Vehicle routing problem with drones considering restricted area

Journal Information

J. Hefei Univ. Tech. (Nat. Sci.), Jan.2026, Vol.49 No.1: 13-21

DOI: 10.3969/j.issn.1003-5060.2026.01.002

Authors

MA Huawei ^1,2, CHEN Zhenkun ^1,2

(1. School of Management, Hefei University of Technology, Hefei 230009, China; 2. Key Laboratory of Process Optimization and Intelligent Decision Making, Ministry of Education, Hefei 230009, China)

Abstract and Keywords

Abstract: Considering the regional restrictions imposed on vehicles and drones due to traffic congestion and air transport control, as well as the issues of prolonged delivery times and low efficiency in logistics distribution, a vehicle-drone cooperative delivery mode is proposed. This mode leverages the unique characteristics of both drones and vehicles. To address the challenge of vehicle-drone cooperative path planning under regional restrictions, a two-stage algorithm is developed with the primary aim of minimizing the total delivery time for vehicle-drone operations. In the first stage, an initial path is generated using the nearest neighbor algorithm, while the second stage employs an improved sub-heuristic algorithm to optimize the path. By integrating simulated annealing mechanisms into the genetic algorithm, the risk of falling into local optima is mitigated. Moreover, various crossover and mutation operators are designed to enhance the global optimization capability of the algorithm. The performance and superiority of the model and algorithm are robustly evaluated through comprehensive numerical experiments on a diverse set of examples. The results demonstrate that the proposed algorithm effectively solves the problem of vehicle-drone cooperative path planning under regional restrictions.

Keywords: vehicle-drone cooperation; restricted area; path planning; drone delivery for multi-customer; two-stage sub-heuristic algorithm(TSA)

作者信息

马华伟 ^1,2，陈臻琨 ^1,2

(1. 合肥工业大学管理学院，安徽合肥 230009；2. 过程优化与智能决策教育部重点实验室，安徽合肥 230009)

摘要和关键词

摘要: 考虑到交通拥堵、空运管制等原因造成的车辆、无人机行驶区域限制以及物流配送中存在的耗时长、效率低等问题，结合无人机和车辆的各自特点，文章采用“车辆＋无人机”协同配送模式，针对区域限制下的车机协同路径规划问题，提出一种以最小化配送总时长为目标的两阶段求解算法，第1阶段利用最近邻算法生成初始路径，第2阶段采用改进的亚启发式算法对路径进行优化。引入模拟退火机制，避免该算法陷入局部最优；同时设计多种交叉算子和变异算子，进一步提升算法的全局寻优能力；最后，在算例集上进行多种数值实验，验证所提模型和算法的性能及优越性。结果表明，文章算法能有效解决区域限制下的车机协同路径规划问题。

关键词: 车机协同；区域限制；路径规划；无人机多点配送；两阶段亚启发式算法

Funding

国家重点研发计划资助项目（2019YFE0110300）；国家自然科学基金资助项目（72271076）

合肥工业大学学报(自然科学版)

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