Truck path planning method for truck and drone synchronous operation cooperative distribution

Abstract

The application discloses a truck path planning method for synchronous operation and cooperative distribution of a truck and a drone, and belongs to the field of vehicle path planning. First, two groups of truck stop points corresponding to distribution tasks can be executed at the same time. When the truck completes all the drone release work in the current group of tasks, the truck goes to the release point of the drone in the next group of truck stop points to perform the drone release work of the next group of distribution tasks. Then, the truck returns to the truck stop point for drone recovery in the previous group of distribution tasks to perform the drone recovery. Finally, the truck goes to the truck stop point for drone recovery in the next group of distribution tasks to complete the drone recovery work in the second group of distribution tasks, so as to obtain the driving path of the truck and the minimum total distribution time of the synchronous operation and cooperative distribution of the truck and the drone. This aspect realizes efficient truck and drone logistics cooperative distribution.

Description

Technical fields:

[0001] This invention relates to a truck route planning method for synchronous operation and collaborative delivery of trucks and drones, which belongs to the field of vehicle route planning. Background technology:

[0002] (1) Vehicle routing planning research

[0003] Dantzig[1] first proposed the vehicle routing problem, which refers to using logistics centers to transport demand points while meeting various material requirements, thereby minimizing the shortest distance or time, and defined it as the TSP problem. Nowadays, many new variants of the vehicle routing problem have emerged, such as: vehicle routing problem with vehicle load limit (CVRP), multi-vehicle vehicle routing problem (MTVRP), vehicle routing problem considering logistics distribution (VRPPD), multi-stochastic demand vehicle routing problem (CRPSD), multi-warehouse vehicle routing problem (MDVRP), multi-objective vehicle routing problem (MOVRP), etc. The algorithms used to solve vehicle routing problems mainly include exact algorithms and heuristic algorithms. For small-scale problems, exact algorithms are generally used to solve them, while for large-scale problems with a lot of data, heuristic algorithms are generally used. The exact algorithms mainly include: branch and bound method, minimum spanning tree method, cutting plane method, etc. The heuristic algorithms mainly include: genetic algorithm, ant colony algorithm, simulated annealing algorithm, tabu search algorithm, etc.

[0004] In summary, while much research has been conducted on vehicle routing problems, these studies have the following shortcomings when considering the context of this patent's simultaneous truck and drone collaborative delivery scenario: they rarely consider situations where vehicles collaborate with other carriers, and vehicles can serve multiple functions such as temporary charging stations and delivery points. Therefore, this patent, based on research into vehicle routing problems, establishes a truck routing model for a simultaneous truck and drone collaborative delivery scenario. This model fully considers the truck's carrying function, temporary charging station function, and delivery function, while allowing two delivery tasks to be executed simultaneously, thus better reflecting the real-world context of truck and drone collaborative delivery.

[0005] (2) Research on collaborative delivery route planning of trucks and drones

[0006] Research on route planning for truck and drone collaborative delivery can generally be divided into three categories: single truck and single drone, single truck and multiple drones, and multiple trucks and multiple drones.

[0007] Single truck, single drone

[0008] Ha[2] proposed a model with minimizing operating costs as the objective function, and developed a greedy stochastic adaptive search algorithm for this purpose. The algorithm starts with the dedicated truck route, uses the splitting principle to remove customer points from the truck route and assigns them to drones, and finally uses local search to improve the route between the drone and the truck. Yurek[3] developed an iterative two-stage algorithm. In the first stage, the truck route is obtained. In the second stage, the drone route planning model is solved to arrange the time and location of the drone launch and retrieval from the truck. Wen Tingxin[4] considered the congestion at different times during the delivery process, used the speed distribution function to characterize the vehicle speed, and considered that the drone carries multiple packages each time and can serve multiple customers. A mathematical model was established and the model was solved by the hybrid particle swarm algorithm. Marinell[5] set the truck to be able to transport and pick up drones not only at the nodes, but also along the route arc (in the middle). The path between the truck and the drone was solved by a new greedy heuristic optimization method. Cohen[6] discretized the original continuous problem of vehicle and drone path, explicitly representing it as an integer optimization problem. He developed a performance bound as a function of the discretization level and the number of targets. Through numerical research, he proved that the bound is more applicable to environments with densely distributed targets when the minimum vehicle turning radius is relatively large compared to the distance between the target and the target. Savuran[7] took the shortest total delivery time as the objective, considering that the truck only serves as the take-off and landing position of the drone and does not deliver packages to customers. He determined the location of the drone take-off and landing site and the path of the drone, solved the relevant model by genetic algorithm, and compared the results with those solved by the nearest neighbor heuristic algorithm. Li Yanfeng[8] considered that the customer's needs could be split, established a mixed integer programming model with the goal of minimizing transportation costs and truck labor costs, and designed an improved variable neighborhood search algorithm to solve the problem.

[0009] Single truck with multiple drones

[0010] Chang[9] set that after the truck retrieves all the drones at the original location, it will drive to the next truck stop, and the truck stop is selected from the cluster center of the drone service customer point. Then the path between the truck and the drone is determined. Lin Yi

[10] considered the time-varying characteristics of road network traffic, established a model of drone vehicle path problem, and proposed an improved two-stage heuristic algorithm composed of CW algorithm and dynamic programming heuristic algorithm to solve the problem. Yoon

[11] proposed a MILP formula based on TSP and used a small example problem as a test case. For this purpose, a heuristic method based on adaptive large neighborhood search was developed to solve the problem. Liu Changshi

[12] aimed at the emergency material distribution with the goal of minimizing the total delivery time, established a dynamic collaborative delivery path planning model of truck and drone, and designed an adaptive genetic algorithm to solve the problem. Tu

[13] adjusted the greedy random adaptive search process and proposed an adaptive large neighborhood search heuristic method to solve the problem of collaborative delivery of one truck and multiple drones. Campbell

[14] proposed that the number of trucks be fixed at one, but the number of drones can vary from one to eight. He established a nonlinear programming model. First, he found the cluster center of the customer point. The drones can go from the cluster center to the customer and then return to the truck. The trucks themselves do not deliver goods directly to the customer. The truck route passes through the cluster center. Liu Wusheng

[15] considered that the vehicles do not need to stop at fixed points to wait for the drones. He took the minimum total delivery distance as the objective function and designed a simulated annealing algorithm with terminal optimization to solve the problem. The results verified the feasibility of the model. (Note: n and m are integers greater than 1).

[0011] Multi-truck multi-drone

[0012] Ham

[16] considered that drones can perform two different types of tasks: delivery and pickup. After the drone completes the delivery, it can fly back to the warehouse to transport other packages or fly to another customer to pick up the package. He developed a variable sorting heuristic algorithm to solve the path between drones and trucks. Ulmer

[17] proposed a heterogeneous fleet of multiple drones and vehicles to solve the same-day delivery route problem. He used dynamic programming to generate dynamic vehicle routes to serve new customer orders and used the dynamic programming method of parameter strategy function to solve the problem. Wang

[18] considered multiple trucks, each of which carries one or more drones. He studied the maximum time savings that can be obtained by different numbers of drones, analyzed several worst cases, and provided a more applicable model and proof for the worst case. The worst case depends on the number of drones in each truck and the speed of the drone relative to the speed of the truck. Jiang Li

[19] proposed a two-level programming model, which regards the problem as a user allocation master problem and a capacity vehicle path subproblem. First, the facility point visited by the truck is determined, then the driving path of the truck is solved, and finally the delivery path of the drone is determined. Pugliese extended VRPD, proposing a vehicle-drone route problem with time windows, aiming to minimize the total transportation cost while meeting the time window requirements. The CPLEX solver was used for this purpose. Kitjacharoenchai

[21] proposed a mixed integer programming problem, first constructing the truck's driving path and then planning the drone's journey. An adaptive insertion heuristic algorithm was developed, and a large problem with up to 100 locations was solved through experiments. Gao Jiaojiao

[22] established a mixed integer programming model with the minimum delivery cost as the objective function, and developed a hybrid algorithm based on scanning algorithm and improved large-scale neighborhood search to solve the model.

[0013] In summary, in the context of this invention using a truck and multiple drones for collaborative delivery, the path planning research for trucks and drones has the following shortcomings:

[0014] ① The impact of the drone's payload and its climb, level flight, and landing states on the drone's actual endurance was not fully considered, resulting in inaccurate actual drone path planning;

[0015] ② The truck routes are selected only from the customer point cluster center, without fully considering that the determination of the truck routes will affect the overall delivery cost and delivery time.

[0016] To address the aforementioned shortcomings, this invention establishes a truck route planning model that considers the impact of the final truck route on the overall delivery time and plans the final driving route of the truck.

[0017] References involved:

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[0021] [4] Wen Tingxin, Lü Yanhua. Time-varying path optimization method for truck and drone joint delivery considering customer value [J]. Computer Applications Research, 2022, 39(10):2984-2988.

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[0025] [8] Li Yanfeng, Li Jia, Xiang Ting. Demand-decomposable UAV-truck cooperative path optimization problem [J]. Industrial Engineering, 2022, 25(01):54-63.

[0026] [9]Chang YS,Lee H J.Optimal delivery routing with wider drone-delivery areas along a shorter truck-route[J].Expert Systems withApplications,2018,104:307-317.

[0027]

[10] Lin Yi, Lü Jing, Jiang Yonglei. Research on optimization of urban and rural express delivery drone delivery considering traffic time-varying characteristics [J]. Computer Applications Research, 2020, 37(10):2984-2989.

[0028]

[11] Yoon J J. The traveling salesman problem with multiple drones: anoptimization model for last-mile delivery[D]. Massachusetts Institute of Technology, 2018.

[0029]

[12] Liu Changshi, Wu Zhang, Zhou Yufeng, et al. Optimization of dynamic collaborative delivery route of truck-UAV for emergency supplies in epidemic areas [J]. Systems Science and Mathematics, 2022, 42(11):3027-3043.7.

[0030]

[13] Tu PA,Dat NT,Dung P Q.Traveling salesman problem with multipledrones[C] / / -Proceedings of the Ninth International Symposium on Informationand Communication Technology.2018:46-53.

[0031]

[14] Campbell JF, Sweeney D, Zhang J. Strategic design for delivery with trucks and drones[J]. Supply Chain Analytics Report SCMA(04 2017), 2017:47-55.

[0032]

[15] Liu Wusheng, Li Wang, Zhou Qing, et al. Optimization model and algorithm for delivery route of "unmanned aerial vehicle-vehicle" [J]. Transportation Systems Engineering and Information, 2021, 21(06):176-186.

[0033]

[16] Ham A M.Integrated scheduling of m-truck,m-drone,and m-depotconstrained by time-window,drop-pickup,and m-visit using constraintprogramming[J].Transportation Research Part C:Emerging Technologies,2018,91:1-14.

[0034]

[17] Ulmer MW,Thomas B W.Same-day delivery with heterogeneous fleets of drones and vehicles[J].Networks,2018,72(4):475-505.

[0035]

[18] Wang

[0036]

[19] Jiang Li, Liang Changyong, Zang Xiaoning. A two-layer heuristic algorithm for contactless delivery problem in collaboration between trucks and drones [J]. Chinese Management Science, 2022: 1-11.

[0037]

[20] Di Puglia Pugliese L, Guerriero F.Last-mile deliveries by using drones and classical vehicles[C] / / International Conference on Optimizationand Decision Science.Springer,Cham,2017:557-565.

[0038]

[21] Kitjacharoenchai P,Ventresca M,Moshref-Javadi M,et al.Multipletraveling salesman problem with drones:Mathematical model and heuristicapproach[J].Computers&Industrial Engineering,2019,129:14-30.

[0039]

[22] Gao Jiaojiao, Guo Xiuping. Research on vehicle routing problem under truck-drone collaborative delivery mode [J]. Industrial Engineering and Management, 2022: 1-16. Summary of the Invention:

[0040] This invention provides a truck route planning method for synchronous operation and collaborative delivery of trucks and drones in order to solve the problems existing in the prior art. Based on the completion of truck stop location selection and drone route planning, the method plans the truck driving route to solve the total delivery time.

[0041] The technical solution adopted in this invention is: a truck route planning method for synchronous operation and collaborative delivery of trucks and drones, characterized by the following steps:

[0042] (1) Based on the completion of truck parking point selection and UAV path planning, plan the truck driving route and solve the total delivery time;

[0043] (2) Consider that the delivery tasks corresponding to two sets of truck docking points can be executed at the same time. After the truck completes the release of all drones in this set of tasks, it goes to the release point of the drones in the next set of truck docking points to release drones for the next set of delivery tasks. Then it returns to the truck docking point where the drones were retrieved in the previous set of delivery tasks to retrieve the drones. Finally, it goes to the truck docking point where the drones were retrieved in the next set of delivery tasks to complete the drone retrieval work in the second set of delivery tasks.

[0044] (3) Establish a truck route planning model for synchronous operation and collaborative delivery of trucks and drones;

[0045] (4) Solve the problem using a genetic algorithm and simulate the problem using relevant examples to obtain the truck's driving path and the total delivery time for the truck and drone to work together in a coordinated manner.

[0046] This invention offers the following advantages: In previous truck-drone collaborative delivery systems, the planning of truck routes in synchronous operation involved considering that a drone could only execute one set of delivery tasks corresponding to a single truck stop at a time. This resulted in trucks having to wait at the next truck stop to retrieve the drone after releasing it, leading to low overall delivery efficiency. This invention first analyzes the five processes of truck-drone collaborative delivery when two sets of delivery tasks corresponding to two sets of truck stops are running simultaneously. Then, considering the calculation of the total delivery time for both sets of tasks, it summarizes delivery time calculation formulas for ten different scenarios. Based on this, a truck route planning model for synchronous truck-drone collaborative delivery is established. Finally, a genetic algorithm is used to solve the total delivery time for three different drone models under different customer point scales. The calculation results show that the proposed synchronous truck-drone collaborative delivery planning scheme reduces the total delivery time by 25.59%, 34.19%, 29.09%, and 31.89% respectively compared to the previous asynchronous truck-drone collaborative delivery mode, at customer point scales of 25, 50, 75, and 100. Attached image description:

[0047] Figure 1 This diagram illustrates the simultaneous execution of a set of delivery tasks corresponding to a group of truck stops.

[0048] Figure 2 This diagram illustrates the simultaneous execution of delivery tasks corresponding to two sets of truck stops.

[0049] Figure 3 This is a time diagram for scenario 1.

[0050] Figure 4This is a time diagram for scenario 2.

[0051] Figure 5 This is a time diagram for scenario 3.

[0052] Figure 6 This is a time diagram for scenario 4.

[0053] Figure 7 This is a time diagram for scenario 5.

[0054] Figure 8 This is a time diagram for scenario 6.

[0055] Figure 9 This is a time diagram for scenario 7.

[0056] Figure 10 Situation 8 Time Diagram

[0057] Figure 11 This is a time diagram for scenario 9.

[0058] Figure 12 This is a time diagram for scenario 10.

[0059] Figure 13 To determine the chromosome crossing range diagram.

[0060] Figure 14 This is a gene copy diagram.

[0061] Figure 15 To generate a chromosome map for offspring.

[0062] Figure 16 To generate another offspring chromosome map.

[0063] Figure 17 This is a diagram of chromosome variations.

[0064] Figure 18 This is a graph showing the iteration curve of the genetic algorithm.

[0065] Figure 19 This chart compares the total delivery time for three different machine types and trucks under varying customer point numbers.

[0066] Figure 20 This graph shows the total delivery time at different truck speeds.

[0067] Figure 21 This is a comparison chart of delivery times for this patent model and the model in the reference [Li Yanfeng, Li Jia, Xiang Ting. Demand-decomposable UAV and truck collaborative path optimization problem [J]. Industrial Engineering, 2022, 25(01):54-63.] under different numbers of customer points. Detailed implementation method:

[0068] The invention will now be further described with reference to the accompanying drawings.

[0069] The present invention provides a truck route planning method for synchronized and collaborative delivery of trucks and drones, comprising the following steps:

[0070] (1) Based on the completion of truck parking point selection and drone path planning, the truck driving route is planned in order to solve the total delivery time.

[0071] (2) It is considered that two sets of truck docking points can be executed at the same time. After the truck completes the release of all drones in the current set of tasks, it goes to the release point of the drones in the next set of truck docking points to release drones for the next set of delivery tasks. Then it returns to the truck docking point where the drones were retrieved in the previous set of delivery tasks to retrieve the drones. Finally, it goes to the truck docking point where the drones were retrieved in the next set of delivery tasks to complete the drone retrieval work in the second set of delivery tasks.

[0072] (3) Establish a truck route planning model for synchronous operation and collaborative delivery of trucks and drones.

[0073] (4) The solution is obtained through a genetic algorithm and relevant simulation examples to obtain the truck's driving path and the total delivery time for the truck and drone to operate synchronously and collaboratively. Compared with the delivery mode in the prior art, the results show that the truck path optimization model for truck and drone synchronous operation and collaborative delivery proposed in this invention has a smaller total delivery time and is more in line with the requirements of actual delivery.

[0074] The truck was performing two delivery tasks simultaneously.

[0075] Once the truck's parking location, the drone's route, and delivery time are determined, the final step is to plan the truck's route.

[0076] In traditional truck and drone collaborative delivery operations, the delivery tasks corresponding to a set of truck stop locations are planned as a whole. After completing the delivery tasks for one set of truck stop locations, the next set of truck stop locations' delivery tasks begins. Assume the two sets of truck stop locations correspond to delivery tasks i and i+1, respectively, and the truck stop location for the previous set of tasks is a. i d i The truck stop corresponding to the second set of tasks is point a. i+1 d i+1 The completion times for the two delivery tasks are T and T respectively. i T i+1 ,like Figure 1 As shown, planning truck routes in this way results in low overall delivery efficiency and underutilization of trucks.

[0077] Therefore, this invention proposes to plan the delivery tasks corresponding to two sets of truck docking points as a whole. It considers that after a truck completes the release of all drones at the first set of truck docking points, it proceeds to the next set of truck docking points to release the next set of drones for the task. Then, it returns to the truck docking point where drones were retrieved in the previous delivery task to retrieve them. Finally, it proceeds to the truck docking point where drones were retrieved in the next delivery task to complete the drone retrieval work for the second delivery task (e.g., ...). Figure 2 This allows for the simultaneous execution of delivery tasks at two sets of truck docking points, increasing the efficiency of synchronized and collaborative delivery between trucks and drones, saving total delivery time, and better completing delivery tasks.

[0078] The truck and drone delivery process considered in this invention is as follows: Process 1, the truck first serves customer point a. i and from the truck stop a of the i-th task group i Release the drone to perform the delivery mission; in process 2, the truck begins to move towards the truck docking point a for the (i+1)th task group. i+1 Driving; Process 3, truck service completed at truck stop a i+1 Then from the truck stop point a of the (i+1)th task group i+1 Release the drone to perform the group's delivery mission; in process 4, the truck heads towards the truck docking point d for the i-th group's mission. i Driving; Process 5, Truck service completed at point d i Afterwards, the drones used in the i-th group of missions are retrieved at this location, and finally the truck heads towards the truck docking point d for the (i+1)-th group of missions. i+1 Driving, truck service completed at point d i+1 Then, the drones used for the (i+1)th group of tasks are retrieved at that location. This process of releasing and retrieving drones alternately continues until all customer deliveries are completed.

[0079] Truck route planning model for synchronized and collaborative delivery using trucks and drones

[0080] Model assumptions

[0081] (1) The coordinates of the customer points where each drone performs its delivery tasks and the truck docking points where the drone is released and retrieved are known.

[0082] (2) The distance of the drone flight is calculated according to the Euclidean distance between each customer point, and the distance of the truck travel is calculated according to the road distance between each customer point.

[0083] (3) After the drone lands on the truck, the charging time and loading time are ignored.

[0084] (4) The drone is fully charged every time it takes off.

[0085] (5) The truck maintained a constant speed throughout the journey.

[0086] (6) A truck can assist drones in completing all delivery tasks.

[0087] (7) Ignore the time it takes for the drone to be released from and retrieved from the truck.

[0088] (8) Ignore the time spent at truck service customer points.

[0089] (9) Allow trucks to wait for drones or drones to wait for trucks at truck stops.

[0090] (10) A maximum of two delivery tasks corresponding to two truck stops are allowed to be carried out at the same time.

[0091] Model parameters and variables

[0092] The variables for the truck routing model are shown in Table 1:

[0093] Table 1 Variables for Truck Route Planning Model

[0094]

[0095]

[0096] objective function

[0097] Next, we should rationally plan the truck routes and determine the execution order of delivery tasks corresponding to each group of truck stops, so as to minimize the total time for completing the entire delivery task. Let |d i -a i | Indicates that the truck travels from the truck parking point. i Drive to truck parking point d i The road distance.

[0098] The objective function is to minimize the total delivery time for truck and drone collaborative delivery, as shown in equation (1):

[0099]

[0100] Model constraints

[0101] ① The constraints are:

[0102]

[0103]

[0104] Equation (2) indicates that when the time for the UAV to complete the task corresponding to the i-th group of truck stops is less than a time for the truck to leave the i-th group of truck stops... i Drive to the (i+1)th truck stop point ai+1 The time taken;

[0105] Equation (3) indicates that the time for the UAV to complete the task corresponding to the (i+1)th truck stop is less than the time for the truck to depart from the (i+1)th truck stop. i+1 Drive to the d stop of the i-th group of trucks i Time taken.

[0106] The time analysis diagram for scenario 1 is shown below (the diagram does not depict the case where the equality holds). Figure 3 As shown.

[0107] As shown in the graph, the total time for completing the i-th and i+1-th delivery tasks in scenario 1 is:

[0108]

[0109] ②The constraints are:

[0110]

[0111]

[0112] Equation (5) indicates that when the time for the UAV to complete the task corresponding to the i-th group of truck stops is less than a time for the truck to leave the i-th group of truck stops... i Drive to the (i+1)th truck stop point a i+1 The time taken;

[0113] Equation (6) indicates that the time it takes for the UAV to complete the task corresponding to the (i+1)th truck stop is greater than or equal to the time it takes for the truck to leave the (i+1)th truck stop. i+1 Drive to the d stop of the i-th group of trucks i The time taken is less than the time it takes for the truck to leave the truck docking point d. i Drive to d i+1 Time and truck from truck stop a i+1 Drive to d i The sum of the times.

[0114] The time analysis diagram for scenario 2 is as follows: Figure 4 As shown.

[0115] As shown in the graph, the total time for completing the i-th and i+1-th delivery tasks in scenario 2 is:

[0116]

[0117] ③ The constraints are:

[0118]

[0119]

[0120] Equation (8) indicates that when the time for the UAV to complete the task corresponding to the i-th group of truck stops is less than a time for the truck to leave the i-th group of truck stops... i Drive to the (i+1)th truck stop point a i+1 The time taken;

[0121] Equation (9) indicates that the time it takes for the UAV to complete the task corresponding to the (i+1)th truck stop is greater than or equal to the time it takes for the truck to leave the truck stop d. i Drive to d i+1 Time and truck from truck stop a i+1 Drive to d i The sum of the times.

[0122] The time analysis diagram for scenario 3 is as follows: Figure 5 As shown.

[0123] As shown in the graph, the total time for completing the i-th and i+1-th delivery tasks in scenario 3 is:

[0124]

[0125] ④ The constraints are:

[0126]

[0127]

[0128] Equation (11) indicates that when the time for the UAV to complete the task corresponding to the i-th truck stop is greater than or equal to the time for the truck to leave the i-th truck stop, the time for the UAV to complete the task is greater than or equal to the time for the truck to leave the i-th truck stop. i Drive to the (i+1)th truck stop point a i+1 The time taken is less than a from the truck's stop in the i-th group of trucks. i Drive to the (i+1)th truck stop point a i+1 The time taken is related to the time taken by the truck from the i-th truck stop point a i+1 Drive to the (i+1)th truck stop d i The sum of the time used;

[0129] Equation (12) indicates that the time for the UAV to complete the task corresponding to the (i+1)th truck stop is less than the time for the truck to depart from the (i+1)th truck stop. i+1 Drive to the d stop of the i-th group of trucks i Time taken.

[0130] The time analysis diagram for scenario 4 is as follows: Figure 6 As shown.

[0131] As shown in the figure, the total time for completing the i-th and i+1-th delivery tasks in scenario 4 is:

[0132]

[0133] ⑤ The constraints are:

[0134]

[0135]

[0136] Equation (14) indicates that when the time for the UAV to complete the task corresponding to the i-th truck stop is greater than or equal to the time for the truck to leave the i-th truck stop, the time for the UAV to complete the task is greater than or equal to the time for the truck to leave the i-th truck stop. i Drive to the (i+1)th truck stop point a i+1 The time taken is less than a from the truck's stop in the i-th group of trucks. i Drive to the (i+1)th truck stop point a i+1 The time taken is related to the time taken by the truck from the i-th truck stop point a i+1 Drive to the (i+1)th truck stop d i The sum of the time taken.

[0137] Equation (15) indicates that the time it takes for the UAV to complete the task corresponding to the (i+1)th truck stop is greater than or equal to the time it takes for the truck to leave the (i+1)th truck stop from point a. i+1 Drive to the d stop of the i-th group of trucks i The time taken is less than or equal to the time the truck takes from the truck stop point d. i Drive to d i+1 Time and truck from truck stop a i+1 Drive to d i The sum of the times.

[0138] The time analysis diagram for situation 5 is as follows: Figure 7 As shown.

[0139] As shown in the graph, the total time for completing the i-th and i+1-th delivery tasks in scenario 5 is:

[0140]

[0141] ⑥ The constraints are:

[0142]

[0143]

[0144] Equation (17) indicates that when the time for the UAV to complete the task corresponding to the i-th truck stop is greater than or equal to the time for the truck to leave the i-th truck stop, the time for the UAV to complete the task is greater than or equal to the time for the truck to leave the i-th truck stop. iDrive to the (i+1)th truck stop point a i+1 The time taken is less than a from the truck's stop in the i-th group of trucks. i Drive to the (i+1)th truck stop point a i+1 The time taken is related to the time taken by the truck from the i-th truck stop point a i+1 Drive to the (i+1)th truck stop d i The sum of the time taken.

[0145] Equation (18) indicates that the time for the UAV to complete the task corresponding to the (i+1)th truck stop point is greater than the time for the truck to leave the truck stop point d. i Drive to d i+1 Time and truck from truck stop a i+1 Drive to d i The sum of the times.

[0146] The time analysis diagram for situation 6 is as follows: Figure 8 As shown.

[0147] As shown in the graph, the total time for completing the i-th and i+1-th delivery tasks in scenario 6 is:

[0148]

[0149] ⑦ The constraints are:

[0150]

[0151]

[0152] Equation (20) indicates that the time it takes for the UAV to complete the task corresponding to the i-th group of truck stops is greater than or equal to the time it takes for the truck to leave the i-th group of truck stops. i Drive to the (i+1)th truck stop point a i+1 The time taken is related to the time taken by the truck from the i-th truck stop point a i+1 Drive to the (i+1)th truck stop d i The sum of the time taken.

[0153] Equation (21) indicates that the time for the UAV to complete the task corresponding to the (i+1)th truck stop is less than the time for the truck to depart from the (i+1)th truck stop. i+1 Drive to the d stop of the i-th group of trucks i Time taken.

[0154] The time analysis diagram for situation 7 is as follows: Figure 9 As shown.

[0155] As shown in the graph, the total time for completing the i-th and i+1-th delivery tasks in scenario 7 is:

[0156]

[0157] ⑧ The constraints are:

[0158]

[0159]

[0160] Equation (23) indicates that the time it takes for the UAV to complete the task corresponding to the i-th truck stop is greater than or equal to the time it takes for the truck to leave the i-th truck stop. i Drive to the (i+1)th truck stop point a i+1 The time taken is related to the time taken by the truck from the i-th truck stop point a i+1 Drive to the (i+1)th truck stop d i The sum of the time taken.

[0161] Equation (24) indicates that the time it takes for the UAV to complete the task corresponding to the (i+1)th truck stop is greater than or equal to the time it takes for the truck to leave the (i+1)th truck stop from point a. i+1 Drive to the d stop of the i-th group of trucks i The time taken is less than the time it takes for the truck to leave the truck docking point d. i Drive to d i+1 Time and truck from truck stop a i+1 Drive to d i The sum of the times.

[0162] The time analysis diagram for situation 8 is as follows: Figure 10 As shown.

[0163] As shown in the graph, the total time for completing the i-th and i+1-th delivery tasks in situation 8 is:

[0164]

[0165] ⑨ The constraint conditions are:

[0166]

[0167]

[0168]

[0169] Equation (26) indicates that the time it takes for the UAV to complete the task corresponding to the i-th truck stop is greater than or equal to the time it takes for the truck to leave the i-th truck stop. i Drive to the (i+1)th truck stop point a i+1 The time taken is related to the time taken by the truck from the i-th truck stop point a i+1 Drive to the (i+1)th truck stop di The sum of the time taken.

[0170] Equation (27) indicates that the time for the UAV to complete the task corresponding to the (i+1)th truck stop point is greater than the time for the truck to leave the truck stop point d. i Drive to d i+1 Time and truck from truck stop a i+1 Drive to d i The sum of the times.

[0171] Equation (28) represents the time it takes for the UAV to complete the task corresponding to the i-th group of truck stops and the time it takes for the truck to leave the i-th group of truck stops d. i Drive to truck stop d in group i i+1 The sum of the times is less than or equal to the time it takes for the drone to complete the task corresponding to the (i+1)th group of truck stops and the time it takes for the truck to leave the i-th group of truck stops. i Drive to the (i+1)th truck stop point a i+1 The sum of the times.

[0172] The time analysis diagram for situation 9 is as follows: Figure 11 As shown.

[0173] As shown in the graph, the total time for completing the i-th and i+1-th delivery tasks in situation 9 is:

[0174]

[0175] ⑩ The constraints are:

[0176]

[0177]

[0178]

[0179] Equation (30) indicates that the time it takes for the UAV to complete the task corresponding to the i-th group of truck stops is greater than or equal to the time it takes for the truck to leave the i-th group of truck stops. i Drive to the (i+1)th truck stop point a i+1 The time taken is related to the time taken by the truck from the i-th truck stop point a i+1 Drive to the (i+1)th truck stop d i The sum of the time taken.

[0180] Equation (31) indicates that the time for the UAV to complete the task corresponding to the (i+1)th truck stop point is greater than the time for the truck to leave the truck stop point d. i Drive to d i+1 Time and truck from truck stop a i+1 Drive to d i The sum of the times.

[0181] Equation (32) represents the time it takes for the UAV to complete the task corresponding to the i-th group of truck stops and the time it takes for the truck to leave the i-th group of truck stops d. i Drive to truck stop d in group i i+1 The sum of the times is greater than the time it takes for the drone to complete the task corresponding to the (i+1)th group of truck stops and the time it takes for the truck to leave the i-th group of truck stops a. i Drive to the (i+1)th truck stop point a i+1 The sum of the times.

[0182] The time analysis diagram for situation 10 is as follows: Figure 12 As shown.

[0183] As shown in the graph, the total time for scenario 10 to complete the delivery tasks for the i-th and i+1th groups is:

[0184]

[0185] Genetic Algorithm for Solving Truck Path Planning

[0186] To determine the total delivery time for a collaborative delivery system involving synchronized truck and drone operations, it's necessary to calculate the truck's travel path. Traditional truck path planning often uses minimizing the total truck path length as the objective function. However, in the context of collaborative truck and drone delivery, the truck's stopping locations and the corresponding drone path planning for each truck stopping point are already determined. Therefore, truck path planning also involves drone delivery time. Since solving the truck path planning problem can be viewed as solving a shortest distance problem, accurate calculations are computationally complex given the large amount of data. Genetic algorithms are widely used in such problems, and this patent employs a genetic algorithm (GA) to solve this problem.

[0187] The solution process is as follows:

[0188] (1) Initialization: Set the population size I, crossover probability pc, mutation probability pm, and maximum number of iterations maxT. Read the truck stop data obtained from the previous solution, and then randomly generate an initial population, with each chromosome representing a truck driving path.

[0189] (2) In the population, each chromosome corresponds to a truck driving path. The generated truck driving paths are numbered in ascending order of their starting points, with the numbers being 1, 2, 3, ..., n, where n is the number of truck stops.

[0190] (3) Calculate fitness: Take any chromosome, first determine which of the two adjacent groups of truck stops belong to Equation (2), Equation (11), Equation (20), then determine which of the two groups belong to Equation (3), Equation (6), Equation (9), and finally obtain the completion time formula for the two groups of delivery tasks to be carried out simultaneously according to Equation (4), Equation (10), Equation (22), Equation (25). Then calculate the fitness of each chromosome according to Equation (1). The objective function of the truck path planning model for synchronous operation and collaborative delivery of trucks and drones in this invention is to minimize the total delivery time. The fitness f of the truck path can be expressed by the reciprocal of the total delivery time. Based on this, the subsequent calculation can be made more convenient.

[0191] (4) Selection Operator: To obtain better chromosomes, screening operations must be used to remove chromosomes with poor fitness. This invention uses a sorting method to screen chromosomes. First, the I chromosomes in the population are arranged according to their fitness. Individuals ranked higher perform best and are directly added to the next generation. The remaining I-1 chromosomes can be selected with a certain probability to replace chromosomes with high fitness, thus selecting a population with better fitness while maintaining the same population size.

[0192] (5) Chromosome Crossover: Chromosomes are crossed over according to the crossover probability pc. The path representation encoding method used in this invention ensures that each truck stop appears exactly once in the truck path; therefore, no two identical gene codes are allowed on each chromosome. First, two parent chromosomes α1 and α2 are taken (gene code 0 is included to demonstrate the chromosome crossover and mutation process; however, gene code 0 does not exist in the actual encoding of this invention). Then, genes of the same length are randomly selected to determine the crossover range of the two chromosomes, such as... Figure 13 As shown.

[0193] Then, a chromosome without the gene is produced as an offspring. A gene segment selected from the paternal line is then copied onto the corresponding offspring chromosome, such as... Figure 14 As shown.

[0194] Next, the genes that are identical on the parent chromosome α2 and the offspring chromosome α'1 are removed, and the remaining genes are used to fill the blanks in α'1, thus generating a new, complete offspring chromosome, such as... Figure 15 As shown.

[0195] Next, the genes that are identical on the parent chromosome α1 and the offspring chromosome α'2 are removed, and the remaining genes are used to fill in the blanks, thus generating a new, complete offspring chromosome α'2, as follows. Figure 16 As shown.

[0196] (6) Chromosomal Mutation: For all chromosomes in the population, a mutation probability pm is used to determine whether a mutation has occurred. The ASO mutation operator was used in the design of the mutation operator, which randomly generates a random number ψ with the same length as the existing chromosomes. i , and ψ i The value range is [0,1]. Then, for the random number ψ... i Compare with the magnitude of the mutation probability pm, if ψ i If <pm, then the gene is shifted one position to the right; if ψ i If φ is greater than or equal to pm, then the genes on the chromosome remain unchanged. For example, for chromosome α1 (7460953812), after evaluation, ψ2, ψ6, and ψ9 are all less than pm, so the resulting ASO(α1) is (7160943852). The process is as follows: Figure 17 As shown.

[0197] (7) Increment the iteration count by one, and determine the size of the current iteration count compared to the maximum iteration count. If the maximum iteration count has not been reached, continue iterating.

[0198] (8) When the maximum number of iterations is reached, the optimal solution is output, and the truck route and total delivery time are obtained.

[0199] Numerical Experiment

[0200] Data Acquisition

[0201] This patent sets the truck's speed to 50 km / h, and the parameters of the genetic algorithm are shown in Table 2.

[0202] Table 2 Genetic Algorithm Parameter Settings

[0203]

[0204] This patent takes a scale of 100 customer points as an example to calculate the delivery time of truck and drone collaborative delivery. Based on the drone path planning results mentioned above, the delivery tasks under the scale of 100 customer points are divided into ten groups. Based on the truck stop location results, the coordinates of truck stops and demand information in the truck path are obtained, as shown in Table 3.

[0205] Table 3. Latitude and longitude coordinates and demand information for truck parking spots

[0206]

[0207]

[0208] Solution results and analysis

[0209] To determine the total delivery time for truck-drone collaborative delivery, we use the truck stop location selection results and drone path planning results to determine the final truck route, thus obtaining the overall delivery process plan. The truck stop locations constitute the truck's route, and the drone path planning solution yields the drone delivery completion time for each group of truck stop locations. This patent utilizes an improved genetic algorithm to solve delivery tasks for 100 customer locations, determining the final truck route and the total truck-drone delivery time.

[0210] Depend on Figure 18 It can be seen that, with a customer base of 100, the total delivery time for truck and drone collaborative delivery calculated using the genetic algorithm reaches its optimum around the 80th generation.

[0211] Calculations show that, for a scale of 100 customer points, the truck travel path for synchronized collaborative delivery using trucks and Keweitai X6L drones is 5-1-12-14-20-49-47-38-58-29-35-51-26-57-97-68-69-79-87-70, with a total delivery time of 15851(s). Table 4 shows the ten scenarios corresponding to adjacent truck stops executing delivery tasks simultaneously, as described in this patent.

[0212] Table 4. Order and Time of Task Completion

[0213]

[0214] For a customer base of 100 locations, the following delivery solution considers the simultaneous operation of trucks and drones to collaboratively deliver goods, capable of executing two sets of delivery tasks at the same time:

[0215] The truck, carrying delivery packages and drones, first departs from truck stop 5. The truck makes deliveries to truck stop 5 and releases two drones there. One drone delivers to customer point 9, and the other drone delivers to customer points 13 and 15. The truck then travels to truck stop 1, makes deliveries there, and releases three drones there. One drone delivers to customer points 10 and 8, one drone delivers to customer points 4, 3, 2, and 11, and one drone delivers to customer points 7 and 6. The truck then travels to truck stop 12, makes deliveries there, and then retrieves the drones that have landed. After retrieval, the truck travels to truck stop 14, makes deliveries there, and then retrieves the drones that have landed.

[0216] After the retrieval is complete, the truck travels to truck stop 20, where it makes deliveries and releases three drones. One drone delivers to customer points 21 and 19, one to customer points 18 and 17, and one to customer points 16, 40, and 36. The truck then travels to truck stop 49, where it makes deliveries and releases four drones. One drone delivers to customer points 59 and 48, one to customer points 43, 42, 41, and 50, one to customer points 33 and 39, and one to customer points 23 and 22. The truck then travels to truck stop 47, where it makes deliveries and waits for the drones to be retrieved. After the retrieval is complete, the truck travels to truck stop 38, where it serves the customer and waits for the drones to be retrieved.

[0217] After the retrieval is complete, the truck travels to truck stop 58, where it serves that point first. Simultaneously, four drones are released from the truck: one drone delivers to customer points 37 and 46, one to 33 and 34, one to 80 and 32, and one to 60, 62, 64, and 35. The truck then travels to truck stop 29, where it serves that point first, and then releases four drones: one to serve customer points 92 and 91, one to serve customer points 28, 25, and 24, one to serve customer points 53 and 52, and one to serve customer points 31, 30, and 27. The truck then travels to truck stop 35, where it serves that point first, and then waits for the drones to be retrieved. After the retrieval is complete, the truck travels to truck stop 51, where it serves that point first, and then waits for the drones to be retrieved.

[0218] After recovery, the truck proceeds to truck stop 26, where it serves the customer. Simultaneously, it releases three drones: one to serve customer points 93, 94, and 96; one to serve customer points 45, 98, and 91; and one to serve customer points 95, 55, and 54. The truck then proceeds to truck stop 57, where it serves the customer. It then releases three more drones: one to serve customer points 100, 99, and 63; one to serve customer points 64, 56, and 73; and one to serve customer points 67 and 65. The truck then proceeds to truck stop 97, where it serves the customer. After recovery, the truck proceeds to truck stop 68, where it serves the customer. Finally, it recovers the drones that have landed. The truck travels to truck stop 69, serves this point first, and releases two drones from the truck. One drone delivers to customer points 88 and 82, and the other drone delivers to customer points 83, 77, 76, and 75. The truck then travels to truck stop 79, serves this point first, and releases four drones from the truck. One drone serves customer points 74, 84, and 89; one drone serves customer points 66, 71, and 72; one drone serves customer points 85, 86, and 90; and one drone serves customer points 78 and 81. The truck then travels to truck stop 87, serves this point first, and then recovers the landed drones. After recovery, the truck travels to truck stop 70, serves this point first, and then recovers the landed drones, completing all delivery tasks.

[0219] Next, this patent solves for the delivery time and truck route of the Zhihang Lingyun II drone and truck at 100 customer points. At the same time, it also solves for the delivery time and truck route of the Xunyi RA3 drone and truck at 100 customer points. The total delivery time of the Zhihang Lingyun II drone and truck collaborative delivery is calculated to be 18539(s), and the delivery time of the Xunyi RA3 drone and truck at 100 customer points is calculated to be 24832(s).

[0220] To study delivery times under different customer point scales, the total delivery times for three drone models—Keweitai X6L, Zhihang Lingyun II, and Xunyi RA3—were calculated for customer point scales of 25, 50, 75, and 100 customer points. The results are as follows: Figure 19As shown in the figure, the total delivery time for the three different drone models operating synchronously with trucks gradually increases with the increase in the number of customer points. Furthermore, at any scale, the delivery time for the Keweitai X6L drone operating synchronously with trucks is shorter than that for the Zhihang Lingyun II drone and the Xunyi RA3 drone operating synchronously with trucks. This is because the actual flight range of the Keweitai X6L is greater than that of the other two drones, allowing it to deliver to more customer points in the same amount of time, thus reducing delivery time. It was also found that when the number of customer points increases from 25 to 50, the increase in delivery time is less than the increase from 50 to 75. This is because customer points numbered 25-50 are more densely distributed than those numbered 50-75, allowing drones and trucks to deliver customers more quickly.

[0221] To investigate the impact of truck speed on the total delivery time of collaborative delivery between trucks and drones operating synchronously, the Kewetech X6L drone was selected. With a customer point scale of 100 and the truck parking point selection and drone path planning results remaining unchanged, the truck speed was set to 30km / h, 40km / h, 50km / h, 60km / h, 70km / h, 80km / h, 90km / h, and 100km / h respectively. The completion time of collaborative delivery between trucks and Kewetech X6L drones operating synchronously was calculated sequentially. The results are as follows: Figure 20 As shown.

[0222] As shown in the figure, the total time for coordinated delivery between trucks and drones gradually decreases as truck speed increases. The decrease in total delivery time is less pronounced when truck speed increases from 70 km / h to 100 km / h compared to the increase from 30 km / h to 70 km / h. This is because initially, increasing truck speed reduces travel time between truck stops, allowing trucks to quickly reach drone retrieval points and reduce delivery time. However, as truck speed continues to increase, even if the truck quickly reaches the drone retrieval point, the drone's delivery task is not yet complete, and retrieval can only proceed after the task is finished. Therefore, only the truck's travel time between truck stops is reduced, resulting in a smaller decrease in the total delivery time as truck speed decreases.

[0223] This patent takes the collaborative delivery of trucks and drones in last-mile logistics as its background. It considers the collaborative delivery of trucks and drones operating synchronously, completes the selection of truck stop locations, determines the composition of truck routes, completes the drone route planning, determines the order of drone delivery to customer points and the number of drones required for each group of truck stop locations for the corresponding delivery task, and uses a genetic algorithm to solve the total delivery time and truck running route for the collaborative delivery of trucks and drones operating synchronously.

[0224] Compared to existing delivery models, this invention differs in the following ways: ① This patent proposes a collaborative delivery model involving simultaneous operation of trucks and drones. During the truck stop selection and drone path planning stages, the impact of the drone's payload on its actual flight range is fully considered, along with the influence of takeoff, landing, and level flight status on its actual flight capability. ② In the truck stop selection process, trucks are allowed to serve customer delivery points, enabling them to retrieve drones at the next truck stop after release, expanding the drone's service range and increasing the selectivity of takeoff and landing. ③ In drone path planning, it considers that a single drone launch can serve multiple customer points, improving delivery efficiency, reducing costs, and better achieving balanced drone delivery. ④ In the stage of calculating the total truck and drone delivery time and planning truck routes, it considers that two sets of delivery tasks corresponding to truck stops can be executed simultaneously, reducing the total delivery time and improving the efficiency of collaborative truck and drone delivery.

[0225] Using the customer point data, truck speed data, and drone-related data from Zigong City obtained through this patent, and adopting the existing truck-drone collaborative delivery model, the total delivery time was calculated for four customer point scales: 25 customer points, 50 customer points, 75 customer points, and 100 customer points. The results were then compared with those obtained through this patent. Figure 21 As shown in the figure, the total delivery time of the truck and drone synchronous operation collaborative delivery mode proposed in this patent is less than that of the mode proposed in the reference under four different customer point scales. This proves that the overall planning mode of truck and drone synchronous operation collaborative delivery proposed in this patent is more efficient and can improve the actual last-mile logistics delivery efficiency.

[0226] (2) Comparative Analysis of Example Results

[0227] In the traditional asynchronous collaborative delivery model of trucks and drones, based on the existing truck stop location results and drone path planning results, the execution order of each group of delivery tasks is determined by the truck's driving path at the truck stop. At any given time, only one group of delivery tasks corresponding to the truck stop can be executed. When solving for the total delivery time, the delivery time corresponding to each group of truck stops is directly added together, and the driving time of the truck between the truck stops is added to obtain the total time of asynchronous collaborative delivery between trucks and drones.

[0228] The collaborative delivery model proposed in this patent, which involves the simultaneous operation of trucks and drones, considers the possibility of executing delivery tasks corresponding to two sets of truck stops at the same time, based on the existing truck stop location selection results and drone path planning results. This allows for the occurrence of trucks waiting for drones or drones waiting for trucks, fully leveraging the transportation role of trucks, rationally planning the truck driving routes, determining the execution order of delivery tasks corresponding to each set of truck stops, and finally solving for the total time of collaborative delivery with trucks and drones operating simultaneously.

[0229] To verify the effectiveness of the truck and drone synchronous operation collaborative delivery model in this patent and to avoid the influence of the number of customer points on the total delivery time of truck and drone collaborative delivery, the Keweitai X6L drone was selected, and 25, 50, 75, and 100 customer points were selected. The total delivery time of truck and drone asynchronous operation collaborative delivery and the total delivery time of truck and drone synchronous operation collaborative delivery were calculated for four different customer point scales. In order to avoid the influence of randomness in the results caused by the genetic algorithm used, the calculation was performed ten times for each scale, and the average of the ten calculations was taken as the total delivery time for each customer point scale. In order to more intuitively compare the truck and drone synchronous operation collaborative delivery mode with the traditional truck and drone asynchronous operation mode, the time change rate was set as shown in equation (34), and the calculation results are shown in the table.

[0230]

[0231] Table 5. Comparison of total delivery time for the two delivery modes under different customer location sizes.

[0232]

[0233] As shown in the table, under four customer point scales of 25, 50, 75, and 100 customer points, the total delivery time of the truck and drone synchronous operation collaborative delivery mode proposed in this patent is less than that of the traditional truck and drone asynchronous operation collaborative delivery mode. The total delivery time is reduced by 25.59%, 34.19%, 29.09%, and 31.89%, respectively. Therefore, the truck and drone synchronous operation collaborative delivery mode proposed in this paper, which considers truck parking point selection, drone path planning, and truck path planning in sequence, is more suitable for actual logistics delivery scenarios and can significantly improve delivery efficiency. This has positive significance for the booming drone logistics industry.

[0234] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A truck route planning method for synchronized and collaborative delivery by trucks and drones, characterized in that: The steps are as follows: (1) Based on the completion of truck parking point selection and UAV path planning, plan the truck driving route and solve the total delivery time; (2) Consider that the delivery tasks corresponding to two sets of truck stops can be executed at the same time. After the truck completes the release of all drones in this set of tasks, it goes to the release point of the drone in the next set of truck stops to release the drones for the next set of delivery tasks. Then it returns to the truck stop where the drones were retrieved in the previous set of delivery tasks to retrieve the drones. Finally, it goes to the truck stop where the drones were retrieved in the next set of delivery tasks to complete the drone retrieval work in the second set of delivery tasks. (3) Establish a truck route planning model for synchronous operation and collaborative delivery of trucks and drones; (4) Solve the problem using a genetic algorithm and simulate the problem using relevant examples to obtain the truck's driving path and the total delivery time for the truck and drone to work together in a coordinated manner. The truck routing model for coordinated delivery using trucks and drones operating synchronously is as follows: set up Indicates the truck from the truck stop. Drive to the truck parking area Given the road distance, the objective function is to minimize the total delivery time for truck and drone collaborative delivery, as shown in equation (1): （1） Model constraints The constraints are: （2） （3） In the formula: The time required to complete all delivery tasks, For each pair of truck stop locations, there is a corresponding set of delivery tasks. The task corresponding to each pair of truck stop points. The tasks corresponding to a single truck stop. To release truck docking point locations for drones during delivery missions. The time allotted for trucks and drones to complete delivery tasks corresponding to two sets of truck docking points. To enable drones to complete single-unit truck drop-off and delivery tasks Time required To aggregate delivery tasks for a single group of truck stops. In order to carry out delivery tasks Location of the truck drop-off point for the drone at that time. In order to carry out delivery tasks Location of the drone recovery truck parking point at that time. The speed at which the truck travels; Equation (2) indicates that when the first In the task corresponding to the truck docking point, the time for the drone to complete the task is less than the time for the truck to leave the first truck docking point. Truck parking spots Drive to the Truck parking spot The time taken; Equation (3) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is less than the time for the truck to leave the first truck docking point. Truck parking spots Drive to the Truck parking spots Time taken.

2. The truck route planning method for synchronized and collaborative delivery of trucks and drones as described in claim 1, characterized in that: Case 1 completes the first and The total time for the two delivery tasks is: （4） The constraints are: （5） （6） Equation (5) indicates that when the first In the task corresponding to the truck docking point, the time for the drone to complete the task is less than the time for the truck to leave the first truck docking point. Truck parking spots Drive to the Truck parking spot The time taken; Equation (6) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the docking point. Truck parking spots Drive to the Truck parking spots The time taken is less than the time it takes for the truck to leave the truck docking point. Drive to Time and truck from truck dock Drive to The sum of the times.

3. The truck route planning method for synchronized and collaborative delivery of trucks and drones as described in claim 2, characterized in that: Case 2 completes the first and The total time for the two delivery tasks is: （7） The constraints are: （8） （9） Equation (8) indicates that when the first In the task corresponding to the truck docking point, the time for the drone to complete the task is less than the time for the truck to leave the first truck docking point. Truck parking spots Drive to the Truck parking spot The time taken; Equation (9) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the truck docking point. Drive to Time and truck from truck dock Drive to The sum of the times.

4. The truck route planning method for synchronized and collaborative delivery of trucks and drones as described in claim 2, characterized in that: Case 3 completed and The total time for the two delivery tasks is: （10） The constraints are: （11） （12） Equation (11) indicates that when the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the docking point. Truck parking spots Drive to the Truck parking spot The time taken was less than that of the truck from the first Truck parking spots Drive to the Truck parking spot The time taken and the truck from the first Truck parking spots Drive to the Truck parking spot The sum of the time used; Equation (12) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is less than the time for the truck to leave the first truck docking point. Truck parking spots Drive to the Truck parking spots Time taken.

5. The truck route planning method for synchronized and collaborative delivery of trucks and drones as described in claim 2, characterized in that: Case 4 Completed and The total time for the two delivery tasks is: （13） The constraints are: （14） （15） Equation (14) indicates that when the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the docking point. Truck parking spots Drive to the Truck parking spot The time taken was less than that of the truck from the first Truck parking spots Drive to the Truck parking spot The time taken and the truck from the first Truck parking spots Drive to the Truck parking spot The sum of the time used; Equation (15) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the docking point. Truck parking spots Drive to the Truck parking spots The time taken is less than or equal to the time the truck takes from the truck stop. Drive to Time and truck from truck dock Drive to The sum of the times.

6. The truck route planning method for synchronized and collaborative delivery of trucks and drones as described in claim 2, characterized in that: Case 5 completed and The total time for the two delivery tasks is: （16） The constraints are: （17） （18） Equation (17) indicates that when the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the docking point. Truck parking spots Drive to the Truck parking spot The time taken was less than that of the truck from the first Truck parking spots Drive to the Truck parking spot The time taken and the truck from the first Truck parking spots Drive to the Truck parking spot The sum of the time used; Equation (18) represents the first In the task corresponding to the truck docking point, the time it takes for the drone to complete the task is longer than the time it takes for the truck to leave the truck docking point. Drive to Time and truck from truck dock Drive to The sum of the times.

7. The truck route planning method for synchronized and collaborative delivery of trucks and drones as described in claim 2, characterized in that: Case 6 completed and The total time for the two delivery tasks is: （19） The constraints are: （20） （21） Equation (20) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the docking point. Truck parking spots Drive to the Truck parking spot The time taken and the truck from the first Truck parking spots Drive to the Truck parking spot The sum of the time used; Equation (21) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is less than the time for the truck to leave the first truck docking point. Truck parking spots Drive to the Truck parking spots Time taken.

8. The truck route planning method for synchronized and collaborative delivery of trucks and drones as described in claim 2, characterized in that: Case 7 completed and The total time for the two delivery tasks is: （22） The constraints are: （23） （24） Equation (23) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the docking point. Truck parking spots Drive to the Truck parking spot The time taken and the truck from the first Truck parking spots Drive to the Truck parking spot The sum of the time used; Equation (24) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the docking point. Truck parking spots Drive to the Truck parking spots The time taken is less than the time it takes for the truck to leave the truck docking point. Drive to Time and truck from truck dock Drive to The sum of the times.

9. The truck route planning method for synchronized and collaborative delivery of trucks and drones as described in claim 2, characterized in that: Case 8 completed and The total time for the two delivery tasks is: （25） The constraints are: （26） （27） （28） Equation (26) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the docking point. Truck parking spots Drive to the Truck parking spot The time taken and the truck from the first Truck parking spots Drive to the Truck parking spot The sum of the time used; Equation (27) represents the first In the task corresponding to the truck docking point, the time it takes for the drone to complete the task is longer than the time it takes for the truck to leave the truck docking point. Drive to Time and truck from truck dock Drive to The sum of time; Equation (28) represents the first The time it takes for the drone to complete the task corresponding to the truck docking point is related to the time it takes for the truck to start from the [number]th [location]. Truck parking spot Drive to the Truck parking spots in the group The sum of the times is less than or equal to the first The time it takes for the drone to complete the task corresponding to the truck docking point is related to the time it takes for the truck to start from the [number]th [location]. Truck parking spot Drive to the Truck parking spot The sum of the times.

10. The truck route planning method for synchronized and collaborative delivery of trucks and drones as described in claim 2, characterized in that: Case 9 completed and The total time for the two delivery tasks is: （29） The constraints are: （30） （31） （32） Equation (30) represents the first In the task corresponding to the truck docking point, the time for the drone to complete the task is greater than or equal to the time it takes for the truck to leave the docking point. Truck parking spots Drive to the Truck parking spot The time taken and the truck from the first Truck parking spots Drive to the Truck parking spot The sum of the time used; Equation (31) represents the first In the task corresponding to the truck docking point, the time it takes for the drone to complete the task is longer than the time it takes for the truck to leave the truck docking point. Drive to Time and truck from truck dock Drive to The sum of time; Equation (32) represents the first The time it takes for the drone to complete the task corresponding to the truck docking point is related to the time it takes for the truck to start from the [number]th [location]. Truck parking spot Drive to the Truck parking spots in the group The sum of the times is greater than the first The time it takes for the drone to complete the task corresponding to the truck docking point is related to the time it takes for the truck to start from the [number]th [location]. Truck parking spot Drive to the Truck parking spot The sum of the times.

11. The truck route planning method for synchronized and collaborative delivery of trucks and drones as described in claim 2, characterized in that: Case 10 Completed and The total time for the two delivery tasks is: （33）。

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