引入车辆窗的定制公交线路优化

doi:10.13229/j.cnki.jdxbgxb.20230710

摘要/Abstract

摘要：

针对多车型定制公交线路优化研究中考虑因素不够贴近实际情况的问题，本文引入车辆窗来研究定制公交的线路优化问题。首先，引入车辆窗概念，以描述不同公交车辆的发车成本、行驶成本、车辆容量和行驶速度。其次，构建引入车辆窗的整数线性规划模型，以乘客时空窗和车辆窗为输入，以企业运营成本和乘客出行成本最小化为目标。最后，针对大多采取混合编码所导致站点服务顺序混乱与寻优效率低的问题，结合模型特点，设计了包括公交车辆、上车点和下车点的三段式混合编码的遗传算法对模型进行求解，并在Sioux Falls网络开展算例分析。结果表明：引入车辆窗后能够得到更贴合实际的线路方案，且车辆的车速比差值越大对方案的影响也越大。

关键词: 交通运输规划与管理, 定制公交, 线路优化, 车辆窗, 遗传算法

Abstract:

The vehicle window was introduced to the study to address the problem that the factors considered in the route optimization study of multi-vehicle customized bus are not close to the actual situation. Firstly， the concept of vehicle window was introduced to describe the departure cost， travelling cost， vehicle capacity and travelling speed of different type of customized bus. Secondly， an integer linear programming model with vehicle window was constructed. The model has passenger time-space window and vehicle window as input， and the minimization of enterprise operation cost and passenger travel cost as objective. Finally， a three-segment hybrid encoding genetic algorithm including the customized bus， boarding point and alighting point was designed to solve the model according to the characteristics. It solves the problems of chaotic service order and low optimization efficiency caused by hybrid coding in most stations.An example analysis was carried out in the Sioux Falls network. The results show that： The model with vehicle window is more suitable to the actual scheme， and the greater the difference of vehicle speed ratio， the greater the impact on the scheme.

Key words: transportation planning and management, customized bus, route optimization, vehicle window, genetic algorithm

中图分类号:

U491.1

岳昊,常笑,刘建业,曲秋莳. 引入车辆窗的定制公交线路优化[J]. 吉林大学学报(工学版), 2025, 55(4): 1266-1274.

Hao YUE,Xiao CHANG,Jian-ye LIU,Qiu-shi QU. Customized bus route optimization with vehicle window[J]. Journal of Jilin University(Engineering and Technology Edition), 2025, 55(4): 1266-1274.

图/表 16

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符号说明"

符号类别	符号	定义
集合	$N$	物理网络中节点的集合
	$M$	物理网络中有向弧的集合
	$T$	时空网中时空点的集合
	$A$	时空网中时空弧的集合
	$V$	车辆集合
	$V m$	车型 $m$ 的车辆集合
	$P$	乘客集合
	$A v$	时空网中车辆 $v$ 所属的时空弧的集合
	$A v p$	时空网中车辆 $v$ 对乘客 $p$ 的服务弧的集合
参数	$v$	车辆索引
	$p$	乘客索引
	$k$	迭代次数索引
	$s p$	乘客 $p$ 的上车点
	$d p$	乘客 $p$ 的下车点
	$i, t 、 j, s$	时空点
	$i, j, t, s$	时空弧
	$ω$	权重系数
	$C i j t s v$	车辆 $v$ 经过时空弧 $i, j, t, s$ 的运输成本
	$C v$	车辆 $v$ 单位距离行驶成本
	$L i j t s v$	车辆 $v$ 经过时空弧 $i, j, t, s$ 的行驶距离
	$G v$	车辆 $v$ 的发车成本
	$C p$	乘客的单位出行时间成本
	$t i j p$	乘客 $p$ 从 $i$ 点到 $j$ 点的行驶时间
	$B c a p v$	车辆 $v$ 的座位数
	$t v p$	车辆 $v$ 到达乘客 $p$ 下车点的时刻
	$e p$	乘客 $p$ 下车时间窗的上界
	$l p$	乘客 $p$ 下车时间窗的下界
	$o v$	车辆 $v$ 的起点
	$d v$	车辆 $v$ 的终点
	$e v$	车辆 $v$ 的工作起始时段
	$l v$	车辆 $v$ 的工作结束时段
	$D$	迭代次数
	$s$	种群规模
	$p c$	交叉概率
	$p m$	变异概率
决策变量	$x i j t s v$	车辆路径变量（如果车辆 $v$ 选择时空弧 $(i, j,$ $t, s)$ ， $x i j t s v = 1$ ；否则， $x i j t s v = 0$ ）

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参考文献 17

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预约乘客数	上车地点	下车地点	期望到达时间
8	2	4	8：00
12	3	5	8：30

	方案一	方案二	方案三
最优运输方案	B：2-3 B：4-6	A：2-3 B：4-6	A：2-3 B：4-6
发车成本/元	50	40	40
行驶成本/元	33	30	30
企业运营成本/元	83	70	70
乘客总出行时间/min	384.0	384.0	342.8

交叉前	染色体1	\|a-b-c\|-\|1-［2，3］-4-5\|-\|6-7-8-9-10\|
交叉前	染色体2	\|b-a-c\|-\|5-［4-3］-2-1\|-\|10-9-8-7-6\|
交叉后	子代1	\|a-b-c\|-\|1-4-3-2-5\|-\|6-7-8-9-10\|
交叉后	子代2	\|b-a-c\|-\|5-2-3-4-1\|-\|10-9-8-7-6\|

乘客预约数	上车地点	下车地点	下车时间窗/min
2	3	7	［56，60］
1	4	8	［56，60］
3	5	18	［56，60］
5	11	8	［56，60］
3	12	7	［56，60］
4	20	18	［56，60］
2	21	7	［56，60］
2	22	8	［56，60］
5	23	7	［56，60］
3	24	18	［56，60］

发车时间	车型	路径	服务乘客数/人	座位利用率/%	到达时间
7：14	A	13-12-11-4-5-6-8	6	60	8：00
7：16	A	13-24-23-22-20-18-7-8	7	70	8：00
7：21	B	13-24-21-20-18-7	5	100	8：00
7：24	B	13-12-3-4-5-6-8-7-18	3	60	8：00
7：27	B	13-12-3-4-5-6-8-7	5	100	8：00
7：34	B	13-24-21-20-18	4	80	8：00