城市轨道交通跨环线的跨线列车开行方案优化

doi:10.13229/j.cnki.jdxbgxb.20230326

Abstract

Abstract:

To alleviate the pressure on transfer station and enhance the service level of urban rail transport， the planning model for the cross-line operation scheme between the loop line and radial line was constructed by taking the combination of loop line and radial line as the research object. The objective was to maximize the number of direct passengers， minimize total passenger travel time and the distance traveled by trains. Taking into account constraints such as departure intervals， passenger load factors， and the number of trains， and considering passenger flow distribution based on the characteristics of the loop line， a genetic algorithm was designed that includes OD passenger flow distribution to solve the model. The case study shows that compared to independent operation， the cross-line operation between the loop line and radial line can optimize the allocation of capacity resources and improve passenger directness and service quality. When the coefficient weights of the objective function were set to a ratio of 3：1：1， 33.76% （11，000 passengers） of the transfer passengers can avoid transfers and achieve direct travel， resulting in a 1.11% reduction in total passenger travel time and a 1.05% reduction in distance traveled by trains.

Key words: urban rail transit, loop line, cross-line operation, operation scheme, genetic algorithms, passenger flow distribution

CLC Number:

U292.4

Pei-ning TIAN,Rui-yong TONG,Hai-peng WANG,Bao-hua MAO,Hao-xiang ZHANG,Xia LU. Optimization of cross-line train operation across the urban rail transit loop line[J].Journal of Jilin University(Engineering and Technology Edition), 2025, 55(1): 132-140.

Figures/Tables 11

Fig.1

Table 1

Definition of model-related symbols"

符号	含义	符号	含义
$A = m o d e 1, m o d e 2$	运营模式集合， $m o d e 1$ 代表独立运营模式， $m o d e 2$ 代表跨线运营模式	$T P i, P j$	起点为 $P i$ 区段、终点为 $P j$ 区段乘客的总出行时间/min
$S = s 1, s 2, ? ? ?, s t r, ? ? ?, s a, ? ? ?, s n$	组合线路的车站集合， $s t r$ 代表换乘站， $s a$ 代表跨线交路折返站， $t r 、 a$ 分别为换乘站、跨线交路折返站编号	$L A$	$A$ 模式下的车辆走行公里数/（veh·km^-1）
$S'$	具有折返能力的车站集合	$U A$	$A$ 模式下的小时运用列车数/列
$M h 、 M b$	环线、半径线的车站数/站	$m$	列车编组数/（辆·列^-1）
$o 、 d, o, d ∈ S$	$o$ 表示乘客的起点站， $d$ 表示乘客的终点站	$C$	车辆额定载员/（人·辆^-1）
$J = N, S, B, E$	交路集合，分别表示外环交路、内环交路、半径线交路、跨线交路	$l h 、 l b$	环线、半径线的线路长度/km
$f J A$	$A$ 模式下 $J$ 交路的开行频率/［（对·h^-1）^-1］	$l i$	第 $i$ 站的站间距/km
$q o d, o, d ∈ S$	以车站 $o$ 为起点、 $d$ 为终点的OD客流量/（人·h^-1）	$l z$	折返走行距离/km
$q E$ 、 $q Z$	跨线直达乘客数、跨线需求总乘客数/人	$t J$	$J$ 交路的列车周转时间/min
$P i, i = 1,2, 3$	第 $i$ 个OD区段	$t t 、 t z 、 t r$	停站、折返、换乘走行时间/min
$Q P i +$	$P i$ 区段上行区间的小时断面客流量集合/（人·h^-1）	$η m a x$	最大满载率/%
$Q P i -$	$P i$ 区段下行区间的小时断面客流量集合/（人·h^-1）	$f m i n 、 f m a x$	最小、最大发车频率/［（对·h^-1）^-1］
$T A$	$A$ 模式下的乘客总出行时间/min	$ω i, i = 1,2, 3$	第 $i$ 个目标的权重系数

Table 1

Table 2

Routing of passengers under cross-line operation mode"

OD区段	$d ∈ P 1$	$d ∈ P 2$	$d ∈ P 3$
$o ∈ P 1$	$B ? o r ? E$	$E$	$① B ? o r ? E → S, s t r + λ < d ② E → N, o > d, s t r + λ ≥ d$
$o ∈ P 2$	$E$	$① E ? o r ? N, o < d ② E ? o r ? S, o > d$	$① N, d ≤ o + λ ?? ② S, d > o + λ$ $③ N, d < o + λ ?? ④ S, d > o + λ ⑤ S ? o r ? N, d = o + λ$
$o ∈ P 3$	$① N → B ? o r ? E, s t r + λ < o ② S → E, o > d, s t r + λ ≥ o$	$① N, d ≤ o + λ ② S, d > o + λ$	$① N, d ≤ o + λ ?? ② S, d > o + λ$ $③ N, d < o + λ ?? ④ S, d > o + λ ⑤ S ? o r ? N, d = o + λ$

Table 2

Table 3

Passenger flow volume for each routing"

OD区段

d ∈ P 1

d ∈ P 2

d ∈ P 3

o ∈ P 1

∑ d = 1 s t r ∑ o = 1 s t r q o d

∑ d = s t r s a ∑ o = 1 s t r - 1 q o d

① ∑ d = s t r + λ + 1 s n ∑ o = 1 s t r - 1 q o d ? ② ∑ d = s a s t r + λ ∑ o = 1 s t r - 1 q o d

o ∈ P 2

∑ d = 1 s t r - 1 ∑ o = s t r s a q o d

① ∑ d = o + 1 s a ∑ o = s t r s a q o d ? ② ∑ d = s t r o - 1 ∑ o = s t r s a q o d

$① ∑ d = s a + 1 o + λ ∑ o = s t r s a q o d ? ② ∑ d = o + λ + 1 s n ∑ o = s t r s a q o d$

$③ ∑ d = s a + 1 o + λ ∑ o = s t r s a q o d ? ④ ∑ d = o + λ + 1 s n ∑ o = s t r s a q o d ⑤ ∑ d = o + λ s n ∑ o = s t r s a q o d$

o ∈ P 3

① ∑ d = 1 s t r - 1 ∑ o = s t r + λ + 1 s n q o d ② ∑ d = 1 s t r - 1 ∑ o = s a s t r + λ q o d

① ∑ o = d + λ + 1 s n ∑ d = s t r s a q o d ? ② ∑ o = s a + 1 d + λ ∑ d = s t r s a q o d

$① ∑ d = o + 1 s n ∑ o = s a + 1 s n q o d ? ② ∑ d = s a + 1 o - 1 ∑ o = s a + 1 s n q o d$

$③ ∑ d = s a + 1 o + λ ∑ o = s t r s a q o d ? ④ ∑ d = o + λ + 1 s n ∑ o = s t r s a q o d ⑤ ∑ d = o + λ s n ∑ o = s t r s a q o d$

Table 3

Table 4

Average travel time for passengers in the cross-line operation mode"

OD区段	$d ∈ P 1$	$d ∈ P 2$	$d ∈ P 3$
$o ∈ P 1$	$30 / f B m o d e 2 + f E m o d e 2$	$30 / f E m o d e 2$	$① 30 / f B m o d e 2 + f E m o d e 2 + t r + 30 / f S m o d e 2 ② 30 / f E m o d e 2 + 60 / f N m o d e 2 + f E m o d e 2$
$o ∈ P 2$	$30 / f E m o d e 2$	$① 30 / f N m o d e 2 + f E m o d e 2 ? ② 30 / f S m o d e 2 + f E m o d e 2$	$① 30 / f N m o d e 2 ? ② 30 / f S m o d e 2$ $③ 30 / f N m o d e 2 ? ④ 30 / f S m o d e 2 ⑤ 30 / f N m o d e 2 + f S m o d e 2$
$o ∈ P 3$	$① 30 / f B m o d e 2 + f E m o d e 2 + t r + 30 / f N m o d e 2 ② 30 / f S m o d e 2 + 60 / f S m o d e 2 + f E m o d e 2$	$① 30 / f N m o d e 2 ? ② 30 / f S m o d e 2$	$① 30 / f N m o d e 2 ? ② 30 / f S m o d e 2$ $③ 30 / f N m o d e 2 ? ④ 30 / f S m o d e 2 ⑤ 30 / f N m o d e 2 + f S m o d e 2$

Table 4

Fig.2

Fig.3

Fig.4

Fig.5

Table 5

Solving result"

运营模式

开行方案

函数目

标值

乘客出行时间/min

车辆走行公里数/（veh·km^-1）

跨线直达乘客数/人

运用列车数/列

s a

f B A

f E A

f N A

f S A

独立运营

372 820

1 148

跨线运营

0.835 0

373 190

1 148

13 455

Table 5

Table 6

Solving results for different weights"

$ω 1 : ω 2 : ω 3$	开行方案					目标函数值	乘客出行时间变化率/%	车辆走行公里数变化率/%	跨线直达乘客数占比	运用车数/辆
$ω 1 : ω 2 : ω 3$	$s a$	$f B A$	$f E A$	$f N A$	$f S A$	目标函数值	乘客出行时间变化率/%	车辆走行公里数变化率/%	跨线直达乘客数占比	运用车数/辆
3：3：4	17	8	6	12	12	0.835 0	0.10%	0	41.34%	41
2：2：1	15	8	6	12	12	0.931 1	2.16%	-2.53%	33.76%	40
3：1：1	15	7	7	12	12	0.923 7	-1.11%	-1.05%	33.76%	41
1：3：1	13	8	6	12	12	0.930 0	4.46%	-5.05%	24.41%	39

Table 6

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Optimization of cross-line train operation across the urban rail transit loop line

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