Path planning method for collaborative distribution of truck and unmanned aerial vehicle

Abstract

The invention discloses a path planning method for collaborative distribution of a truck and an unmanned aerial vehicle. The method comprises the following steps: S1, selecting a truck stop point by using an improved k-means + + clustering algorithm; and S2, through an improved simulated annealing algorithm, calculating a distribution center, a truck stop point and a client point, respectively generating optimal paths of the truck and the unmanned aerial vehicle, and combining the optimal paths with constraint conditions to finally obtain an optimal scheme of truck-unmanned aerial vehicle cooperative distribution. According to the method, cost minimization and time reliability maximization are combined, so that actual requirements are better met.

Description

Technical Field

[0001] The invention relates to a path planning method for truck-unmanned aerial vehicle collaborative delivery. Background Art

[0002] With the advancement of technology, unmanned aerial vehicles (UAVs), as an innovative technology, have the advantages of being fast, flexible and cost-effective, and have demonstrated their effectiveness in various fields such as aerial photography, agriculture, firefighting, medical care and logistics. Due to their unique advantages, drones have considerable research potential in the field of logistics and distribution. In 2013, Amazon in the United States first proposed the use of drones for commodity delivery. By 2024, companies such as SF Express, JD.com and Meituan have successfully implemented standardized drone delivery routes. However, due to the small size of drones and their ability to perform short-distance and small-batch delivery, they are limited in delivering to customers with small demand and close distances, while trucks have a large load capacity and the ability to transport long distances. By combining vehicles with drones for delivery, efficiency can be maximized. Therefore, the concept of drone-truck collaborative delivery problem (TSP-D) was first proposed in 2015, involving trucks and drones working together to deliver goods. Since then, some studies have proposed the problem of truck-drone pickup and delivery, and the problem of truck-drone collaborative delivery to minimize economic costs. Efficient logistics delivery should be timely and economical to reduce delivery time. Another study proposed an innovative real-time method for truck-drone collaborative delivery. In this strategy, the drone takes off from a specific truck stop and returns to the truck after completing the package delivery. The truck is used as a warehouse, and the drone is launched at a designated location. A mixed integer programming model with the goal of minimizing cost is established. In addition, some studies have proposed a planning model with the goal of minimizing delivery time when the drone can carry multiple packages. In addition, a vehicle routing problem (VRPTWDR) ​​with time windows as constraints in the scenario of one truck and multiple drones is proposed. The above content mainly focuses on the scenario of a single truck, aiming to minimize delivery time or delivery cost, but fails to balance these two goals at the same time. However, in actual logistics operations, the huge delivery volume makes it very difficult for a single truck and drone to complete the delivery work. For logistics companies, minimizing delivery costs and ensuring service quality are crucial to their growth; for customers, faster package arrival improves satisfaction.

[0003] Therefore, in response to the above problems, a path planning method for truck-UAV collaborative delivery is provided. Summary of the invention

[0004] The purpose of the present invention is to overcome the existing defects and provide a path planning method for truck-UAV collaborative delivery, combining cost minimization with time reliability maximization to better meet actual needs.

[0005] The technical solution to achieve the above purpose is: A path planning method for truck-UAV collaborative delivery, comprising: Step S1, using the improved k-means++ (an algorithm for selecting initial values ​​for the k-means clustering algorithm) clustering algorithm to select truck stops; Step S2, through the improved simulated annealing algorithm, the distribution center, truck stop points and customer points are calculated to generate the optimal paths for trucks and drones respectively, and then they are combined with the constraints to finally obtain the optimal solution for truck-drone collaborative delivery.

[0006] Preferably, in step S1, improving the k-means++ clustering algorithm includes: Set the number of clusters for clustering range of values ​​and use the current Clustering of values; from Randomly select from customer points points as the initial cluster centers, i.e., truck stops, and initialize the capacity of each category; Calculate the Euclidean distance between each customer point and each cluster center, that is: ; In the formula, is the distance matrix from each customer point to the cluster center, For customers, is the cluster center matrix, For the Customer points, To include Customer point Cluster centers; According to the Euclidean distance between each customer point and each cluster center, a cluster center is assigned to the current customer point and the total capacity of the current category is calculated at the same time; Determine whether the addition of the current customer point causes the current category to exceed the capacity constraint. If so, find a category with unfilled capacity other than the previous category based on the Euclidean distance and return to the previous step. Otherwise, determine whether the current allocatable customer points are zero, otherwise recalculate the total capacity of the current category; If yes, calculate the average coordinates of the customer points in each category and use it as the new cluster center of the category; Determine whether the threshold between the new cluster center and the old cluster center exceeds the set center change threshold. If so, reinitialize the capacity of each category. Otherwise, exit the iteration, calculate and save each The silhouette coefficient of the values ​​is compared Worth the silhouette coefficient, choose the one with the highest silhouette coefficient The value is used as the final number of clusters, that is: ; ; In the formula, For the One The silhouette coefficient of the value clustering, For the The average distance between a customer point and the customer point of the nearest cluster that is not its own cluster, For the The average distance between a customer point and other customer points in its cluster, is the matrix of new cluster centers, It is A collection of data points that are clustered; Save the coordinates and demand of the cluster center and customer points in each category, where the demand of the cluster center is the sum of the demand of the customer points it contains.

[0007] Preferably, in step S1, the selection of the truck stop is constrained by the load capacity of the drone at the truck stop not exceeding the load capacity of the corresponding truck and the total demand of the customer points included in each truck stop for truck delivery is not greater than the total load capacity of the drones on the truck, that is: ; ; In the formula, For the current The drone belongs to When a truck otherwise , For the The load capacity of the drone, For the The load of the truck, For the collection of trucks, For the current Truck stops include When a customer clicks otherwise , For the The demand of each customer point, For truck By Point to point When delivering to a point, otherwise , For the current The drone When a truck stop takes off, otherwise , A collection of truck stops.

[0008] Preferably, in step S2, the initial temperature and Metropolis criterion are improved based on traditional simulated annealing, including: By giving the initial temperature according to the characteristics of the sample set, the sample information is fully utilized and the performance of the algorithm is optimized. The initial temperature and cooling function are: ; ; In the formula, and are randomly selected in the solution space. The maximum and minimum values ​​of the function values ​​corresponding to the feasible solutions, is the initial temperature, For attenuation The temperature after the is the cooling factor; from Randomly generated from customer points The initial feasible solution of , decodes it to get the initial optimal solution, and initializes it as the current global optimal solution; Generate new solutions through neighborhood structures, where neighborhood structures include exchange, reversal, and insertion structures; Update the optimal solution and set two ways to accept new solutions in the simulated annealing algorithm, namely: The first one is that if the current solution is better, the current solution is updated to the optimal solution. The second one is that if the current solution is a worse solution, the worse solution will be accepted with a certain probability according to the improved Metropolis (acceptance-rejection criterion for Monte Carlo simulation) criterion. After determining whether the current solution is the optimal solution, that is, the optimal path, and updating it, the simulated annealing algorithm will save the optimal solution of each iteration. When the number of iterations reaches the set maximum value, the algorithm terminates.

[0009] Preferably, in step S2, by adding an influencing factor The probability of accepting a worse solution is increased, and the Metropolis criterion is improved. The improved Metropolis criterion formula is as follows: ; ; In the formula, is the improved Metropolis criterion formula, is the impact factor.

[0010] Preferably, in step S2, the goal of planning the path is to minimize the total economic cost and maximize the time reliability, that is, to obtain the optimal path, wherein: Minimize the total economic cost objective: ; ; ; In the formula, is the total economic cost, For the cost of the truck, For the cost of drones, is the maintenance cost of each truck, For truck By Point to point When delivering to a point, otherwise , For the Point to The distance of the points, is the delivery cost per kilometer of the truck, For the collection of drones, is the maintenance cost of each drone, For drones By Point to point When delivering to a point, otherwise , is the delivery cost per kilometer of the drone, It is a collection of customer points and truck delivery points; Maximize time reliability: The objective function for maximizing temporal reliability is: ; ; ; ; ; ; When calculating the time reliability of a truck, ; When calculating the time reliability of a drone, ; In the formula, is the total time reliability of the truck, is the total time reliability of the UAV, For Point to Time reliability of each point, For the Truck from Point to Time reliability of each point, For the The drone from Point to Time reliability of each point, For Point to A point in time, for The critical time is equal to 1, for The time is equal to 0 o'clock, For trucks from Point to A point in time, For drones from Point to A point in time, is the speed of the truck, is the speed of the drone, The latest time limit for trucks, The latest time limit for the drone.

[0011] Preferably, in step S2, on the premise of planning the path and obtaining the optimal path, the following constraints are also included: The cargo storage capacity of the distribution center shall not be less than the total load capacity of the truck: ; In the formula, For the The load of the truck, The capacity of the distribution center; The total load of the trucks is not less than the total demand of the customer points: ; In the formula, For the The demand of customer points at truck stops; Each truck and drone will travel no more than its maximum mileage: ; ; In the formula, is the maximum mileage of the truck, is the maximum mileage of the drone; Each truck stop is served by exactly one truck: ; Each customer point has only one drone service: ; Trucks and drones enter and exit from the same node when servicing truck stops and customer points: ; ; Each truck and each drone must meet the latest time limit when delivering the goods: ; .

[0012] The beneficial effects of the present invention are as follows: the present invention establishes a complete multi-objective mathematical model, the first objective function aims to minimize costs, including the transportation and daily maintenance costs of trucks and drones, and the second objective function aims to maximize time reliability by implementing soft time windows and customized time reliability functions, thereby meeting the needs of enterprises and customers, and selecting truck stops through an improved k-means++ clustering algorithm; generating optimal paths for trucks and drones respectively through an improved simulated annealing algorithm, and then combining them with constraints to finally obtain the optimal solution for truck-drone collaborative delivery; solving the problem of collaborative delivery paths for trucks and drones with time windows. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flow chart of a path planning method for truck-UAV collaborative delivery of the present invention; Figure 2 is a flow chart of truck-drone collaborative delivery in the present invention; Figure 3 is a flowchart of the improved k-means++ in the present invention; Figure 4 It is a flow chart of the improved simulated annealing algorithm in the present invention; Figure 5 is a path diagram of the switching structure in the present invention; Figure 6 is a path diagram of the inversion structure in the present invention; Figure 7 is a path diagram of the insertion structure in the present invention; Figure 8 It is a clustering effect diagram of different center thresholds in the present invention; Fig. 9 is a schematic diagram of the time reliability function in the present invention; Fig.10 It is a visualization effect diagram of different cooling factors of the truck drone in the present invention. DETAILED DESCRIPTION

[0014] The technical solution of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. In the description of the present invention, it should be noted that the terms "center", "up", "down", "left", "right", "vertical", "horizontal", "inside", "outside" and the like indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings, which are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operated in a specific direction, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", and "third" are used for descriptive purposes only and cannot be understood as indicating or implying relative importance.

[0015] The present invention will be further described below in conjunction with the accompanying drawings.

[0016] like Figure 1 , 2 As shown, a path planning method for truck-drone collaborative delivery includes: Step S1, using the improved k-means++ clustering algorithm to select truck stops.

[0017] like Figure 3 As shown, the k-means++ clustering algorithm is improved, including: Set the number of clusters for clustering range of values ​​and use the current Clustering of values; from Randomly select from customer points points as the initial cluster centers, i.e., truck stops, and initialize the capacity of each category; Calculate the Euclidean distance between each customer point and each cluster center, that is: ; In the formula, is the distance matrix from each customer point to the cluster center, For customers, is the cluster center matrix, For the Customer points, To include Customer point Cluster centers; According to the Euclidean distance between each customer point and each cluster center, a cluster center is assigned to the current customer point and the total capacity of the current category is calculated at the same time; Determine whether the addition of the current customer point causes the current category to exceed the capacity constraint. If so, find a category with unfilled capacity other than the previous category based on the Euclidean distance and return to the previous step. Otherwise, determine whether the current allocatable customer points are zero, otherwise recalculate the total capacity of the current category; If yes, calculate the average coordinates of the customer points in each category and use it as the new cluster center of the category; Determine whether the threshold between the new cluster center and the old cluster center exceeds the set center change threshold. If so, reinitialize the capacity of each category. Otherwise, exit the iteration, calculate and save each The silhouette coefficient of the values ​​is compared Worth the silhouette coefficient, choose the one with the highest silhouette coefficient The value is used as the final number of clusters, that is: ; ; In the formula, For the One The silhouette coefficient of the value clustering, For the The average distance between a customer point and the customer point of the nearest cluster that is not its own cluster, For the The average distance between a customer point and other customer points in its cluster, is the matrix of new cluster centers, It is A collection of data points that are clustered; Save the coordinates and demand of the cluster center and customer points in each category, where the demand of the cluster center is the sum of the demand of the customer points it contains.

[0018] In the embodiment, the selection of the truck stop is constrained by the load capacity of the drone at the truck stop not exceeding the load capacity of the corresponding truck and the total demand of the customer points included in each truck stop for truck delivery is not greater than the total load capacity of the drones on the truck, that is: ; ; In the formula, For the current The drone belongs to When a truck otherwise , For the The load capacity of the drone, For the The load of the truck, For the collection of trucks, , For the current Truck stops include When a customer clicks otherwise , For the The demand of each customer point, For truck By Point to point When delivering to a point, otherwise , For the current The drone When a truck stop takes off, otherwise , A collection of truck stops. .

[0019] In the embodiment, the center change threshold The values ​​of are respectively [0.001, 0.006] for experiments, wherein the present invention selects the changes of clustering effects of some samples within the threshold range for visualization, such as Figure 8 As shown, When the silhouette coefficient of the samples exceeds 0.55 and compared with other values, The silhouette coefficient is the largest when , so in the improved k-means++, this paper uses the center threshold Set to 0.002.

[0020] Step S2, through the improved simulated annealing algorithm, the distribution center, truck stop points and customer points are calculated to generate the optimal paths for trucks and drones respectively, and then they are combined with the constraints to finally obtain the optimal solution for truck-drone collaborative delivery.

[0021] The simulated annealing algorithm (SA) is an intelligent optimization algorithm that introduces appropriate random factors and a physical annealing process. The basic idea is to continuously generate new solutions from the initial solution, determine whether the current solution is the optimal solution, and be able to accept a poor solution with a certain probability. As the solid temperature continues to decay, the probability of accepting a poor solution also changes until the global optimal solution to the optimization problem is found. The present invention will generate the optimal paths for trucks and drones respectively, and then combine them to finally obtain the optimal solution for truck-drone collaborative delivery.

[0022] like Figure 4 As shown in the figure, the initial temperature and Metropolis criterion are improved based on the traditional simulated annealing, including: In order to avoid the loss of sample information and the large influence of the initial temperature on the solution effect, the present invention improves the initial temperature. Compared with the traditional simulated annealing algorithm that directly gives the initial temperature and causes a waste of algorithm performance, the present invention gives the initial temperature according to the characteristics of the sample set, so that the sample information is fully utilized and the performance of the algorithm is more optimized, wherein the initial temperature and the cooling function are: ; ; In the formula, and are randomly selected in the solution space. The maximum and minimum values ​​of the function values ​​corresponding to the feasible solutions, is the initial temperature, For attenuation The temperature after the is the cooling factor; from Randomly generated from customer points The initial feasible solution of , decodes it to get the initial optimal solution, and initializes it as the current global optimal solution; Generate new solutions through neighborhood structures, where neighborhood structures include exchange, reversal, and insertion structures; ①Switch structure Exchange the positions of two nodes in a line. The diagram of the exchange structure is as follows Figure 5 As shown; ②Reversal structure Reverse sorting of a segment of nodes, the structure diagram of the reverse structure is as follows Figure 6 As shown; ③Insert structure Insert a node into a new position. The structure diagram of the inserted structure is as follows Figure 7 As shown; Update the optimal solution and set two ways to accept new solutions in the simulated annealing algorithm, namely: The first one is that if the current solution is better, the current solution is updated to the optimal solution. The second one is that if the current solution is a worse solution, the worse solution will be accepted with a certain probability according to the improved Metropolis criterion. After determining whether the current solution is the optimal solution, that is, the optimal path, and updating it, the simulated annealing algorithm will save the optimal solution of each iteration. When the number of iterations reaches the set maximum value, the algorithm terminates.

[0023] In the embodiment, in order to avoid the combinatorial optimization problem The order of magnitude difference leads to unstable acceptance probability and the Metropolis criterion is too dependent on temperature regulation, which makes the algorithm fall into the local optimal solution. By adding an influencing factor The probability of accepting a worse solution is increased, and the Metropolis criterion is improved. The improved Metropolis criterion formula is as follows: ; ; In the formula, is the improved Metropolis criterion formula, is the impact factor.

[0024] In the embodiment, the goal of planning the path is to minimize the total economic cost and maximize the time reliability, that is, to obtain the optimal path, wherein: Minimize the total economic cost objective: ; ; ; In the formula, is the total economic cost, For the cost of the truck, For the cost of drones, is the maintenance cost of each truck, For truck By Point to point When delivering to a point, otherwise , For the Point to The distance of the points, is the delivery cost per kilometer of the truck, For the collection of drones, , is the maintenance cost of each drone, For drones By Point to point When delivering to a point, otherwise , is the delivery cost per kilometer of the drone, is the collection of customer points and truck delivery points. ; Maximize time reliability: like Fig. 9 As shown, the objective function of maximizing time reliability is: ; ; ; ; ; ; When calculating the time reliability of a truck, ; When calculating the time reliability of a drone, ; In the formula, is the total time reliability of the truck, is the total time reliability of the UAV, For Point to Time reliability of each point, For the Truck from Point to Time reliability of each point, For the The drone from Point to Time reliability of each point, For Point to A point in time, for The critical time is equal to 1, for The time is equal to 0 o'clock, For trucks from Point to A point in time, For drones from Point to A point in time, is the speed of the truck, is the speed of the drone, The latest time limit for trucks, The latest time limit for the drone.

[0025] In the embodiment, the following constraints are also included under the premise of planning the path and obtaining the optimal path: The cargo storage capacity of the distribution center shall not be less than the total load capacity of the truck: ; In the formula, For the The load of the truck, The capacity of the distribution center; The total load of the trucks is not less than the total demand of the customer points: ; In the formula, For the The demand of customer points at truck stops; Each truck and drone will travel no more than its maximum mileage: ; ; In the formula, is the maximum mileage of the truck, is the maximum mileage of the drone; Each truck stop is served by exactly one truck: ; Each customer point has only one drone service: ; Trucks and drones enter and exit from the same node when servicing truck stops and customer points: ; ; Each truck and each drone must meet the latest time limit when delivering the goods: ; .

[0026] In SA, the setting of cooling factor will affect the convergence speed and performance of the model, so setting a suitable cooling factor is very important for the simulated annealing algorithm. This paper selects some data, sets the number of iterations in ISAA to 2000, and conducts experiments with cooling factor alpha in the range of 0.94-0.99, and visualizes the results of one of the examples, such as Fig.10As shown, when alpha=0.99, the cost is the lowest and the solution result is the best, so the present invention sets the cooling factor to 0.99, and sets other parameters such as the penalty coefficient for violating the constraint, the number of iterations, and the probability of selecting, exchanging, and reversing the structure according to the strictness of the constraint, the optimization degree of the algorithm, and the parameters of traditional simulated annealing.

[0027] Since there are many parameters in the algorithm and there is correlation between parameters, in order to obtain the optimal parameter combination, this paper uses the irace package in R language to solve the optimal parameters. Finally, the penalty coefficient is determined to be 20, the maximum number of outer iterations is 1000, the maximum number of inner iterations is 500, the cooling factor is 0.99, and the probabilities of exchange, reversal, and insertion are 0.2, 0.4, and 0.4 respectively.

[0028] The modified examples are solved for the established truck-UAV collaborative delivery path optimization model and the single truck delivery path optimization model, and the solution results are shown in Tables 1 and 2.

[0029] The solution results for the example of small load and large scale (50 customer points) are shown in Table 1. It can be seen from Table 1 that compared with the single truck delivery model, the truck-drone collaborative delivery model saves 15%-30% of the cost, with a maximum saving of 38%, and reduces the time cost by 30%-50%, with a maximum reduction of 53% of the delivery time. Among them, the time reliability is mostly better than the time reliability of single truck delivery.

[0030] Table 1 Large-scale example solution results The solution results for small and medium-scale examples are shown in Table 2. It can be seen from Table 2 that compared with the single truck delivery model, the truck-drone collaborative delivery model saves 5%-15% of the cost, with a maximum saving of 18%, and reduces the time cost by 15%-40%, with a maximum reduction of 47% of the delivery time. The time reliability is much better than the time reliability of single truck delivery.

[0031] Table 2 Solution results of small and medium-scale examples In summary, in both small-scale and large-scale examples, the truck-drone collaborative delivery model is superior to the single truck delivery model in terms of comprehensive cost, delivery time, and time reliability, indicating that truck-drone collaborative delivery can greatly save costs and delivery time and improve delivery time reliability, and the effectiveness and necessity of drones in path optimization problems. Compared with small-scale and medium-scale delivery, the model of the present invention has a greater proportion of cost savings and delivery time reduction in large-scale delivery, so the model of the present invention also solves the defect of the truck-drone collaborative delivery model that can only deliver on a small scale to a certain extent.

[0032] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments may still be modified, or some or all of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A path planning method for truck-drone collaborative delivery, characterized in that: include: Step S1, using the improved k-means++ clustering algorithm to select truck stops; Step S2, through the improved simulated annealing algorithm, the distribution center, truck stop points and customer points are calculated to generate the optimal paths for trucks and drones respectively, and then they are combined with the constraints to finally obtain the optimal solution for truck-drone collaborative delivery.

2. A path planning method for truck-UAV collaborative delivery according to claim 1, characterized in that: In step S1, improving the k-means++ clustering algorithm includes: Set the number of clusters for clustering range of values ​​and use the current Clustering of values; from Randomly select from customer points points as the initial cluster centers, i.e., truck stops, and initialize the capacity of each category; Calculate the Euclidean distance between each customer point and each cluster center, that is: ； In the formula, is the distance matrix from each customer point to the cluster center, For customers, is the cluster center matrix, For the Customer points, To include Customer point Cluster centers; According to the Euclidean distance between each customer point and each cluster center, a cluster center is assigned to the current customer point and the total capacity of the current category is calculated at the same time; Determine whether the addition of the current customer point causes the current category to exceed the capacity constraint. If so, find a category with unfilled capacity other than the previous category based on the Euclidean distance and return to the previous step. Otherwise, determine whether the current allocatable customer points are zero, otherwise recalculate the total capacity of the current category; If yes, calculate the average coordinates of the customer points in each category and use it as the new cluster center of the category; Determine whether the threshold between the new cluster center and the old cluster center exceeds the set center change threshold. If so, reinitialize the capacity of each category. Otherwise, exit the iteration, calculate and save each The silhouette coefficient of the values ​​is compared Worth the silhouette coefficient, choose the one with the highest silhouette coefficient The value is used as the final number of clusters, that is: ； ； In the formula, For the One The silhouette coefficient of the value clustering, For the The average distance between a customer point and the customer point of the nearest cluster that is not its own cluster, For the The average distance between a customer point and other customer points in its cluster, is the matrix of new cluster centers, It is A collection of clustered customer points; Save the coordinates and demand of the cluster center and customer points in each category, where the demand of the cluster center is the sum of the demand of the customer points it contains.

3. The path planning method for truck-UAV collaborative delivery according to claim 2 is characterized in that: In step S1, the selection of truck stops is constrained by the load capacity of the drone at the truck stop not exceeding the load capacity of the corresponding truck and the total demand of customer points included in each truck stop for truck delivery is not greater than the total load capacity of the drones on the truck, that is: ； ； In the formula, For the current The drone belongs to When a truck otherwise , For the The load capacity of the drone, For the The load of the truck, For the collection of trucks, For the current Truck stops include When a customer clicks otherwise , For the The demand of each customer point, For truck By Point to point When delivering to a point, otherwise , For the current The drone When a truck stop takes off, otherwise , A collection of truck stops.

4. The path planning method for truck-UAV collaborative delivery according to claim 3 is characterized in that: In step S2, the initial temperature and Metropolis criterion are improved based on the traditional simulated annealing, including: By giving the initial temperature according to the characteristics of the sample set, the sample information is fully utilized and the performance of the algorithm is optimized. The initial temperature and cooling function are: ； ； In the formula, and are randomly selected in the solution space. The maximum and minimum values ​​of the function values ​​corresponding to the feasible solutions, is the initial temperature, For attenuation The temperature after the is the cooling factor; from Randomly generated from customer points The initial feasible solution of , decodes it to get the initial optimal solution, and initializes it as the current global optimal solution; Generate new solutions through neighborhood structures, where neighborhood structures include exchange, reversal, and insertion structures; Update the optimal solution and set two ways to accept new solutions in the simulated annealing algorithm, namely: The first one is that if the current solution is better, the current solution is updated to the optimal solution. The second one is that if the current solution is a worse solution, the worse solution will be accepted with a certain probability according to the improved Metropolis criterion. After determining whether the current solution is the optimal solution, that is, the optimal path, and updating it, the simulated annealing algorithm will save the optimal solution of each iteration. When the number of iterations reaches the set maximum value, the algorithm terminates.

5. The path planning method for truck-UAV collaborative delivery according to claim 4 is characterized in that: In step S2, by adding an impact factor The probability of accepting a worse solution is increased, and the Metropolis criterion is improved. The improved Metropolis criterion formula is as follows: ； ； In the formula, is the improved Metropolis criterion formula, is the impact factor.

6. A path planning method for truck-UAV collaborative delivery according to claim 5, characterized in that: In step S2, the optimal path is obtained by minimizing the total economic cost and maximizing the time reliability as the goal of planning the path, wherein: Minimize the total economic cost objective: ； ； ； In the formula, is the total economic cost, For the cost of the truck, For the cost of drones, is the maintenance cost of each truck, For truck By Point to point When delivering to a point, otherwise , For the Point to The distance of the points, is the delivery cost per kilometer of the truck, For the collection of drones, is the maintenance cost of each drone, For drones By Point to point When delivering to a point, otherwise , is the delivery cost per kilometer of the drone, It is a collection of customer points and truck delivery points; Maximize time reliability: The objective function for maximizing temporal reliability is: ； ； ； ； ； ； When calculating the time reliability of a truck, ; When calculating the time reliability of a drone, ; In the formula, is the total time reliability of the truck, is the total time reliability of the UAV, For Point to Time reliability of each point, For the Truck from Point to Time reliability of each point, For the The drone from Point to Time reliability of each point, For Point to A point in time, for The critical time is equal to 1, for The time is equal to 0 o'clock, For trucks from Point to A point in time, For drones from Point to A point in time, is the speed of the truck, is the speed of the drone, The latest time limit for trucks, The latest time limit for the drone.

7. The path planning method for truck-UAV collaborative delivery according to claim 6 is characterized in that: In step S2, on the premise of planning the path and obtaining the optimal path, the following constraints are also included: The cargo storage capacity of the distribution center shall not be less than the total load capacity of the truck: ； In the formula, For the The load of the truck, The capacity of the distribution center; The total load of the trucks is not less than the total demand of the customer points: ； In the formula, For the The demand of customer points at truck stops; Each truck and drone will travel no more than its maximum mileage: ； ； In the formula, is the maximum mileage of the truck, is the maximum mileage of the drone; Each truck stop is served by exactly one truck: ； Each customer point has only one drone service: ； Trucks and drones enter and exit from the same node when servicing truck stops and customer points: ； ； Each truck and each drone must meet the latest time limit when delivering the goods: ； 。

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