基于载荷-电池柔性配置的车机协同路由智能优化方法

张志远; 宋韬; 谷雪晨; 林德福

doi:10.12382/bgxb.2026.0463

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基于载荷-电池柔性配置的车机协同路由智能优化方法

更新时间：2026-09-08

- 基于载荷-电池柔性配置的车机协同路由智能优化方法
- Intelligent Optimization Method for Truck-Drone Collaborative Routing Based on Payload–Battery Flexible Configuration
- 兵工学报 2026年
- 作者机构：
  
  北京理工大学空天科学与技术学院, 北京100081
- 作者简介：
  
  邮箱：7520240237@bit.edu.cn
- 基金信息：
- DOI：10.12382/bgxb.2026.0463
  中图分类号： V71
- 收稿：2026-05-17，
  
  修回：2026-09-01，
  
  录用：2026-07-30，
- 稿件说明：
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张志远, 宋韬, 谷雪晨, 等. 基于载荷-电池柔性配置的车机协同路由智能优化方法[J/OL]. 兵工学报, 2026.

ZHANG Zhiyuan, SONG Tao, GU Xuechen, et al. Intelligent Optimization Method for Truck-Drone Collaborative Routing Based on Payload–Battery Flexible Configuration[J/OL]. Acta Armamentarii, 2026.
张志远, 宋韬, 谷雪晨, 等. 基于载荷-电池柔性配置的车机协同路由智能优化方法[J/OL]. 兵工学报, 2026. DOI： 10.12382/bgxb.2026.0463.

ZHANG Zhiyuan, SONG Tao, GU Xuechen, et al. Intelligent Optimization Method for Truck-Drone Collaborative Routing Based on Payload–Battery Flexible Configuration[J/OL]. Acta Armamentarii, 2026. DOI： 10.12382/bgxb.2026.0463.

摘要

针对低空经济下车机协同配送受限于无人机固定载荷与电池配置、导致应用场景受限的问题，本文研究了考虑载荷-电池柔性配置的车机协同路由问题（Vehicle Routing Problem with Drones and Battery Allocation

VRPD-BA）。首先，提出了物理机理驱动的无人机能耗模型，设计了以任务需求为导向的机载模块电池与载荷动态配置策略，通过“载荷-电池”的柔性耦合实现对不同航程与载荷需求的自适应匹配。其次，提出了一种数据结构与启发式规则深度融合的智能优化方法。该方法基于模因算法框架，构建了面向柔性配置决策的能量-载荷映射数据结构以降维决策空间，并设计了嵌入能耗约束的启发式搜索算子，实现了配置策略和路由规划的协同优化。仿真结果表明：在小规模算例中所提算法能获得与数学规划求解器一致的最优解，且计算效能提升90%以上；在中、大规模算例中，其求解精度显著优于主流启发式方法，且经秩和检验显著性更优。研究证实，载荷-电池柔性配置策略能有效突破固定参数限制，在极端载荷与航程需求工况下具有更优适配性，为低空智能物流的高效调度提供理论依据与决策支持。

Abstract

Cooperative truck-drone delivery under the low-altitude economy is often constrained by fixed drone payloads and battery configurations

which severely limits its application scenarios. To address this issue

this paper investigates the Vehicle Routing Problem with Drones and Battery Allocation (VRPD-BA) considering flexible payload-battery configurations. First

a physics-driven drone energy consumption model is constructed

and a task-demand-oriented dynamic allocation mechanism for airborne battery modules and payloads is established. Through the flexible coupling of "payload-battery"

adaptive matching for diverse flight ranges and payload demands is achieved. Second

an intelligent optimization method characterized by a deep integration of data structures and heuristic rules is proposed. Within the framework of a memetic algorithm

an energy-payload mapping data structure tailored for flexible configuration decisions is designed to reduce the dimensionality of the decision space

and heuristic search operators embedded with energy consumption constraints are developed

thereby achieving the collaborative optimization of configuration strategies and routing plans. Simulation results demonstrate that the proposed algorithm can obtain the same optimal solutions as mathematical programming solvers in small-scale instances while improving computational efficiency by over 90%. For medium- and large-scale instances

it significantly outperforms mainstream heuristic approaches in solution quality

with superior statistical significance verified by the Wilcoxon rank-sum test. This study confirms that the flexible payload-battery configuration strategy effectively breaks through the limitations of fixed parameters and offers superior adaptability under extreme payload and range conditions

providing a theoretical insights and decision support for the efficient scheduling of low-altitude intelligent logistics.

关键词

Keywords

references

LIU C , ZHANG Z , DING X . Opportunities and technical challenges for electric motor drives in low-altitude economy [J/OL ] . Chinese Journal of Aeronautics , 2025 , 38 ( 8 ): 103529 . DOI: 10.1016/j.cja.2025.103529 http://dx.doi.org/10.1016/j.cja.2025.103529 .

ZHAI R , MEI Y , GUO T , et al . A Collaborative Drone-Truck Delivery System With Memetic Computing Optimization- [J/OL ] . IEEE Transactions on Systems , Man, and Cyber-netics: Systems, 2024 , 54 ( 6 ): 3618 - 3630 . DOI: 10.1109/TSMC.2024.3371471 http://dx.doi.org/10.1109/TSMC.2024.3371471 .

AMINE MASMOUDI M , MANCINI S , BALDACCI R , et al . Vehicle routing problems with drones equipped with multi-package payload compartments [J/OL ] . Transpor-tation Research Part E: Logistics and Transportation Review , 2022 , 164 : 102757 . DOI: 10.1016/j.tre.20-22.102757 http://dx.doi.org/10.1016/j.tre.20-22.102757 .

MURRAY C C , CHU A G . The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery [J/OL ] . Transportation Research Part C: Emerging Technologies , 2015 , 54 : 86 - 109 . DOI: 10.10-16/j.trc.20-15.03.005 http://dx.doi.org/10.10-16/j.trc.20-15.03.005 .

AGATZ N , BOUMAN P , SCHMIDT M . Optimization Approaches for the Traveling Salesman Problem with Drone [J/OL ] . Transportation Science , 2018 , 52 ( 4 ): 965 - 981 . DOI: 10.1287/trsc.2017.0791 http://dx.doi.org/10.1287/trsc.2017.0791 .

MURRAY C C , RAJ R . The multiple flying sidekicks traveling salesman problem: Parcel delivery with multi-ple drones [J/OL ] . Transportation Research Part C: Emerging Technologies , 2020 , 110 : 368 - 398 . DOI: 10.1016/j.trc.20-19.11.003 http://dx.doi.org/10.1016/j.trc.20-19.11.003 .

WANG X , POIKONEN S , GOLDEN B . The vehicle routing problem with drones: several worst-case results [J/OL ] . Optimization Letters , 2017 , 11 ( 4 ): 679 - 697 . DOI: 10.10-07/s11590-016-1035-3 http://dx.doi.org/10.10-07/s11590-016-1035-3 .

BABAEE TIRKOLAEE E , CAKMAK E , KARADAYI-USTA S . Traveling salesman problem with drone and bicycle: Multimodal last-mile e-mobility [J/OL ] . Inter-national Transactions in Operational Research , 2025 , 32 ( 6 ): 3232 - 3258 . DOI: 10.1111/itor.13452 http://dx.doi.org/10.1111/itor.13452 .

RAMADHAN F , IRAWAN C A , SALHI S , et al . The truck traveling salesman problem with drone and boat for humanitarian relief distribution in flood disaster: Math-ematical model and solution methods [J/OL ] . European Journal of Operational Research , 2025 , 322 ( 1 ): 270 - 291 . DOI: 10.1016/j.ejor.2024.10.022 http://dx.doi.org/10.1016/j.ejor.2024.10.022 .

LUO Z , POON M , ZHANG Z , et al . The multi-visit traveling salesman problem with multi-drones [J/OL ] . Transportation Research Part C: Emerging Technologies , 2021 , 128 : 103172 . DOI: 10.1016/j.trc.2021.103172 http://dx.doi.org/10.1016/j.trc.2021.103172 .

GU R , POON M , LUO Z , et al . A hierarchical solution evaluation method and a hybrid algorithm for the vehicle routing problem with drones and multiple visits [J/OL ] . Transportation Research Part C: Emerging Technologies , 2022 , 141 : 103733 . DOI: 10.1016/j.trc.2022.103733 http://dx.doi.org/10.1016/j.trc.2022.103733 .

TAMKE F , BUSCHER U . The vehicle routing problem with drones and drone speed selection [J/OL ] . Computers & Operations Research , 2023 , 152 : 106112 . DOI: 10.10-16/j.cor.2022.106112 http://dx.doi.org/10.10-16/j.cor.2022.106112 .

XING J , SU L , HONG W , et al . Aerial-ground collaborative routing with time constraints [J/OL ] . Chinese Journal of Aeronautics , 2023 , 36 ( 2 ): 270 - 283 . DO-I:10.1016/j.cja.20-22.09.009.

ZHANG J , CAMPBELL J F , SWEENEY II D C , et al . Energy consumption models for delivery drones: A comparison and assessment [J/OL ] . Transportation Re-search Part D: Transport and Environment , 2021 , 90 : 102668 . DOI: 10.1016/j.trd.2020.102668 http://dx.doi.org/10.1016/j.trd.2020.102668 .

JEONG H Y , SONG B D , LEE S . Truck-drone hybrid delivery routing: Payload-energy dependency and No-Fly zones [J/OL ] . International Journal of Production Eco-nomics , 2019 , 214 : 220 - 233 . DOI: 10.10-16/j.ijpe.20-19.01.010 http://dx.doi.org/10.10-16/j.ijpe.20-19.01.010 .

WU G , MAO N , LUO Q , et al . Collaborative Truck-Drone Routing for Contactless Parcel Delivery During the Epidemic [J/OL ] . IEEE Transactions on Intelligent Trans-portation Systems , 2022 , 23 ( 12 ): 25077 - 25091 . DOI: 10.1109/TITS.2022.3181282 http://dx.doi.org/10.1109/TITS.2022.3181282 .

GÜREL Ö , SERDARASAN S . Drone-Assisted Last-Mile Delivery Under Windy Conditions: Zero Pollution Solutions [J/OL ] . Smart Cities , 2024 , 7 ( 6 ): 3437 - 3457 . DOI: 10.3390/smartcities7060134 http://dx.doi.org/10.3390/smartcities7060134 .

CAVANI S , IORI M , ROBERTI R . Exact methods for the traveling salesman problem with multiple drones [J/OL ] . Transportation Research Part C: Emerging Technologies , 2021 , 130 : 103280 . DOI: 10.10-16/j.trc.2021.103280 http://dx.doi.org/10.10-16/j.trc.2021.103280 .

TINIÇ G O , KARASAN O E , KARA B Y , et al . Exact solution approaches for the minimum total cost traveling salesman problem with multiple drones [J/OL ] . Trans-portation Research Part B: Methodological , 2023 , 168 : 81 - 123 . DOI: 10.1016/j.trb.2022.12.007 http://dx.doi.org/10.1016/j.trb.2022.12.007 .

MAHMOUDINAZLOU S , KWON C . A hybrid genetic algorithm with type-aware chromosomes for traveling salesman problems with drone [J/OL ] . European Journal of Operational Research , 2024 , 318 ( 3 ): 719 - 739 . DOI: 10.1016/j.ejor.2024.05.009 http://dx.doi.org/10.1016/j.ejor.2024.05.009 .

SHUAIBU A S , MAHMOUD A S , SHELTAMI T R . A Review of Last-Mile Delivery Optimization: Strategies, Technologies, Drone Integration, and Future Trends [J/OL ] . Drones , 2025 , 9 ( 3 ): 158 . DOI: 10.3390-/drones9030158 http://dx.doi.org/10.3390-/drones9030158 .

TANG C , WEI Q , HE J , et al . A Deep Reinforcement Learning-Based Hyper-Heuristic for Time-Dependent Green Logistics With Crowdsourcing [J/OL ] . IEEE Transactions on Intelligent Transportation Systems , 2026 , 27 ( 4 ): 4766 - 4781 . DOI: 10.1109/TITS.2025.3641646 http://dx.doi.org/10.1109/TITS.2025.3641646 .

GUO T , MEI Y , ZHANG M , et al . Learning-Aided Neighborhood Search for Vehicle Routing Problems [J/OL ] . IEEE Transactions on Pattern Analysis and Machine Intelligence , 2025 , 47 ( 7 ): 5930 - 5944 . DOI: 10.1109/TP-AMI.2025.3554669 http://dx.doi.org/10.1109/TP-AMI.2025.3554669 .

GUO T , MEI Y , ZHANG M , et al . Enhanced Evolution of Parallel Algorithm Portfolio for Vehicle Routing Problem via Transfer Optimization [J/OL ] . IEEE Transactions on Evolutionary Computation , 2025 : 1 - 1 . DOI: 10.1109/TE-VC.2025.3616385 http://dx.doi.org/10.1109/TE-VC.2025.3616385 .

ZENG W , ZHAO H , LI J Y , et al . Bi-Learning Evolutionary Optimization with Substructure Preservation for the Capa-citated Vehicle Routing Problem [J/OL ] . IEEE Transactions on Evolutionary Computation , 2026 : 1 - 1 . DOI: 10.1109/T-EVC.2026.3687601 http://dx.doi.org/10.1109/T-EVC.2026.3687601 .

LI S , LIAO T , WU G , et al . Drone on-demand delivery routing problem considering order splitting and battery swapping [J/OL ] . Computers & Industrial Engineering , 2025 , 208 : 111388 . DOI: 10.1016/j.cie.2025.111388 http://dx.doi.org/10.1016/j.cie.2025.111388 .

BARTH M , YOUNGLOVE T , SCORA G . Development of a Heavy-Duty Diesel Modal Emissions and Fuel Consumption Model [R/OL ] . 2005[ 2026-03-27 ] . https : /-/escholarship . org/uc/item/ 67 f 0 v3zf.

CHENG C , ADULYASAK Y , ROUSSEAU L M . Drone routing with energy function: Formulation and exact algorithm [J/OL ] . Transportation Research Part B: Methodological , 2020 , 139 : 364 - 387 . DOI: 10.1016/j.tr-b.2020.06.011 http://dx.doi.org/10.1016/j.tr-b.2020.06.011 .

MLADENOVIĆ N , HANSEN P . Variable neighborhood search [J/OL ] . Computers & Operations Research , 1997 , 24 ( 11 ): 1097 - 1100 . DOI: https://doi.org/10.1016/S0305-0548(97)00031-2 https://doi.org/10.1016/S0305-0548(97)00031-2 .

SOLOMON M M . Algorithms for the vehicle routing and scheduling problems with time window constraints [J ] . Operations Research , 1987 , 35 ( 2 ): 254 - 265 .

LARRAÑAGA P , KUIJPERS C M H , MURGA R H , et al . Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators [J/OL ] . Artificial Intelligence Review , 1999 , 13 ( 2 ): 129 - 170 . DOI: 10.1023/A:1006529012972 http://dx.doi.org/10.1023/A:1006529012972 .

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