时变网络下多目标空地协同取送货任务分配

doi:10.7527/S1000-6893.2026.33191

Abstract

Abstract:

Aiming at the problems of ignoring road network time-variability， single objective， and insufficient constraint integration in existing vehicle-Unmanned Aerial Vehicle （UAV） collaborative delivery research， this study focuses on the scenario of pickup and delivery with multiple distribution centers. Taking “minimizing total path length， minimizing penalty cost， and minimizing total energy consumption” as the decision-making objectives， it integrates multiple constraints such as time-varying speed， soft time windows， UAV endurance， and load capacity. A time-varying speed model based on time segment division and a penalty mechanism for soft time windows are proposed， and a multi-objective and multi-constraint optimization model is constructed. On the basis of NSGA-Ⅱ， a three-layer chromosome coding structure of “customer sequencing-distribution center allocation-UAV service marking” is designed. This structure is combined with a hybrid crossover operator， three types of mutation operators （crossover mutation， single-point mutation， and bit-flipping mutation）， and a two-layer selection strategy （tournament selection and elitism preservation）， thus establishing an improved NSGA-Ⅱ algorithm to solve the model. A case study is carried out based on 4 distribution centers and 36 customers. The results show that the total path length of the improved NSGA-Ⅱ algorithm ranges from 100.35 km to 291.21 km， the penalty cost ranges from 831.69 yuan to 12，323.58 yuan， and the total energy consumption ranges from 20.88 kW·h to 66.67 kW·h. The generated Pareto frontier has a uniform distribution， and its comprehensive performance in terms of HV， IGD， and Spacing indicators is significantly better than that of other multi-objective algorithms such as SPEA2， MOEA/D， and NSGA-Ⅲ. Furthermore， verification is conducted using the real road network of some main urban areas in Tianjin as the scenario. Actual road distance data are obtained by integrating the Amap API， and a delivery network with multi-type customer demands under a real city environment is constructed. The results indicate that the optimized scheme can adapt to the characteristics of complex urban road networks and heterogeneous demands， while balancing the objectives of efficiency， cost， and low carbon. The study confirms that the constructed model and algorithm are feasible and effective， and can provide decision support for logistics enterprises that is consistent with practical scenarios.

Key words: low-altitude economy, vehicle-drone collaborative delivery, task assignment, time-varying network, soft time window, multi-objective optimization, NSGA-Ⅱ

CLC Number:

V355.1

Fei WANG, Haofan XU. Multi-objective air-ground collaborative pickup and delivery task allocation under time-varying networks[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(16): 333191.

Figures/Tables 22

Table 1

Fig.1

Fig.2

Table 2

Distribution of parameter settings for time-varying speed

时段	时间范围/min	时段特征	平均速度 $μ$ /（km·h^-1）	标准差 $σ$ /（km·h^-1）
1	［0，390］	凌晨自由流	40	5
2	［390，540］	早高峰拥堵	15	3
3	［540，690］	早高峰过渡	30	4
4	［690，990］	日间正常	38	5
5	［990，1 140］	晚高峰拥堵	12	2
6	［1 140，1 440］	夜间自由流	45	6

Table 2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 3

Parameter settings for vehicles and UAVs

参数	取值	参数	取值
车辆载重能力 $Q$ /kg	160	无人机回收操作时间 $S R$ /min	1
车辆行驶速度 $v t$ /（km·h^-1）	30	无人机充电时间 $T c$ /min	5
车辆基础能耗系数 $α$ /（kW·h·km^-1）	0.15	无人机服务时间 $S e i d$ /min	1
车辆载重能耗系数 $β$ /（kW·h·km^-1·kg^-1）	0.001	无人机等待成本系数 $W d$ /（元·min^-1）	0.5
车辆服务时间 $S e i t$ /min	2	无人机旋翼数量 $N R$	6
车辆等待成本系数 $W t$ /（元·min^-1）	1.0	空气密度 $ρ$ /（km·m^-3）	1.204
无人机载重能力 $Q D$ /kg	12	无人机旋转叶片圆盘面积 $ζ$ /m²	0.2
无人机飞行速度 $v d$ /（km·h^-1）	50	早到惩罚系数 $Z 1$ /（元·min^-1）	10
无人机续航时间 $E$ /min	20	晚到惩罚系数 $Z 2$ /（元·min^-1）	25
无人机自重 $m d$ /kg	3	种群规模 $N$	100
无人机发射准备时间 $S L$ /min	1	最大迭代次数 $G m a x$	500

Table 3

Fig.11

Fig.12

Fig.13

Fig.14

Table 4

Table 5

Fig.15

Fig.16

Fig.17

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文献来源	目标函数数量		配送中心数量		时间窗类型			速度类型		任务类型		能源消耗
文献来源	单个	多个	单个	多个	软时间窗	硬时间窗	未考虑	时变速度	固定速度	仅配送	取送货	能源消耗
［11］	√		√				√		√	√		不考虑能耗
［10］	√		√				√		√	√		与距离相关
［6-7］	√		√				√		√	√		与距离和载荷相关
［8］	√		√				√	√		√		与距离和载荷相关
［21］	√		√		√			√			√	与时间相关
［15］		√	√		√				√	√		与距离和载荷相关
［19］		√		√		√			√	√		与距离和载荷相关
本文		√		√	√			√			√	与时间、距离和载荷相关

配送中心	服务客户总数（占比）	车辆总行驶距离/km	无人机飞行距离/km	车辆取送货路线	无人机取送货路线
DC1	11 个（30.6%）	64.63	12.67	DC1→C31［送3.7 kg，取3.1 kg］→C30［送22.7 kg，取11.6 kg］→C34［送 0.4 kg，取 2.6 kg］→C29［送 1.8 kg，取 3.0 kg］→C2［送 8.1 kg，取 6.5 kg］→C24［送 84.1 kg，取 36.9 kg］→C14［送 0.9 kg，取 2.1 kg］→C17［送 8.7 kg，取 19.5 kg］→C25［送 4.1 kg，取 2.9 kg］→C10［送 16.8 kg，取 4.7 kg］→DC1	发射点C30→服务客户C3［送4.4 kg，取 2.5 kg］→回收点C34
DC2	7 个（19.4%）	60.08		DC2→C13［送 0.8 kg，取 2.8 kg］→C21 ［送 1.6 kg，取 3.3 kg］→C27 ［送 0.8 kg，取 3.5 kg］→C19 ［送 23.4 kg，取 5.4 kg］→C4 ［送5.4 kg，取 19.5 kg］→C26［送20.4 kg，取 5.2 kg］→C1 ［送 4.8 kg，取 3.0 kg］→DC2
DC3	12 个（33.3%）	81.65	7.58	DC3→C23 ［送 4.1 kg，取 0.5 kg］→C15 ［送 4.6 kg，取 1.2 kg］→C18［送 23.8 kg，取 18.3 kg］→C33［送 13.6 kg，取 4.4 kg］→C16［送 11.2 kg，取 12.3 kg］→C5［送 44.9 kg，取 35.9 kg］→C20［送 0.5 kg，取 1.4 kg］→C36［送 2.2 kg，取 3.1 kg］→C22 ［送 1.6 kg，取 2.3 kg］→C7 ［送 1.7 kg，取 2.5 kg］→C35 ［送 2.7 kg，取 3.6 kg］→DC3	发射点C15→服务客户C28［送11.6 kg取 5.0 kg］→回收点C18
DC4	6 个（16.7%）	59.50	5.10	DC4→C11 ［送 8.4 kg，取 5.0 kg］→C9 ［送 4.0 kg，取 1.0 kg］→C12 ［送 97.6 kg，取 73.5 kg］→C8 ［送 1.7 kg，取 1.6 kg］→C32 ［送 20.4 kg，取 11.9 kg］→DC4	发射点C12→服务客户C6［送1.7 kg，取 2.2 kg］→回收点C32

算法	HV平均值	IGD平均值	Spacing平均值	总路径/km	惩罚成本/元	总能耗/（kW·h）
NSGA-Ⅱ	0.948 5	0.061 3	0.013 7	100.35~291.21	831.69~12 323.58	20.88~66.67
SPEA2	0.841 2	0.114 8	0.018 5	123.22~331.28	751.00~7 786.04	26.82~72.34
MOEA/D	0.930 3	0.084 9	0.077 7	213.33~419.88	4 597.78~21 381.02	43.46~87.72
NSGA-Ⅲ	0.912 8	0.109 1	0.022 3	124.96~331.91	1 591.00~8 935.95	25.64~67.79
GDE3	1.061 3	0.056 4	0.035 0	143.66~423.63	1 236.68~26 119.45	30.92~96.23
MOPSO	1.087 8	0.047 2	0.045 2	167.81~474.69	3 474.62~32 543.51	36.83~98.60

Multi-objective air-ground collaborative pickup and delivery task allocation under time-varying networks

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