10-1-6	15.2	0.63
4号车	5-16-22-23	19.1	0.94
5号车	9-13-15-14	21.0	0.85
6号车	21-20-24-19-17	15.8	0.95

算例编号	节点数量	文献[17]结果			ALNS的最优解
算例编号	节点数量	总距离/km	车辆数	时间/s	总距离/km	车辆数	时间/s
CMT1X	50	478.6	3	7.74	470.4	3	6.59
CMT1Y	50	480.8	3	7.81	470.4	3	6.66
CMT2X	75	688.5	6	24.86	664.8	6	18.32
CMT2Y	75	679.4	6	22.02	667.2	6	17.59
CMT3X	100	744.8	5	94.06	722.0	5	78.35
CMT3Y	100	723.9	5	120.66	731.3	5	85.24
CMT4X	150	887.0	7	501.95	856.2	7	416.45
CMT4Y	150	852.4	7	406.32	880.0	7	412.59
CMT5X	199	1 089.2	10	1 055.83	1 033.6	10	776.32
CMT5Y	199	1 084.3	10	771.71	1 012.1	10	628.46

最大载客量/人	乘客总乘车时间/h	行驶距离/km	车辆数/辆
60	86.67	105.9	8
70	93.85	89.8	7
80	99.02	85.1	6
90	99.63	94.3	6
100	119.18	88.0	5