基于多模式双动态演化的拥堵收费模型

doi:10.13229/j.cnki.jdxbgxb.20230717

Abstract

Abstract:

This paper presents a bi-level model to address congestion pricing in a multi-modal transportation system. The upper level is an optimization model aiming to minimize the total social cost and determine the optimal congestion price for road segments. Meanwhile， the lower level is a doubly dynamical model including day-to-day traffic dynamics and within-day traffic dynamics. Solving the bi-level model employs a genetic algorithm. Three congestion pricing schemes are proposed and compared， namely no congestion pricing（NCP）， congestion pricing for cars（CPC） and congestion pricing for both cars and car-sharing（CPCS）. The results show that compared to the NCP， the CPC and CPCS result in a 17.44% and 14.89% reduction in private car trips， respectively. Additionally， the average travel times for private cars decrease by 7.54% and 30.18% under the CPC and CPCS， respectively. In the CPC scheme， car-sharing could generate maximum revenue and be the mode accounting for the largest share（39.97%） of the multi-modal transportation system.

Key words: engineering of communication and transportation, system urban traffic, congestion pricing, bi-level model, multi-modal transportation system, doubly dynamical evolution, car-sharing

CLC Number:

U491

Cheng-dong ZHOU,Fei SONG,Xiao-mei ZHAO,Jun-jie YAO. Congestion pricing model in multi-modal network based on doubly dynamical evolution[J].Journal of Jilin University(Engineering and Technology Edition), 2025, 55(4): 1319-1327.

Figures/Tables 9

Fig.1

Table 1

Fig.2

Fig.3

Table 2

Basic parameters"

参数	数值	参数	数值
$ω$	0.8	$P s h a r e c o m f$ /（元·次^-1）	3
$ρ$	0.2	$θ$	0.1
$n s$	20	$Q$ /d	30
$W$	120	$t s 2 b c h a n g e$ /min	7
$β v e l$	-0.010	$c c a r, f i x$ /（元·次^-1）	10
$a 1$ /（元·h^-1）	9	$a b u s$	15
$γ b u s$	-0.06	$T b u s d e t o u r$ /min	6
$c 1$ /（元·km^-1）	0.5	$P s 2 b c o m f$ /（元·次^-1）	5
$B b u s q$ /辆	30	$P b 2 s c o m f$ /（元·次^-1）	5
$α$ /（元·h^-1）	50	$T b u s w a i t$ /min	7
$t c 2 b c h a n g e$ /min	5	$α v e l$	30
$t b 2 s c h a n g e$ /min	7	$δ$	0.5
$a 0$ /（元·h^-1）	6	$γ v e l$	-0.3
$T s h a r e d e t o u r$ /min	10	$a, b, c$	1.0，0.3，0.3
$P c 2 b c o m f$ /（元·次^-1）	2	$β b u s$	-0.003
$P c a r p a r k$ /（元·次^-1）	2	$c 2$ /（元·min^-1）	0.3

Table 2

Fig.4

Table 3

Table 4

Table 5

References 13

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输入：	个体形式、优化目标、参数等
输出：	优化过程指标图，优化模型的最优解的方案结果
步骤1	初始化群体。将收费方案作为染色体，随机生成一个初始种群，规模为M。
步骤2	个体评价。对每个收费方案，下层演化模型都能得到对应的目标值，进而将目标值带入上层优化目标函数。本次案例采用上层目标函数作为适应度函数，来衡量一个个体对环境的适应程度。由于本次实验为最小值问题，因此该数值越小则适应度越高，代表该个体有更大的概率生存下来。
步骤3	选择运算。计算选择概率，使用精英保留法选择种群中适应度最高的40%作为精英个体遗传到下一代，淘汰适应度最低的个体。
步骤4	交叉运算。设定交叉概率，使个体间进行配对，即使个体间交换、重组部分基因。
步骤5	变异运算。设定变异概率，随机改变染色体上的基因，通过改变基因生成新的个体。
步骤6	终止条件判断。判断迭代次数是否达到案例设置的最大迭代次数，是则停止计算，进行染色体解码，输出结果；否则返回步骤2。

时段	CPC方案		CPCS方案
时段	平峰	高峰	平峰	高峰
1	5.22	9.8	0.34	1.92
2	5.01	9.38	4.15	7.02
3	4.12	8.99	0.00	0.36
4	0.00	0.81	0.00	0.00
5	2.31	6.01	3.41	6.77
6	0.00	0.61	1.12	3.81
7	4.55	7.76	3.28	6.53
8	5.93	8.72	0.00	0.00
9	1.12	3.11	3.26	6.86
10	7.28	9.42	0.00	0.37
11	2.89	6.01	1.99	4.56
12	5.27	8.68	0.89	2.29
13	3.01	5.72	6.24	8.49
14	3.51	6.90	1.78	3.48
15	2.01	4.76	7.56	9.37
16	1.38	4.90	0.00	0.10
17	1.44	4.89	3.27	5.63
18	6.88	9.82	0.42	2.74
19	2.12	5.25	0.13	1.00

出行模式	NCP比例	CPC比例	CPCS比例
car	34.64	17.2	19.75
share	31.83	39.97	17.71
bus	13.49	27.25	51.10
c2b	7.39	3.46	4.24
s2b	5.93	5.32	3.17
b2s	6.72	6.80	3.76

评价指标	NCP（参考）	CPC	CPCS
STTC/万元	211.97	213.11 （+0.53%）	217.23 （+2.48%）
BSR/万元	5.70	6.48 （+13.68%）	8.76 （+53.68%）
SVSR/万元	26.55	31.24 （+17.66%）	18.15 （-31.63%）
CCR/万元	0	3.42	12.92
TTTC/h	15 233.68	11756.31 （-22.82%）	6802.31 （-55.34%）
ATTC/h	0.53	0.49 （-7.54%）	0.37 （-30.18%）

Congestion pricing model in multi-modal network based on doubly dynamical evolution

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