Research on Bi-objective Vehicle-Cargo Matching Problem Considering Carbon Emissions

doi:10.12068/j.issn.1005-3026.2025.20240095

Abstract

Abstract:

To address the issue of insufficient consideration of carbon emissions in vehicle-cargo matching platform decision-making， a bi-objective vehicle-cargo matching model that considers both carbon emissions and platform revenue was proposed. Firstly， an optimization model was constructed with the objectives of minimizing total carbon emissions and maximizing vehicle-cargo matching platform revenue， with load and time constraints. Secondly， to address the model’s multi-objective and non-deterministic polynomial （NP） hard nature， a multi-objective particle swarm optimization （PSO） algorithm was designed， including encoding rules embedded in feasibility analysis， an adaptive elite retention strategy， and a nonlinear decreasing inertia weight. Comparative results on three large-scale examples demonstrate that the proposed algorithm outperforms the NSPSO algorithm， the improved NSGA-II algorithm， and the multi-objective grey wolf algorithm in terms of convergence and uniformity， and it is superior to the latter two algorithms in terms of runtime. Finally， by analyzing the impact of carbon emissions per truck and consignors’ delivery time requirements on carbon emissions， the proposed algorithm provides management insights for platform decision-making.

Key words: vehicle-cargo matching, multi-objective optimization, intra-city freight, carbon emission, particle swarm optimization algorithm

CLC Number:

N 949

Min HUANG, Ye-xin DU, Hao YU, Xing-wei WANG. Research on Bi-objective Vehicle-Cargo Matching Problem Considering Carbon Emissions[J]. Journal of Northeastern University(Natural Science), 2025, 46(12): 9-18.

Figures/Tables 13

Table 1 Symbol definitions

符号	含义
$i ∈ V$	车主集合
$j ∈ J$	货主集合
$D i j$	车主与货主之间的距离
$D j$	货主与运送目的地之间的距离
$v$	货车行驶的平均速度
$C i j$	货主支付的费用
$q$	平台对货主支付费用的抽成比例
$e i$	车主驾驶车辆的单位碳排放
$W i$	车主驾驶车辆的最大载重
$m i$	车主驾驶车辆的空载质量
$m j$	货主的货物质量
$T G, j$	货主要求货物送达目的地时间，假设匹配时刻为计时零点
$x j ∈ 0,1$	车主和货主的匹配情况，匹配为1，反之为0

Table 1 Symbol definitions

符号	含义
$i ∈ V$	车主集合
$j ∈ J$	货主集合
$D i j$	车主与货主之间的距离
$D j$	货主与运送目的地之间的距离
$v$	货车行驶的平均速度
$C i j$	货主支付的费用
$q$	平台对货主支付费用的抽成比例
$e i$	车主驾驶车辆的单位碳排放
$W i$	车主驾驶车辆的最大载重
$m i$	车主驾驶车辆的空载质量
$m j$	货主的货物质量
$T G, j$	货主要求货物送达目的地时间，假设匹配时刻为计时零点
$x j ∈ 0,1$	车主和货主的匹配情况，匹配为1，反之为0

Fig.1 Traditional elite retention strategy rules

Fig.2 Adaptive elite retention strategy rules

Table 2 Consignor information

货主编号	货源地经度/（°）	货源地纬度/（°）	目的地经度/（°）	目的地纬度/（°）	要求送达时间/h	货物质量/t
1	120.343 7	30.289 2	117.217 4	39.153 4	16	28
2	120.959 4	30.051 9	117.017 2	39.132 1	35	25
3	120.278 4	30.416 5	116.157 2	39.750 1	22	10
…	…	…	…	…	…	…

Table 3 Vehicle model information

车型	最大载重/t	车辆自重/t	单位碳排放/（kg·km^-1）	起步价/元	单价/（元·km^-1）
1	8	6.5	0.040	470	4.5
2	13	8.8	0.045	600	6.0
3	18	13.5	0.050	750	6.5
4	25	16.0	0.055	900	7.5
5	30	18.0	0.060	1 200	8.0

Table 4 Car owner information

车主编号	车主经度/（°）	车主纬度/（°）	车型
1	120.257 6	30.227 5	2
2	119.886 9	29.179 0	5
3	120.259 4	30.096 7	4
…	…	…	…

Fig.3 Solution results of the supply-demand ratio for three types of vehicle-cargo matching examples

Table 5 Comparison of performance indicators for six algorithms

规模	算法	$I L e b e s g u e$ 均值	$I L e b e s g u e$ 方差	$I S p a c i n g$ 均值	$I S p a c i n g$ 方差	t/s
10货主与 20车主	NSPSO	0.469 9	0.001 732	0.052 0	0.000 463	1.365 8
	AERS-MPSO	0.337 9	0.001 645	0.035 9	0.000 427	1.475 0
	ND-MPSO	0.536 6	0.001 794	0.056 0	0.000 504	1.586 0
	改进后的NSGA-Ⅱ^[15]	0.523 4	0.001 691	0.045 9	0.000 472	1.768 0
	MOGWO	0.525 7	0.001 758	0.053 8	0.000 562	1.948 0
	AERSND-MPSO	0.527 0	0.001 506	0.037 1	0.000 384	1.759 2
30货主与 50车主	NSPSO	1.326 7	0.012 829	0.113 9	0.000 205	2.854 0
	AERS-MPSO	1.312 2	0.011 830	0.088 3	0.000 194	2.879 0
	ND-MPSO	1.528 7	0.013 730	0.121 3	0.000 210	2.899 0
	改进后的NSGA-Ⅱ^[15]	1.450 3	0 .009 435	0.106 6	0.000 190	3.780 0
	MOGWO	1.480 4	0.011 250	0.120 5	0.002 58	4.386 0
	AERSND-MPSO	1.524 5	0.008 220	0.098 2	0.000 183	3.682 4
60货主与 100车主	NSPSO	1.821 8	0.008 236	0.109 0	0.000 268	4.684 0
	AERS-MPSO	1.627 2	0.008 046	0.086 3	0.000 210	4.703 4
	ND-MPSO	2.578 4	0.007 945	0.114 6	0.000 238	4.824 5
	改进后的NSGA-Ⅱ^[15]	2.035 0	0.007 682	0.098 6	0.000 184	5.895 3
	MOGWO	2.494 0	0.008 280	0.123 8	0.000 305	7.059 0
	AERSND-MPSO	2.567 0	0.006 370	0.086 6	0.000 140	5.273 0

Table 5 Comparison of performance indicators for six algorithms

规模	算法	$I L e b e s g u e$ 均值	$I L e b e s g u e$ 方差	$I S p a c i n g$ 均值	$I S p a c i n g$ 方差	t/s
10货主与 20车主	NSPSO	0.469 9	0.001 732	0.052 0	0.000 463	1.365 8
	AERS-MPSO	0.337 9	0.001 645	0.035 9	0.000 427	1.475 0
	ND-MPSO	0.536 6	0.001 794	0.056 0	0.000 504	1.586 0
	改进后的NSGA-Ⅱ^[15]	0.523 4	0.001 691	0.045 9	0.000 472	1.768 0
	MOGWO	0.525 7	0.001 758	0.053 8	0.000 562	1.948 0
	AERSND-MPSO	0.527 0	0.001 506	0.037 1	0.000 384	1.759 2
30货主与 50车主	NSPSO	1.326 7	0.012 829	0.113 9	0.000 205	2.854 0
	AERS-MPSO	1.312 2	0.011 830	0.088 3	0.000 194	2.879 0
	ND-MPSO	1.528 7	0.013 730	0.121 3	0.000 210	2.899 0
	改进后的NSGA-Ⅱ^[15]	1.450 3	0 .009 435	0.106 6	0.000 190	3.780 0
	MOGWO	1.480 4	0.011 250	0.120 5	0.002 58	4.386 0
	AERSND-MPSO	1.524 5	0.008 220	0.098 2	0.000 183	3.682 4
60货主与 100车主	NSPSO	1.821 8	0.008 236	0.109 0	0.000 268	4.684 0
	AERS-MPSO	1.627 2	0.008 046	0.086 3	0.000 210	4.703 4
	ND-MPSO	2.578 4	0.007 945	0.114 6	0.000 238	4.824 5
	改进后的NSGA-Ⅱ^[15]	2.035 0	0.007 682	0.098 6	0.000 184	5.895 3
	MOGWO	2.494 0	0.008 280	0.123 8	0.000 305	7.059 0
	AERSND-MPSO	2.567 0	0.006 370	0.086 6	0.000 140	5.273 0

Fig.4 Comparison of performance indicators of six algorithms under three different scales

Table 6 Significance test of p-values obtained by AERSND-MPSO algorithm and other algorithms on problems

指标	算法	p值
指标	算法	10货主与20车主	30货主与50车主	60货主与100车主
$I L e b e s g u e$	Al₀与AL₁	0.008	0.001	0.000
	Al₀与AL₂	0.851	0.111	0.000
	Al₀与AL₃	0.946	0.356	0.073
$I S p a c i n g$	Al₀与AL₁	0.133	0.022	0.003
	Al₀与 AL₂	0.368	0.186	0.049
	Al₀与AL₃	0.114	0.004	0.000

Table 6 Significance test of p-values obtained by AERSND-MPSO algorithm and other algorithms on problems

指标	算法	p值
指标	算法	10货主与20车主	30货主与50车主	60货主与100车主
$I L e b e s g u e$	Al₀与AL₁	0.008	0.001	0.000
	Al₀与AL₂	0.851	0.111	0.000
	Al₀与AL₃	0.946	0.356	0.073
$I S p a c i n g$	Al₀与AL₁	0.133	0.022	0.003
	Al₀与 AL₂	0.368	0.186	0.049
	Al₀与AL₃	0.114	0.004	0.000

Fig.5 Impact of ei change on total carbon emissions

Fig.6 Impact of Tj change on total carbon emissions

Table 7 Range of abscissas spanned by three

$T j$	$T 1$	$T 2$	$T 3$
横坐标范围×10^-4/kg	1.406 2	1.506 8	1.170 8

Table 7 Range of abscissas spanned by three

$T j$	$T 1$	$T 2$	$T 3$
横坐标范围×10^-4/kg	1.406 2	1.506 8	1.170 8

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