基于模块化车辆的区域灵活接驳公交线路优化

doi:10.13229/j.cnki.jdxbgxb.20230515

Abstract

Abstract:

The uneven spatial-temporal distribution of passenger demand affects the level of public transportation service. The emerging modular vehicle system can adapt to the spatial-temporal demand changes by changing the number of modular vehicle units flexibly. Therefore， a zonal-based flexible feeder bus routes optimization model considering the modular vehicle system is established. The model aims at minimizing the total system cost consisting of vehicle operation cost， fixed cost and passenger travel time cost， and solves the model using a multi-agent genetic algorithm combining genetic algorithm and multi-intelligence system. Finally， numerical experiments based on the service area and stops of Xi'an “Jie Bus” are designed. The results show that the total cost can be reduced by about 18.31% by considering the modular vehicle system compared with the traditional fixed-capacity feeder bus system， which provides a new idea for the future development of urban public transportation.

Key words: transportation planning and management, zonal-based flexible feeder bus, modular vehicle system, optimization of bus routes, multi-agent genetic algorithm

CLC Number:

U491

Tian-yang GAO,Da-wei HU,Rui-sen JIANG,Xue WU,Hui-tian LIU. Optimization study of zonal-based flexible feeder bus routes based on modular vehicle system[J].Journal of Jilin University(Engineering and Technology Edition), 2025, 55(2): 537-545.

Figures/Tables 17

Fig.1

Fig.2

Table1

Notation for the model"

符号		说明
集合	$N$	乘客需求点集合， $N = 1,2, 3, …, n$
	$K$	车辆集合， $K = {1,2, 3, ?, k}$
	$R$	模块化车辆车节集合， $R = {1,2, 3, ?, r}$
	$D$	公交接驳站点集合， $D = 0, n + 1$
	$V$	公交服务网络中所有节点的集合， $V = N ? D$
参数	$C r$	车节为 $r$ 的模块化车辆的单位运营成本
	$F r$	车节为 $r$ 的模块化车辆的单位固定使用成本
	$C k F C$	固定容量巴士系统中车辆的单位运营成本
	$F k F C$	固定容量巴士系统中车辆的单位固定使用成本
	$β$	乘客乘车的单位时间成本
	$M$	一个无穷大的数
	$n$	单个模块化车辆车节的容量
	$Q k F C$	固定容量巴士系统中车辆的容量
	$d i j$	站点 $i$ 到 $j$ 的行驶距离
	$q i$	站点 $i$ 的乘客人数
	$s i$	车辆在站点 $i$ 处的服务时间
	$t i j$	站点 $i$ 到 $j$ 的行驶时间
	$[e i, l i]$	需求点 $i$ 处乘客的时间窗
	$v$	车辆运行速度
	$T m a x$	允许车辆行驶的最长运行时间
	$n s$	所有站点数量的总和
变量	$u i k$	与子回路消除约束相关的辅助变量
	$L i k$	车辆 $k$ 到达站点 $i$ 时车内的乘客人数
	$T i k$	车辆 $k$ 到达站点 $i$ 的时间
	$y i k$	0-1决策变量， $y i k$ =1，表示车辆 $k$ 服务站点 $i$ ，否则 $y i k$ =0
	$x i j k$	0-1决策变量， $x i j k$ =1，表示车辆 $k$ 经过弧 $(i, j)$ ，否则 $x i j k$ =0
	$y i k F C$	0-1决策变量， $y i k F C$ =1，表示固定容量车辆 $k$ 服务站点 $i$ ，否则 $y i k F C$ =0
	$x i j k F C$	0-1决策变量， $x i j k F C$ =1，表示固定容量车辆 $k$ 经过弧 $(i, j)$ ，否则 $x i j k F C$ =0
	$z k r$	0-1决策变量， $z k r$ =1，表示车辆 $k$ 由 $r$ 个车节组成，否则 $z k r$ =0

Table1

Fig.3

Table 2

Pseudocode of multi-agent genetic algorithm （MAGA）"

Input： $L s i z e$ ， $G i t e r m a x$ ， $S G i t e r m a x$ ， $P c$ ， $P m$ ， $S P m$ ；

Output：最优智能体 $L *$ ，能量值 $E L *$ ；

1 随机生成初始智能体网格 $L$ ，评估智能体的能量值

2 $t 1 ← 1$ ， $t 2 ← 1$

3 while $t 1 ≤ G i t e r m a x$ do

4 for $i = 1 : L s i z e$

5 for $j = 1 : L s i z e$

6 对智能体 $L i j$ 执行邻域竞争操作

7 end

8 end

9 for $i = 1 : L s i z e$

10 for $j = 1 : L s i z e$

11 if 随机产生的值 $p$ 小于邻域交叉概率 $P c$

12 对智能体 $L i j$ 执行邻域交叉操作

13 end

14 end

15 end

16 for $i = 1 : L s i z e$

17 for $j = 1 : L s i z e$

18 if 随机产生的值 $p$ 小于变异概率 $P m$

19 对智能体 $L i j$ 执行变异操作

20 end

21 end

22 end

23 在新的智能体网格中选择能量值最高的 $L b e s t t 1$ 做以下操作

24 while $t 2 ≤ S G i t e r m a x$ do

25 对智能体 $L b e s t t 1$ 执行自学习算子1

26 if 随机产生的值 $p$ 小于变异概率 $S P m$

27 对 $L b e s t t 1$ 执行随机两点变异操作，得到新的 $S L n e w t 2$

28 end

29 if $E S L n e w t 2 > E L b e s t t 1$

30 $L b e s t t 1 ← S L n e w t 2$

31 else

32 对 $L b e s t t 1$ 执行自学习算子2，得到新的 $S L n e w t 2$

33 if $E S L n e w t 2 > E L b e s t t 1$

34 $L b e s t t 1 ← S L n e w t 2$

35 end

36 end

37 $t 2 ← t 2 + 1$

38 end

39 $t 1 ← t 1 + 1$

40 end

Table 2

Table 3

Parameter value of MAGA"

算例规模（需求点）	5~10	15~30	40~50
初始智能体网格大小	3	7	9
MAGA的迭代次数	50	100	200
自学习算子中的迭代次数	10	30	40
交叉概率 $P c$	0.6	0.6	0.6
变异概率 $P m$	0.15	0.15	0.15
自学习算子变异概率 $S P m$	0.15	0.15	0.15

Table 3

Table 4

Fig.4

Fig.5

Table 5

Fig.6

Table 6

Table 7

Values of model parameters"

参数	取值
$r$	［1-6］
$n$	6
$Q k F C$	36
$F r$ /（元·km^-1）	［1.3125，2.625，3.9375，5.25，6.5625，7.875］
$C r$ /（元·km^-1）	［1.001，1.799，2.429，2.919，3.297，3.598］
$F k F C$ /（元·km^-1）	7.875
$C k F C$ /（元·km^-1）	3.598
v/（km·h^-1）	30
$β$ /（元·min^-1）	0.63
$s i$ /min	0.5
$T m a x$ /min	20

Table 7

Table 8

Fig.7

Table 9

Fig. 8

References 17

1	苗一迪. 柔性路径公交车服务区域的决策模型研究[D]. 大连: 大连理工大学经济管理学院, 2011.
	Miao Yi-di. A decision-making model for determining the service area of a flexible-route bus[D]. Dalian: Economics and Management School, Dalian University of Technology, 2011.
2	靳文舟, 胡为洋, 邓嘉怡, 等. 基于混合算法的需求响应公交灵活调度模型[J]. 华南理工大学学报: 自然科学版, 2021, 49(1): 123-133.
	Jin Wen-zhou, Hu Wei-yang, Deng Jia-yi, et al. Flexible scheduling model of demand responsive transit based on hybrid algorithm[J]. Journal of South China University of Technology (Natural Science Edition), 2021, 49(1): 123-133.
3	Huang A L, Dou Z Q, Qi L Z, et al. Flexible route optimization for demand-responsive public transit service[J]. Journal of Transportation Engineering, Part A: Systems, 2020, 146(12): 1-15.
4	Melis L, Sörensen K. The static on-demand bus routing problem: large neighborhood search for a dial-a-ride problem with bus station assignment[J]. International Transactions in Operational Research, 2022, 29(3): 1417-1453.
5	孙继洋, 黄建玲, 陈艳艳, 等. 面向多目标站的灵活型公交路径优化调度模型[J]. 交通运输系统工程与信息, 2019, 19(6): 105-111.
	Sun Ji-yang, Huang Jian-ling, Chen Yan-yan, et al. Flexible bus route optimization scheduling model for multi-target stations[J]. Journal of Transportation Systems Engineering and Information Technology, 2019, 19(6): 105-111.
6	孙继洋, 黄建玲, 陈艳艳, 等. 响应动态需求的灵活型公交路径优化调度模型[J]. 北京工业大学学报, 2021, 47(3): 269-279.
	Sun Ji-yang, Huang Jian-ling, Chen Yan-yan, et al. Flexible bus route optimal scheduling model in response to dynamic demand[J]. Journal of Beijing University of Technology, 2021, 47(3): 269–279.
7	Sun Q, Chien S, Hu D W, et al. Optimizing multi-terminal customized bus service with mixed fleet[J]. IEEE Access, 2020, 8: 156456-156469.
8	汪怡然, 陈景旭, 王岳平, 等. 考虑服务公平性的定制公交动态响应方案[J]. 吉林大学学报: 工学版, 2022, 52(11): 2574-2581.
	Wang Yi-ran, Chen Jing-xu, Wang Yue-ping, et al. Instant demand-responsive scheme for customized bus considering service fairness[J]. Journal of Jilin University (Engineering and Technology Edition), 2022, 52(11): 2574-2581.
9	孙倩, 胡大伟, 钱一之, 等. 考虑车辆随机到站时间的动态需求响应型接驳公交线路优化[J]. 交通运输系统工程与信息, 2022, 22(5): 196-204.
	Sun Qian, Hu Da-wei, Qian Yi-zhi, et al. Dynamic bus routing optimization for demand-responsive feeder transit considering stochastic bus arrival time[J]. Journal of Transportation Systems Engineering and Information Technology, 2022, 22(5): 196-204.
10	杨明, 黄乐. 面向早高峰通勤客流的多车型定制公交线网优化[J]. 长沙理工大学学报: 自然科学版, 2020, 17(3): 71-78.
	Yang Ming, Huang Le. Network optimization of multi-vehicle-type customized bus for commuting demand during morning peak hour[J]. Journal of Changsha University of Science & Technology (Natural Science), 2020, 17(3): 71-78.
11	裴明阳. 灵活公共交通系统营运调度模型与方法研究[D]. 广州: 华南理工大学交通学院, 2020.
	Pei Ming-yang. Operational design models for flexible transit systems[D]. Guangzhou: School of Transportation, South China University of Technology, 2020.
12	Ji Y X, Liu B, Shen Y, et al. Scheduling strategy for transit routes with modular autonomous vehicles[J]. International Journal of Transportation Science and Technology, 2021, 10: 121-135.
13	范文博, 陈香, 刘涛. 模块化自动驾驶穿梭公交服务频率优化及时刻表设计[J]. 交通运输工程与信息学报, 2023, 21(2): 160-176.
	Fan Wen-bo, Chen Xiang, Liu Tao. Modular autonomous shuttle transit service: frequency setting and timetabling[J]. Journal of Transportation Engineering and Information, 2023, 21(2): 160-176.
14	Dai Z, Liu X Y, Chen X, et al. Joint optimization of scheduling and capacity for mixed traffic with autonomous and human-driven buses: a dynamic programming approach[J]. Transportation Research Part C: Emerging Technologies, 2020, 114: 598-619.
15	Pei M Y, Lin P Q, Du J, et al. Vehicle dispatching in modular transit networks: a mixed-integer nonlinear programming model[J]. Transportation Research Part E: Logistics and Transportation Review, 2021, 147: 102240.
16	Liu X H, Qu X B, Ma X L. Improving flex-route transit services with modular autonomous vehicles[J]. Transportation Research Part E: Logistics and Transportation Review, 2021, 149: 102331.
17	吴典文, 彭宇, 田奇, 等. 基于停靠站选址的响应型接驳公交调度优化[J]. 公路工程, 2021, 46(5): 176-182.
	Wu Dian-wen, Peng Yu, Tian Qi, et al. Scheduling optimization for responsive feeder transit based on the stop location[J]. Highway Engineering, 2021, 46(5): 176-182.

Related Articles 15

[1]	Yi-yong PAN,Yi-wen YOU,Jing-ting WU. Analysis of heterogeneity and transferability of factors influencing severity of lane change accidents [J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(2): 520-528.
[2]	Yao SUN,Bao-zhen YAO,Zi-jian BAI. Evaluate the validity of traffic congestion dispersion based on random forest method [J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(2): 512-519.
[3]	Fa-cheng CHEN,Guang-quan LU,Qing-feng LIN,Hao-dong ZHANG,She-qiang MA,De-zhi LIU,Hui-jun SONG. Review of drivers' takeover behavior in conditional automated driving [J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(2): 419-433.
[4]	Rong-han YAO,Wen-yan QI,Hong-yu HU,Xiao-jing DU,Yan-feng QIAO,Li-bing WANG. Multi-lane cellular automata model considering bus-high occupancy vehicle lane [J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(1): 162-174.
[5]	De-lin LI,Jun-xian CHEN,Yong-gang WANG,Lu WANG,Zhao-qing SHEN. Identification of driving behavior on steep sharp curves based on latent class model [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(12): 3526-3533.
[6]	Yi-yong PAN,Jing-ting WU,Xuan-ye Miao. Temporal instability analysis of factors affecting injury severities of elderly drivers [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(10): 2819-2826.
[7]	Jin XU,Zheng-huan CHEN,Qi-shuo LIAO,Zhan-ji ZHENG,He-shan ZHANG. Mental workload of drivers at high-density interchanges of freeways based on ECG data [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(10): 2807-2818.
[8]	Hui-ying WEN,Zi-qi HE,Qiu-ling LI,Sheng ZHAO. Traffic conflict prediction and influencing factors analysis of truck lane change on expressway [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(10): 2827-2836.
[9]	Chun-jiao DONG,Yu-xiao LU,She-qiang MA,Peng-hui LI. Identification of E⁃bike violation behaviors by considering waiting tolerance time [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(9): 2540-2546.
[10]	Chang-jiang ZHENG,Tong-tong TAO,Zhi-chao CHEN. Cascading failure model based on adjustable redistribution of traffic flow [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(9): 2441-2450.
[11]	Xi-zhen ZHOU,He GONG,Dun-dun LI,Yan-jie JI,Jie YAN. Nonlinear model for impact of built environment on curb parking spaces occupancy [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(9): 2520-2530.
[12]	Li-xin YAN,Tao ZENG,Yi HE,Jun-hua GUO,Xin-hui HU. Man-machine takeover behavior sequence coding and analysis of shared driving intelligent vehicle [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(9): 2547-2556.
[13]	Na ZHANG,Feng CHEN,Jian-po WANG,Ya-di ZHU. Recognition of travel patterns for urban rail transit passengers based on spatiotemporal sequence similarity [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(9): 2588-2599.
[14]	Rong-gui ZHOU,Pei GAO,Yu-xuan LI,Jian ZHOU. Abnormal driving behavior thresholds of highway minibuses based on trajectory data [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(9): 2581-2587.
[15]	Da-yi QU,Hao-min LIU,Zi-yi YANG,Shou-chen DAI. Dynamic allocation mechanism and model of traffic flow in bottleneck section based on vehicle infrastructure cooperation [J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(8): 2187-2196.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 0

No Suggested Reading articles found!

算例	LINGO		MAGA
算例	最优值	时间/s	最优值	平均值	平均时间/s
R102-5	3 788.9	641	3 788.9	3 788.9	2.03
R102-10	5 796.6	4 052	5 796.6	5 796.6	5.63
R102-15	—	7 200	8 295.9	8 295.9	14.44
R102-30	—	7 200	16 953.2	16 981.2	51.21
R102-50	—	7 200	31 787.3	31 883.5	165.70

求解结果	SA（2021）^［17］	MAGA（本文算法）
线路1	0-1-10-8-11-0	0-5-18-17-0
线路2	0-7-4-2-3-0	0-7-11-8-10-0
线路3	0-9-16-15-12-0	0-1-4-2-3-6-0
线路4	0-13-14-19-20-0	0-9-16-15-14-0
线路5	0-17-18-5-6-0	0-13-12-19-20-0
总成本最优值	135.86	126.73
平均计算时间/s	-	16.4

站点	位置	人数	时间窗
1	［108.961143，34.158944］	2	［8：00，8：09］
2	［108.967018，34.159049］	3	［8：05，8：16］
3	［108.974744，34.160356］	4	［8：00，8：09］
4	［108.974726，34.152902］	5	［8：00，8：10］
5	［108.97266，34.14751］	2	［8：05，8：13］
?	?	?	?

结果	MVS-ZBFFB	FCFBS
总成本/元	351.06	429.73
车辆数/辆	5	4
车辆容量	［24，24，18，24，6］	［36，36，36，36］
平均满载率/%	94.72	62.5
运营总距离/km	25.17	20.79
运营成本/元	66.73	74.81
固定成本/元	116.04	163.72
乘客时间成本/元	168.29	191.20

线路	优化路径	人数	车型/r	满载率/%
1	23-3-11-19-18-9-17-23	23	4	95.8
2	23-4-22-12-21-23	24	4	100
3	23-1-2-15-5-6-23	17	3	94.4
4	23-14-13-8-7-16-23	20	4	83.3
5	23-20-10-23	6	1	100

Optimization study of zonal-based flexible feeder bus routes based on modular vehicle system

RICH HTML

PDF (PC)