Vehicle-unmanned aerial vehicle distribution path optimization method considering multiple accesses

Abstract

The invention discloses a multi-access-considered vehicle-unmanned aerial vehicle distribution path optimization method, relates to the technical field of vehicle and unmanned aerial vehicle collaborative distribution optimization, and aims to solve a path planning problem caused by complex constraints and multi-target optimization in urban logistics distribution. According to the method, firstly, multiple constraint conditions of vehicle-unmanned aerial vehicle cooperative distribution are analyzed, energy consumption cost and carbon emission factors are fused into a target function, an integer programming model with the minimum time and transportation cost as double targets is constructed, and carbon emission cost is considered in the transportation cost; secondly, solving a vehicle path and an initial solution by adopting an ant colony algorithm; and finally, a large-field search algorithm is used to solve the problem of vehicle-machine cooperation path optimization. According to the method, the vehicle and unmanned aerial vehicle cooperative distribution logistics efficiency is effectively improved, the total cost is reduced, and powerful support is provided for development of green logistics.

Description

Technical Field

[0001] The present invention relates to the field of multi-objective joint path planning, and in particular to a vehicle-UAV delivery path optimization method considering multiple visits. Background Art

[0002] With the explosive growth of e-commerce and demand for instant delivery, traditional logistics systems face severe challenges such as low last-mile delivery efficiency, limited coverage, and high operating costs. Relying solely on ground vehicles for delivery is particularly challenging in congested urban areas and remote mountainous areas, with inherent drawbacks such as rigid routing and insufficient last-mile penetration. Independent drone delivery, however, is limited by battery life, payload limitations, and complex airspace regulations, making it difficult to achieve large-scale commercial application.

[0003] In traditional logistics and distribution systems, both drones and vehicles, as independent transport vehicles, face significant limitations. Vehicles are constrained by road networks, making rapid and flexible delivery difficult. While drones offer the advantage of straight-line flight, their range and payload capacity restrict their application. Existing collaborative delivery solutions often employ simple serial operation models, failing to fully leverage the complementary characteristics of the two vehicle types. This results in low resource utilization and an inability to effectively respond to dynamic delivery demands and complex environmental changes. Summary of the Invention

[0004] The present invention provides a vehicle-UAV delivery path optimization method considering multiple visits. Its purpose is to focus on the path planning problem under complex constraints and multi-objective optimization requirements in urban logistics distribution, and propose an innovative green vehicle-UAV collaborative delivery path optimization method considering multiple visits. It is committed to optimizing delivery routes and times, achieving the goals of green, low-carbon emissions and low energy consumption, and improving the overall efficiency of logistics distribution; breaking through the difficulties of lack of flexibility in path planning and difficulty in last-mile delivery, giving full play to the complementary advantages of vehicles and UAVs, responding to dynamic delivery needs and green goals, and building an efficient and green collaborative delivery system.

[0005] To achieve the above object, the technical solution provided by the present invention is:

[0006] A vehicle-UAV delivery path optimization method considering multiple visits, characterized by comprising the following steps:

[0007] Step S1: Considering the energy consumption cost per kilometer and the carbon emission factor, a dual-objective mixed integer programming model is constructed to minimize the total time cost and transportation cost;

[0008] Step S2: Considering the dynamic delivery constraints of vehicles and drones, a green vehicle and drone delivery path optimization model for multiple access scenarios is established through time coordination constraints, access constraints, and endurance constraints, with the goal of minimizing total time and transportation cost.

[0009] Step S3: For the dynamic delivery of a single vehicle, the ant colony algorithm is used to generate the vehicle delivery path and the initial solution, taking into account the load and endurance constraints, and optimizing the single vehicle delivery path;

[0010] Step S4: For dynamic vehicle-UAV delivery, a large-area search algorithm is used to solve the overall coordination of vehicles and drones. Based on the initial solution of the ant colony algorithm, the vehicle path is adjusted, the drone tasks are dynamically assigned, the total cost of the new solution is evaluated, and the optimal solution is retained to verify the significant advantages of vehicle-UAV collaboration.

[0011] Furthermore, step S1 includes establishing the following optimization objectives:

[0012] The goal Z to minimize the time cost time :

[0013]

[0014] Where N is the set of all distribution points, including warehouses and customer points; t ij It represents the time it takes for a vehicle to travel from point i to point j, which is affected by road conditions, traffic rules, and the vehicle's own speed; ijk represents the flight time of the UAV from point i to point k via point j, which is related to the UAV's flight speed, route, and external interference factors; ij Indicates the vehicle's driving status; y ijk represents the drone delivery path selection;

[0015] The goal Z for minimizing transportation costs cost :

[0016]

[0017] Among them, d ij represents the distance from point i to point j, which can be obtained through geographic information system or actual measurement; d ijk represents the distance from the drone from point i to point k via point j; c truck and c drone denote the unit distance transportation cost of vehicles and drones respectively;

[0018] In the given objective function, the variable x is used to describe the vehicle's driving state. ij , x ij =1 means the vehicle is moving from point i to point j, x ij = 0 means that the driving behavior did not occur; and the variable y describing the drone delivery path selection ijk ,y ijk =1 means the UAV executes the flight path from point i to point k via point j, y ijk=0 means this path is not selected.

[0019] Furthermore, step S2 includes establishing the following constraints:

[0020] Time coordination constraints:

[0021] and i≠j

[0022] Among them, D t (i) and D t (j) represents the time when the drone arrives at point i and point j, represents the flight time from point i to point j, M is a sufficiently large positive number, and N is a natural number set; when the drone does not perform the delivery task from point i to other points, that is, ∑ k∈N y ijk =0, the constraint is automatically satisfied;

[0023] When a drone performs a delivery mission, the time calculation rationality constraints are:

[0024]

[0025] Where, T t (h) and T t (k) are the time when the vehicle arrives at point h and point k respectively, is the travel time of the vehicle from point h to point k, S L (h) and S R (k) represents the service time of the drone taking off at point h and landing at point k, respectively. L and J are the sets of material demand points, M is the set of vehicle-reachable points and destination points, and I is the set of vehicle-reachable points and starting points. When the vehicle does not travel the path from point h to point k, that is, x hk = 0, this constraint holds;

[0026] Origin constraints:

[0027] ∑ j∈N x 0j =1 and∑ i∈N x i0 =1

[0028] Where x 0j with x i0 x ij In the case of i=0 and j=0, ∑ j∈N x 0j =1 means the vehicle starts from the warehouse and can only choose one delivery point as the starting delivery destination; i∈N x i0 =1 means the vehicle can return to the warehouse after completing all delivery tasks;

[0029] Eliminate vehicle sub-loop constraints:

[0030] And i≠j

[0031] Among them, n is the number of material demand points, and u i and u j is an auxiliary variable;

[0032] Access order constraints:

[0033] u i -u j ≥1-(n+2)p ij

[0034] u i -u j ≤-1+(n+2)(1-p ij )

[0035] p ij +p ji =1

[0036] And i≠j

[0037] Where p ij and p ji is a variable used to determine the access order, p ij =1 indicates that the vehicle moves from point i to point j;

[0038] Drone delivery sequence constraints:

[0039]

[0040] Among them, y i,j,k =1 means the drone chooses this path, where i is the launch point, j is the delivery point, k is the recovery point, and y i,j,k =0, the opposite is true

[0041] Furthermore, step S2 also includes establishing the following constraints:

[0042] Time constraints:

[0043]

[0044]

[0045] Constraints on the number of visits:

[0046]

[0047] Constraints on delivery service frequency:

[0048]

[0049] Constraints to ensure drone takeoff and landing on vehicles:

[0050]

[0051] where x ij Indicates whether the vehicle chooses this path. If x is selected ij =1, otherwise x ij =0.

[0052] Furthermore, step S3 includes the following steps:

[0053] Step S31: Collect basic data in the distribution system, including the coordinates of the distribution center, the coordinates and attribute information of the customer points, and clearly distinguish between customer points that can be served by drones and customer points that can only be served by vehicles;

[0054] Step S32: Initializing key parameters in the ant colony algorithm, including but not limited to the number of ants, initial pheromone concentration, heuristic factor, and pheromone volatility coefficient; and simultaneously initializing related parameters required for the large area search algorithm, including but not limited to the neighborhood search range and heuristic rule weight;

[0055] Step S33: Utilize the ant colony algorithm to solve the vehicle path and the initial solution.

[0056] Furthermore, the use of the ant colony algorithm to solve the vehicle path and the initial solution in step S33 specifically includes ant path construction, path evaluation, and pheromone update;

[0057] The ant path construction is specifically as follows:

[0058] Each ant starts at the distribution center and, while constructing a route, uses a roulette wheel selection strategy to determine the next node to visit based on pheromone concentrations and heuristic information between the current node and its neighbors. This selection process considers the delivery capacity constraints of both vehicles and drones, including but not limited to the drone's range and maximum payload, as well as the order in which customers must be served. Once the ant has visited all customer locations, a complete solution for the delivery route, encompassing both vehicles and drones, is formed.

[0059] The path evaluation is specifically as follows:

[0060] Calculate the time cost of each ant building a path based on a preset cost function; the cost function takes into account factors such as vehicle speed, distance traveled, and loading and unloading time.

[0061] The pheromone update is specifically as follows:

[0062] Based on the time cost of each ant building a path, the pheromone on the path is updated. For high-quality paths with low time costs, the pheromone concentration is increased to guide subsequent ants to choose this path more often. At the same time, the pheromone on all paths is evaporated to simulate the natural decay process of pheromones over time.

[0063] Repeat the above steps of ant path construction, path evaluation and pheromone update until the preset maximum number of iterations is reached or the convergence condition is met, and the final single-vehicle delivery path solved by the ant colony algorithm is obtained.

[0064] Furthermore, step S4 includes the following steps:

[0065] Step S41: Initial solution setting: the final delivery path obtained by the ant colony algorithm is used as the initial solution of the large-scale search algorithm;

[0066] Step S42: Neighborhood search: A neighborhood search is performed on the initial solution based on a predefined neighborhood structure. The neighborhood structure includes, but is not limited to, local adjustments to vehicle paths and reallocation of drone delivery tasks. These operations must also meet the delivery capacity constraints of vehicles and drones, as well as the service requirements of customer points.

[0067] Step S43: Solution evaluation and selection: For each new solution obtained from the neighborhood search, evaluate it according to the same cost function as in the ant colony algorithm and calculate its time cost; select the new solution with the lowest time cost as the current optimal solution. If the optimal solution is better than the initial solution, replace the initial solution with it;

[0068] Step S44: Iterative optimization: Repeat the neighborhood search and solution evaluation and selection steps until the preset number of iterations is reached or the termination condition is met, and the delivery path optimized by the large-area search algorithm is obtained.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] (1) The present invention constructs a mixed integer programming model with the dual objectives of minimizing total time cost and transportation cost, fully considering multiple access scenarios and incorporating energy consumption cost per kilometer and carbon emission factors.

[0071] (2) The present invention achieves the spatiotemporal consistency of collaborative delivery through a series of constraints, such as time coordination constraints, access constraints, and endurance constraints.

[0072] (3) The present invention uses the ant colony algorithm to solve the vehicle path and initial solution, and then uses the large-scale search algorithm to introduce drones and perform overall coordination and path planning, ultimately realizing the study of the relationship between the number of customer points and cost.

[0073] (4) The present invention constructs a comprehensive mixed integer programming model and a targeted constraint system to combine the multi-objective optimization requirements in urban logistics distribution with complex constraints.

[0074] (5) Based on the characteristics of actual delivery scenarios, the present invention selects appropriate algorithms for solution and optimization, and deeply analyzes the relationship between cost and the number of customer points, thereby improving the scientificity and effectiveness of vehicle-UAV collaborative delivery path planning, thereby improving the logistics efficiency of vehicle-UAV collaborative delivery, reducing transportation costs, and promoting the development of green logistics. BRIEF DESCRIPTION OF THE DRAWINGS

[0075] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0076] Figure 1 This is a flow chart of a vehicle-UAV collaborative delivery path planning method based on an intelligent algorithm proposed in the present invention;

[0077] Figure 2 Create a bar chart for drone cost analysis;

[0078] Figure 3 Analyze the bar graph for vehicle costs;

[0079] Figure 4 This is a schematic diagram of the vehicle drone delivery model;

[0080] Figure 5 This is a path visualization diagram for a pure vehicle delivery solution;

[0081] Figure 6 Optimizing path visualization for vehicle-drone collaborative delivery;

[0082] Figure 7 Cost optimization comparison chart. DETAILED DESCRIPTION

[0083] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and examples. The present invention discloses a vehicle-drone delivery path optimization method considering multiple visits, which relates to the field of logistics distribution optimization technology and aims to solve the path planning problems caused by complex constraints and multi-objective optimization requirements in urban logistics distribution. The flow chart is as follows Figure 1 As shown, it includes the following steps:

[0084] Step S1: Collect relevant data and determine key variables and parameters. The present invention emphasizes multi-objective cost optimization.

[0085] The specific steps in step S1 include:

[0086] Step S1.1: We minimize the time cost and transportation cost at the same time to obtain a dual objective function. At the same time, for the calculation of the unit distance cost of vehicles and drones, we also consider the basic operating costs and green environmental protection costs of vehicles and drones, making the cost values obtained by simulation more objective and reasonable. The basic operating costs of drones include battery costs, maintenance costs, etc., and green environmental protection costs include environmental costs, carbon emission costs, etc. The basic operating costs of vehicles include fuel costs, maintenance costs, etc., and green environmental protection costs also include environmental costs, carbon emission costs, etc. See for details. Figure 2 shown.

[0087] Step S1.2: Considering the above indicators, we calculated the cost per unit kilometer in ten aspects: battery, maintenance, operator costs, insurance, regulation, environment, carbon emissions, environmentally friendly batteries, energy-saving depreciation, and low-emission incentives. The final cost we calculated was 0.69 yuan / km for drones and 1.35 yuan / km for vehicles.

[0088] Step S1.3: Determine the key variables and parameters to prepare for modeling. The variable parameter table is as follows:

[0089] Table 1 Key variables and parameters of the model

[0090]

[0091]

[0092]

[0093] Step S2: Establish the objective function:

[0094] Objective function 1: Minimum time cost objective function:

[0095]

[0096] Where N is the set of all distribution points, including warehouses and customer points. ij It represents the time it takes for a vehicle to travel from point i to point j, which is affected by factors such as road conditions, traffic regulations, and the vehicle's own speed; ijk represents the flight time of a drone from point i to point k via point j, which is related to the drone's flight speed, route, and external interference factors. This objective function aims to minimize the sum of vehicle travel time and drone flight time throughout the entire delivery process, thereby improving delivery efficiency, reducing goods in transit time, and increasing customer satisfaction.

[0097] Objective function 2: Minimum transportation cost objective function:

[0098]

[0099] For the calculation of the unit distance cost of vehicles and drones, we consider both basic operating costs and green environmental protection costs. ij is the distance from point i to point j, which can be obtained through geographic information system or actual measurement; d ijk c represents the distance from the drone from point i to point k via point j. truck and c drone The unit distance transportation costs for vehicles and drones are respectively, taking into account factors such as fuel consumption, equipment depreciation, green costs and other operating expenses.

[0100] In the given objective function, the key variables include the variable x used to describe the vehicle's driving state. ij , x ij =1 means the vehicle is moving from point i to point j, x ij = 0 means that the driving behavior did not occur; and the variable y describing the drone delivery path selection ijk ,y ijk = 1 means that the UAV executes the flight path from point i to point k via point j, y ijk =0 means this route is not selected. The parameters cover multiple attributes of vehicles and drones, including but not limited to the vehicle unit distance transportation cost c truck , UAV unit distance transportation cost c drone , driving or flying speed, maximum load capacity, and drone battery capacity, etc. These variables and parameters lay the foundation for subsequent model solving and path optimization.

[0101] Step S3: Consider the setting of single vehicle-UAV constraint conditions:

[0102] (1) Time series constraints:

[0103]

[0104] For drone delivery, it holds true for all i,j∈N. Among them, D t (i) and D t (j) are the time when the drone arrives at point i and point j respectively, is the flight time from point i to point j, and M is a sufficiently large positive number. When the drone does not perform the delivery task from point i to other points via point j (i.e. ∑ k∈N y ijk =0), the constraint is automatically satisfied, ensuring the rationality of time calculation.

[0105]

[0106] For vehicle transport, T t (h) and T t (k) are the time when the vehicle arrives at point h and point k respectively, is the travel time from point h to point k, S L (y hlm ) and S R (y ijk ) represent the service time of the drone taking off at point h and landing at point k, respectively. When the vehicle does not travel the path from point h to point k (x hk =0), this constraint holds true, ensuring the correct timing logic when vehicle transportation and drones work together.

[0107] (2) Origin constraints:

[0108] ∑ j∈N x 0j =1 and∑ i∈N x i0 =1

[0109] Constraints ensure the integrity of the vehicle delivery path. j∈N x 0j =1 means the vehicle starts from the warehouse and can only choose one delivery point as the starting delivery destination; i∈N x i0 =1 ensures that the vehicle can return to the warehouse after completing all delivery tasks, maintaining the closed loop of the delivery process.

[0110] (3) Eliminate vehicle sub-loop constraints:

[0111] And i≠j

[0112] Constraints regulate the vehicle's path. i and u j This constraint can effectively prevent vehicles from having sub-loops during the delivery process, ensure that vehicles traverse each delivery point in a reasonable order, avoid invalid driving, and improve transportation efficiency.

[0113] (4) Access order constraints:

[0114] u i -u j ≥1-(n+2)p ij

[0115] u i -u j ≤-1+(n+2)(1-p ij )

[0116] p ij +p ji =1

[0117] And i≠j

[0118] The constraints determine the order in which vehicles visit each delivery point. ij and p ji These conditions work together to accurately plan the driving order of vehicles in the distribution network, avoiding path confusion and waste of resources.

[0119] (5) UAV delivery sequence constraints:

[0120] And l≠i, l≠k

[0121] This constraint ensures the rationality of the order of drones in multiple delivery tasks. If there are two delivery behaviors (i, j, k) and (l, m, n), and i is delivered first and then l, then l must be delivered after k to ensure the orderly execution of delivery tasks.

[0122] Step S4: Consider the setting of vehicle-UAV collaboration constraints:

[0123] (1) Time constraints:

[0124]

[0125] The above constraints ensure that the vehicle and drone are closely coordinated in time. If the vehicle arrives at a delivery point first, it must wait for the drone to arrive to charge or perform other necessary operations. Conversely, if the drone arrives first, it also needs to wait for the vehicle to ensure smooth collaboration between the two.

[0126] (2) Constraints on the number of visits:

[0127]

[0128] The constraint condition limits each delivery point to be visited by a drone at most once, avoiding repeated visits of drones to the same delivery point and improving the efficiency of distribution resource utilization.

[0129]

[0130] The constraints ensure that each delivery point can only be delivered by a vehicle or drone once, eliminating the duplicate allocation of delivery tasks and ensuring the accuracy and efficiency of delivery.

[0131] (3) Constraints to ensure drone takeoff and landing on vehicles:

[0132] as well as

[0133] Constraints ensure that the drone can be launched smoothly from the vehicle and accurately land on the vehicle after completing the delivery mission for operations such as charging or replacing batteries, maintaining the sustainability of the collaborative operation of drones and vehicles.

[0134] Step S5: Use the Ant Colony Algorithm (AOC) and Large Scale Search Algorithm (LNS) to solve and optimize the model. The Ant Colony Algorithm solves the vehicle path and initial solution, while the Large Scale Search Algorithm solves the introduction of drones and overall coordination and path planning. First, establish a data structure framework for storing and calling input data. In an environment with a single starting parking lot, a single vehicle, and a drone, optimize the driving routes of the vehicle and drone to minimize the time it takes for the vehicle to return to the parking lot. The overall code is divided into three parts: data reading, modeling and solving, and result visualization. The specific implementation steps are as follows:

[0135] (1) Data reading and structure initialization. The code defines the Data class to store all input data, including customer coordinates, distance matrix, feasible drone mission sorties, and other information. Subsequently, readData() reads the C101network.txt file, extracts the X / Y coordinates of the customer points, the set of customer points accessible to vehicles and drones, and calculates the Euclidean distance matrix, which is stored in costMatrix for subsequent path optimization. At the same time, the code screens feasible drone mission sorties (i→j→k) based on the drone's range and stores them in P_lst for scheduling optimization. The read data is shown in the following table:

[0136] Table 2. Example of data used in the example

[0137]

[0138] (2) To solve the TSP using only vehicles, the code calls the solveTSP.ACO module and uses the Ant Colony Algorithm (ACO) to calculate the optimal TSP path using only vehicles. ACO simulates the pheromone update mechanism of ants on the path and finds the approximately optimal delivery order in multiple iterations. After obtaining the initial path, the code uses a 2-opt neighborhood search to further optimize it. It traverses each pair of edges in the path and attempts to swap the order of the two cities; calculates the change in the total length of the path; if the swap is better, accepts the change; otherwise, backtracks; this process is iterated until the path converges to a local optimum.

[0139] (3) Heuristic allocation of drone tasks. After obtaining the optimal path using only vehicles, the code inserts drone tasks through the FSTSP_Heuristic() heuristic method. This part involves several key steps: First, the code removes customer points that can be accessed by drones, then traverses the path, identifies customer points suitable for drone delivery, and attempts to remove them from the vehicle path. Next, the path gain (savings) after removing the customer point is calculated, that is, the total time cost saved by reducing the trip. Subsequently, the system evaluates two insertion methods: on the one hand, trying to reinsert the customer point into the vehicle path, find the optimal insertion position, and calculate its corresponding time cost; on the other hand, evaluating the feasibility of entrusting the drone to perform the task, calculating the drone's take-off and landing time, flight time, and ensuring that the task can be completed within the drone's endurance limit. By comparing the time consumption of the two options, the system finally chooses the method with the lowest cost to update. At the same time, in order to ensure the synchronization of vehicle and drone tasks, if a customer point is delivered by a drone, the system will adjust the vehicle's waiting time to ensure that the vehicle can arrive at the next service point on time after the drone completes the task, thereby optimizing the overall delivery efficiency.

[0140] (4) Path optimization iteration and termination: The code repeatedly removes, inserts, and evaluates the optimal solution until there is no further room for optimization (i.e., maxSavings <= 0 or the drone task assignment is completed). By repeatedly adjusting the coordination between vehicle paths and drone tasks, it eventually converges to the optimal hybrid path, which completes the delivery tasks for all customers in the shortest time.

[0141] (5) After the optimization is completed, the code is visualized through plot_show() to intuitively present the vehicle and drone collaborative delivery plan. In the final path diagram, the blue path represents the vehicle's driving trajectory, the red dotted line represents the number of missions performed by the drone, and the black marks are used to mark the starting and ending points of the delivery, making the overall plan clear at a glance. In addition, the code also compares the time costs of the two delivery plans using only vehicles and vehicles + drones: when using vehicles alone, the path is the optimal TSP result solved by the ant colony algorithm (ACO), and the corresponding total time cost is calculated; in the optimization plan combined with drones, some customer points are executed by drones, thereby reducing the overall delivery time, and the final optimized path and time cost savings are output to verify the optimization effect of drone collaboration.

[0142] Comparison of visualization images of the final optimized path and single vehicle delivery path Figure 5As shown. The performance of the ACO (Ant Colony Optimization) algorithm and the FSTSP_Heuristic (Heuristic) algorithm on the path optimization problem is compared. The left subgraph represents the ACO solution with a time cost of 147.58715966087848, and the right subgraph represents the FSTSP_Heuristic solution with a time cost of 135.28866595888556. The latter has better optimization effect. Both contain a warehouse (black square) as the starting point and end point, and use vehicles (blue paths) and drones (red dots) to transport customers respectively. Customers are numbered from 2 to 30, where customers responsible for vehicles are represented by blue dots and customers responsible for drones are represented by red dots. In the ACO solution, the paths of all customers are formed by vehicles, while in the FSTSP_Heuristic solution, there are red dotted lines between drone customers, indicating that drones can fly directly, thereby reducing the driving distance of vehicles. Overall, the FSTSP_Heuristic solution is more efficient. Through better drone scheduling, it reduces the total time cost by about 12.3 and improves transportation efficiency.

[0143] Figure 6 This study shows the relationship between total cost and customer number, comparing two delivery options: a truck-only (Truck Only) and a truck-plus-drone (Truck+UAV) delivery solution. The horizontal axis shows the number of customers increasing from 10 to 90, while the vertical axis represents total time cost. It can be observed that when the number of customers is small, the time costs of the two options are similar. However, as the number of customers increases, the drone-assisted solution (orange curve) significantly reduces the total time cost compared to the truck-only solution (blue curve). The difference between the two curves becomes particularly pronounced in the medium-to-high customer number range (40-80 customers), indicating that drones can reduce vehicle travel time by sharing some customer delivery tasks, thereby improving overall efficiency. However, as the number of customers approaches 90, the time cost gap between the two options narrows, possibly due to the drone's limited flight time or reduced collaborative efficiency caused by task scheduling. Combined with the calculated cost per kilometer, this analysis shows that within a specific customer number range, truck-plus-drone delivery can effectively reduce delivery time, thereby optimizing overall transportation efficiency and costs. This provides valuable insights for optimizing large-scale logistics scheduling.

Claims

1. A vehicle-drone delivery path optimization method considering multiple visits, characterized in that: The following steps are involved: Step S1: Considering the energy consumption cost per kilometer and the carbon emission factor, a dual-objective mixed integer programming model is constructed to minimize the total time cost and transportation cost; Step S2: Considering the dynamic delivery constraints of vehicles and drones, a green vehicle and drone delivery path optimization model for multiple access scenarios is established through time coordination constraints, access constraints, and endurance constraints, with the goal of minimizing total time and transportation cost. Step S3: For the dynamic delivery of a single vehicle, the ant colony algorithm is used to generate the vehicle delivery path and the initial solution, taking into account the load and endurance constraints, and optimizing the single vehicle delivery path; Step S4: For dynamic vehicle-UAV delivery, a large-area search algorithm is used to solve the overall coordination of vehicles and drones. Based on the initial solution of the ant colony algorithm, the vehicle path is adjusted, the drone tasks are dynamically assigned, the total cost of the new solution is evaluated, and the optimal solution is retained to verify the significant advantages of vehicle-UAV collaboration.

2. The vehicle-drone delivery path optimization method considering multiple visits according to claim 1 is characterized in that: The step S1 includes establishing the following optimization objectives: The goal Z to minimize the time cost time : Where N is the set of all distribution points, including warehouses and customer points; t ij It represents the time it takes for a vehicle to travel from point i to point j, which is affected by road conditions, traffic rules, and the vehicle's own speed; ijk represents the flight time of the UAV from point i to point k via point j, which is related to the UAV's flight speed, route, and external interference factors; ij Indicates the vehicle's driving status; y ijk represents the drone delivery path selection; The goal Z for minimizing transportation costs cost : Among them, d ij represents the distance from point i to point j, which can be obtained through geographic information system or actual measurement; d ijk represents the distance from the drone from point i to point k via point j; c truck and c drone denote the unit distance transportation cost of vehicles and drones respectively; In the given objective function, the variable x is used to describe the vehicle's driving state. ij , x ij =1 means the vehicle is moving from point i to point j, x ij = 0 means that the driving behavior did not occur; and the variable y describing the drone delivery path selection ijk ,y ijk =1 means the UAV executes the flight path from point i to point k via point j, y ijk =0 means this path is not selected.

3. The vehicle-drone delivery path optimization method considering multiple visits according to claim 1 is characterized in that: The step S2 includes establishing the following constraints: Time coordination constraints: Among them, D t (i) and D t (j) represents the time when the drone arrives at point i and point j, represents the flight time from point i to point j, M is a sufficiently large positive number, and N is a natural number set; when the drone does not perform the delivery task from point i to other points, that is, When 0, the constraint is automatically satisfied; When a drone performs a delivery mission, the time calculation rationality constraints are: Where, T t (h) and T t (k) are the time when the vehicle arrives at point h and point k respectively, is the travel time of the vehicle from point h to point k, S L (h) and S R (k) represents the service time of the drone taking off at point h and landing at point k, respectively. L and J are the sets of material demand points, M is the set of vehicle-reachable points and destination points, and I is the set of vehicle-reachable points and starting points. When the vehicle does not travel the path from point h to point k, that is, x hk = 0, this constraint holds; Origin constraints: ∑ j∈N x 0j =1 and∑ i∈N x i0 =1 Where x 0j with x i0 x ij In the case of i=0 and j=0, ∑ j∈N x 0j =1 means the vehicle starts from the warehouse and can only choose one delivery point as the starting delivery destination; i∈N x i0 =1 means the vehicle can return to the warehouse after completing all delivery tasks; Eliminate vehicle sub-loop constraints: u i -u j +1≤(n+2)(1-x ij ), and i≠j Among them, n is the number of material demand points, and u i and u j is an auxiliary variable; Access order constraints: u i -u j ≥1-(n+2)p ij u i -u j ≤-1+(n+2)(1-p ij ) p ij +p ji =1 and i≠j Where p ij and p ji is a variable used to determine the access order, p ij =1 indicates that the vehicle moves from point i to point j; Drone delivery order constraints: Among them, y i,j,k =1 means the drone chooses this path, where i is the launch point, j is the delivery point, k is the recovery point, and y i,j,k When =0, the situation is opposite.

4. The vehicle-drone delivery path optimization method considering multiple visits according to claim 1 is characterized in that: The step S2 also includes establishing the following constraints: Time constraints: Visit count constraints: Constraints on delivery service frequency: Constraints to ensure drone takeoff and landing on vehicles: where x ij Indicates whether the vehicle chooses this path. If x is selected ij =1, otherwise x ij =0.

5. The vehicle-drone delivery path optimization method considering multiple visits according to claim 1 is characterized in that: The step S3 comprises the following steps: Step S31: Collect basic data in the distribution system, including the coordinates of the distribution center, the coordinates and attribute information of the customer points, and clearly distinguish between customer points that can be served by drones and customer points that can only be served by vehicles; Step S32: Initializing key parameters in the ant colony algorithm, including but not limited to the number of ants, initial pheromone concentration, heuristic factor, and pheromone volatility coefficient; and simultaneously initializing related parameters required for the large area search algorithm, including but not limited to the neighborhood search range and heuristic rule weight; Step S33: Utilize the ant colony algorithm to solve the vehicle path and the initial solution.

6. The vehicle-drone delivery path optimization method considering multiple visits according to claim 5 is characterized in that: In step S33, the ant colony algorithm is used to solve the vehicle path and the initial solution, which specifically includes ant path construction, path evaluation, and pheromone update; The ant path construction is specifically as follows: Each ant starts at the distribution center and, while constructing a route, uses a roulette wheel selection strategy to determine the next node to visit based on pheromone concentrations and heuristic information between the current node and its neighbors. This selection process considers the delivery capacity constraints of both vehicles and drones, including but not limited to the drone's range and maximum payload, as well as the order in which customers must be served. Once the ant has visited all customer locations, a complete solution for the delivery route, encompassing both vehicles and drones, is formed. The path evaluation is specifically as follows: Calculate the time cost of each ant building a path based on a preset cost function; the cost function takes into account the vehicle's speed, distance traveled, and loading and unloading time. The pheromone update is specifically as follows: Based on the time cost of each ant building a path, the pheromone on the path is updated. For high-quality paths with low time costs, the pheromone concentration is increased to guide subsequent ants to choose this path more often. At the same time, the pheromone on all paths is evaporated to simulate the natural decay process of pheromones over time. Repeat the above steps of ant path construction, path evaluation and pheromone update until the preset maximum number of iterations is reached or the convergence condition is met, and the final single-vehicle delivery path solved by the ant colony algorithm is obtained.

7. The vehicle-drone delivery path optimization method considering multiple visits according to claim 1 is characterized in that: The step S4 comprises the following steps: Step S41: Initial solution setting: the final delivery path obtained by the ant colony algorithm is used as the initial solution of the large-scale search algorithm; Step S42: Neighborhood search: A neighborhood search is performed on the initial solution based on a predefined neighborhood structure. The neighborhood structure includes, but is not limited to, local adjustments to vehicle paths and reallocation of drone delivery tasks. These operations must also meet the delivery capacity constraints of vehicles and drones, as well as the service requirements of customer points. Step S43: Solution evaluation and selection: For each new solution obtained from the neighborhood search, evaluate it according to the same cost function as in the ant colony algorithm and calculate its time cost; select the new solution with the lowest time cost as the current optimal solution. If the optimal solution is better than the initial solution, replace the initial solution with it; Step S44: Iterative optimization: Repeat the neighborhood search and solution evaluation and selection steps until the preset number of iterations is reached or the termination condition is met, and the delivery path optimized by the large-area search algorithm is obtained.

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