Truck-unmanned aerial vehicle collaborative distribution model based on non-contact distribution and two-stage algorithm

Abstract

According to the non-contact delivery-based truck-unmanned aerial vehicle collaborative delivery model and the two-stage algorithm provided by the invention, aiming at the non-contact delivery problem, the expected delivery time of customers is fully considered, and factors such as a truck stop point, a truck path, an unmanned aerial vehicle path, a customer service time window and the like are constructed as variables; and constructing a target-minimized truck-unmanned aerial vehicle cooperative distribution mixed integer programming model according to the sum of the truck operation cost, the unmanned aerial vehicle operation cost and the time window penalty cost. According to the characteristics of the model, a two-stage algorithm is designed, in the first stage of the algorithm, an improved K-Means clustering method is adopted, the maximum flight distance of the unmanned aerial vehicle and client point position coordinates are considered to cluster clients in a region, the unmanned aerial vehicle of the clients in the region can reach and complete service, and a clustering center is a truck stop point and is an unmanned aerial vehicle launching point; and in the second stage, a variable neighborhood simulated annealing algorithm is adopted, a domain structure of a solution is constructed, a truck-unmanned aerial vehicle cooperative distribution path is optimized, and distribution cost minimization is realized.

Description

Technical Field

[0001] The present invention relates to the field of logistics distribution, and in particular to a truck-drone collaborative distribution model and a two-stage algorithm based on contactless distribution. Background Art

[0002] Contactless delivery can be achieved by using emerging smart technologies such as drones to deliver items to customers safely and efficiently, which can improve delivery efficiency and service quality. Drone delivery is fast and less affected by traffic, but it is limited by itself, has a smaller delivery range, and is easily affected by external factors. Traditional trucks have a wide delivery range, but are slow and have high delivery costs. Therefore, the coordinated delivery of trucks and drones can effectively leverage the advantages of both and reduce delivery costs. In order to achieve contactless delivery services, trucks do not participate in delivery tasks, and drones are used to efficiently deliver to customers, providing accurate and diversified services.

[0003] However, in real life, the launch and recovery of drones rely on trucks, which requires that the route planning of trucks and drones must be closely coordinated. At the same time, in real life, customers usually have clear expectations for the arrival time of items after placing an order. They expect the goods to be delivered accurately within the scheduled time and accept a certain degree of delay or advance. Most studies ignore relevant real-life scenarios. Therefore, the present invention proposes a truck-drone collaborative delivery model and method. Starting from the consideration of soft time window constraints, a time penalty function is established to construct a truck-drone collaborative delivery mathematical model with the goal of minimizing total cost; then, a two-stage algorithm combining an improved K-Means algorithm and a variable neighborhood simulated annealing algorithm is designed to obtain the optimal truck stop point and optimized delivery path solution, so as to achieve system optimization of truck and drone routes as a whole under contactless delivery. Summary of the invention

[0004] In view of the above problems, the present invention proposes a truck-UAV collaborative delivery model and a two-stage algorithm based on contactless delivery. First, from the perspective of the customer's geographical location and the maximum flight distance limit of the drone, the launch is avoided beyond the drone's delivery range. The improved K-Means algorithm is used to generate temporary parking points for trucks. The truck drives to this point to launch and recover the drone, and the customers are divided into different sub-areas; secondly, the time penalty function is established by focusing on the customer's requirements for delivery time, thereby proposing a truck-UAV collaborative delivery mathematical model, considering the minimum overall delivery cost, and achieving the purpose of reducing delivery costs. Specifically, it includes the following:

[0005] The truck delivery cost F1 includes the operating cost of each truck and the delivery cost per unit distance of the truck; the drone delivery cost F2 includes the operating cost of each drone and the delivery cost per unit distance of the drone.

[0006] Time penalty cost F3. During the delivery process, customers accept a certain degree of early arrival and late arrival. If the delivery arrives outside the time window, the early arrival or late arrival fee will be increased accordingly. If the delivery arrives within the customer's expected time window, that is, within the time window, the time penalty cost is 0.

[0007] In order to avoid loss of generality, the following assumptions need to be made to construct the model of the present invention: (1) Each customer can only be visited once; (2) The drone is subject to mileage and load constraints; (3) The drone is launched by a truck parked at the stop and can visit multiple customers after a single launch. After completing the delivery mission, the drone must return to the launching truck parked at the origin; (4) The drone's flight time is fixed and constant, and its flight time is not affected by flight speed and cargo capacity; at the same time, loading and unloading time has no effect on the overall situation, and the drone can continue to deliver after replacing the battery or charging on the truck; (5) The truck has sufficient fuel supply for one trip, but it has capacity constraints; (6) The speed of the truck and the drone is constant, and each mileage is measured using Euclidean distance.

[0008] The two-stage algorithm proposed in the present invention is an improved K-means algorithm and a variable domain simulated annealing algorithm. In the first stage, the improved K-means algorithm is used to cluster the temporary stops of trucks, the number of customers and customer points in each sub-area; in the second stage, the variable domain simulated annealing algorithm is used to solve the optimal path of trucks and drones under the minimum total cost.

[0009] The truck delivery cost F1 and drone delivery cost F2 mainly include their respective fixed costs and unit distance delivery costs, and the calculation formula is:

[0010]

[0011] Where d ij represents the distance between truck stops i and j, represents the distance between customer points r and v within truck stop i, N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including stop i, i.e., the drone launch point), C T ,C D They are the fixed costs of using trucks and drones, C vT ,C vD They are the unit transportation costs of trucks and drones, M is the set of trucks, H is the set of drones, When it is 1, it means that truck m travels from temporary stop i to j, otherwise, it is 0. It indicates that UAV h flies from customer point r to customer point v, otherwise, it is 0.

[0012] In order to meet the relevant assumptions proposed by the present invention, the paths of trucks and drones have corresponding constraints, which are as follows:

[0013] (1) Each truck departs from the warehouse and returns to the warehouse, and traverses all stops only once, while ensuring that the flow of the truck line remains balanced. The calculation formula is:

[0014]

[0015] Where N m represents the set of truck stops (including the starting warehouse 0), M represents the set of trucks, When it is 1, it means that truck m travels from temporary stop i to j, otherwise, it is equal to 0. When it is 1, it means that truck m visits temporary stop i, otherwise, it is 0.

[0016] (2) Each drone must take off and return at the same temporary stop, and ensure that each customer point in each zone is served only once, maintaining the flow balance of the drone service route. In addition, the cumulative distance of each drone's single flight must be controlled within the range of its maximum endurance, calculated as follows:

[0017]

[0018] In the formula represents the distance between customer points r and v within truck stop i, N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including stop i, i.e., the drone launch point), L D It is represented by the maximum cruising range / maximum flight radius of the drone, H is the set of drones, indicates that UAV h flies from customer point r to customer point v, otherwise, it is 0.

[0019] (3) The total demand of each temporary stop is equal to the cumulative value of the demand of all customer points in its coverage area. At the same time, the weight of the cargo loaded on each truck must be kept within the maximum load limit, and the total weight of the items that each drone can carry in a single flight must not exceed its maximum load capacity. Using the load balance constraints of trucks and drones, the calculation formula for eliminating sub-loops is:

[0020] And i≠0

[0021]

[0022] Where N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including the stop i, i.e., the drone launch point), M represents the truck set, H represents the drone set, represents the demand of customer r at truck stop i, q i The demand for truck stop i, Q T , Q D Represent the maximum load of trucks and drones, When it is 1, it means that truck m travels from temporary stop i to j, otherwise, it is equal to 0. indicates that UAV h flies from customer point r to customer point v, otherwise, it is 0.

[0023] The time penalty cost F3 proposed by the present invention is the cost incurred when the drone delivery service is not delivered within the time expected by the customer: when arriving earlier than the customer's time window, a waiting cost will be incurred When arriving later than the customer's time window, a late arrival cost will be incurred The penalty cost is 0 when delivering within the customer's time window, and the calculation formula is:

[0024]

[0025] Where N c represents the logistics distribution customer set, H represents the drone set, C1, C2 represent the unit waiting cost and unit delay cost, [a r ,b r ] represents the delivery time window for customer r, a r is the earliest time that customer r expects the goods to be delivered, b r is the latest time that customer r expects the goods to be delivered. Indicates the time when the drone arrives at the customer point.

[0026] Each truck needs to wait at the stop for the drone to complete the delivery task at the current point and return. Therefore, its waiting time is equivalent to the longest time required for the drone on the truck to complete all deliveries at the stop. For a truck, the time to arrive at each node should not be earlier than the sum of the time it arrived at the previous node, the waiting time at the node, and the driving time from the node to the next node. Correspondingly, the time a drone arrives at any customer point must be no earlier than the time it arrived at the previous customer point, the service time at the customer point, the waiting time, and the flight time from the customer point to the next customer point. Regarding the time relationship, the time the drone arrives at the customer point and the time the truck arrives at the temporary stop need to be coordinated with each other; and both the arrival time of the truck and the arrival time of the drone should be strictly greater than 0. The calculation formula is:

[0027]

[0028] Where N c represents the set of logistics distribution customers, N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including the stop i, i.e., the drone launch point), M represents the truck set, H represents the drone set, When it is 1, it means that truck m travels from temporary stop i to j, otherwise, it is equal to 0. is to indicate that the drone h flies from the customer point r to the customer point v, otherwise, it is 0. When it is 1, it means that truck m visits temporary stop i, otherwise, it is 0. Indicates the time when the truck arrives at the temporary stop. Indicates the time when the drone arrives at the customer point, Denote the waiting time of truck and drone respectively, t ij , Represents the driving or flying time of the truck and the drone, represents the delivery time of the drone, s r represents the customer's service time, and W represents an integer that is always large enough.

[0029] The two-stage algorithm proposed in the present invention first uses the improved K-Means algorithm to cluster the customers in the area in the first stage. The traditional K-Means clustering algorithm gives a clustering value in advance. The value size not only affects the clustering effect, but also may affect the subsequent route planning. In addition, due to the complexity of truck-UAV collaborative delivery, after clustering according to the given K value, the distance between some customers and their cluster center exceeds the maximum flight distance of the UAV, which makes the established delivery plan unfeasible. Therefore, a custom clustering radius R is added to the traditional K-Means clustering algorithm. The improved K-Means clustering algorithm can adaptively determine the number of clusters.

[0030] The truck’s stop point is the center point of each clustering category. The clustering radius must not exceed the maximum flight radius of the drone. At the same time, the drone must be able to fly to the customer point in each area. The calculation formula is:

[0031]

[0032] In the formula Represents a truck stop i The distance between internal customer points r and v; R represents the clustering radius; N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including stop i, i.e., the drone launch point), L DIndicates the maximum range / maximum flight radius of the drone.

[0033] In the second stage, the simulated annealing algorithm with variable neighborhood is used to solve the paths of trucks and drones. The simulated annealing algorithm (SA) is inspired by the thermodynamic annealing process. It starts at a higher initial temperature and follows the Metropolis sampling stability criterion. It randomly searches in the neighborhood structure of the solution space and allows a suboptimal solution that is worse than the current solution to be accepted with a certain probability. In order to further enhance the comprehensiveness and search ability of the algorithm, the variable neighborhood search algorithm (VNS) is combined to more comprehensively explore the solution space by dynamically adjusting the search neighborhood range, thereby improving the efficiency of finding a better solution. First, the neighborhood structure of the solution is generated, and then the greedy algorithm is used to generate the initial feasible solution, which is optimized by the variable neighborhood simulated annealing algorithm (SAVN) to minimize the total cost.

[0034] The key to the variable neighborhood simulated annealing algorithm (SAVN) is to construct the neighborhood structure of the solution. First, select a subpath r1 of the truck route, p = 1, and randomly generate two tangent points and exchange subpath lengths - cut1, cut2, crosslen. The crosslen length is randomly generated within (1, min (p, length (r1)) to satisfy the exchange length is less than the subpath length. At the same time, for a sub-drone path r2 contained in the region i of the subpath r1, randomly generate cut3 and cut4, which satisfy the exchange length is less than the length of the drone path r2 excluding the endpoints on both sides, n i ={i,cut3,cut4},n d ={n i ,n j , ...} is the neighborhood structure of the feasible solution of the drone path of all partitions contained in the sub-path r1, generating the sub-neighborhood structure n p ={cut1,cut2,crosslen,n d}, let p = p + 1, and loop to generate the neighborhood structure n of this subpath p ={n1,n2,...,n pmax}, the calculation formula is as follows:

[0035] 1<cut1,cut2<length(r1)-2

[0036] cut1+crosslen<length(r1)-2

[0037] cut2+crosslen<length(r1)-2

[0038] 1<cut3,cut4<length(r2)-2

[0039] p<length(r1) BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a schematic diagram of the model process of the present invention;

[0041] Figure 2 It is a two-stage algorithm framework diagram of the present invention;

[0042] Figure 3 It is the two-stage algorithm coding diagram of the present invention;

[0043] Figure 4 It is a schematic diagram of the two-stage algorithm exchange of the present invention;

[0044] Figure 5 This is a comparison between the present invention and other methods under three data sets: C101 / 201, R101 / 201, RC101 / 201. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, a truck-UAV collaborative delivery model and method based on contactless delivery proposed by the present invention is described in detail below in conjunction with the accompanying drawings. It should be understood that the specific implementation method described herein is only used to explain the present invention and is not used to limit the present invention. Changes, alterations, additions, modifications or substitutions made by ordinary technicians in the technical field within the indicated range of the present invention should be included in the scope of the claims of the present invention.

[0046] Figure 1 This is a specific schematic diagram of a truck-drone collaborative delivery model based on contactless delivery in the present invention. Figure 1It can be seen that contactless delivery is achieved, and the delivery task is completed by drones. In order to ensure that all customer points are within the effective flight distance of the drone, truck stops are selected according to the customer locations in the area, and customers are divided into various sub-areas. Starting from the main warehouse, multiple trucks each carry multiple drones to the nearby area for delivery services. Based on the consideration of the geographical location of customers in the overall area, the cluster radius is determined by the maximum flight radius limit of the drone, and the area is divided, thereby determining the truck stop point, that is, the drone launch point, landing point, and the customer point that the drone needs to serve in each sub-area. The truck stops at a temporary stop (cluster center point), launches the drone and waits for the drone to deliver the items. Its service objects are the customer points included in the cluster area. At the same time, it is allowed to visit multiple customers at a time under its own load limit. After the service is completed, it returns to the launching truck. After the truck recovers all the launched drones, it drives to the next temporary stop point to complete the delivery service until it returns to the warehouse after completing the delivery service for all customers. Compared with traditional single truck delivery, trucks and drones combine the delivery advantages of both, and collaborative delivery expands the service radius and improves the timeliness and flexibility of overall delivery.

[0047] Figure 2 This is a framework diagram of a two-stage algorithm for truck-drone collaborative delivery based on contactless delivery in the present invention. Figure 2 It can be seen that the two-stage algorithm for truck-UAV collaborative delivery based on contactless delivery proposed in the present invention includes an improved K-means clustering and a variable domain simulated annealing two-stage algorithm for optimizing the paths of trucks and UAVs, and the specific implementation steps are as follows:

[0048] Phase 1: Step 1: Set initial K=1, select K| customers as initial cluster centers to cluster all customers, and go to step 2:; Step 2: According to the generated cluster area, calculate each center of gravity as the new K cluster centers, and go to step 3; Step 3: Re-cluster all customers according to the new K cluster centers, and go to step 4; Step 4: Calculate the distance from the customer in each category to the cluster center of the category to which it belongs, and determine whether it meets the maximum flight limit of the drone: If it meets, go to step 6; Otherwise, remove the unsatisfied customers in each category and add them to a newly created empty set O, update the number of cluster centers, set the number of clusters K=K+1, and go to step 3; Step 5: Determine whether the set O is an empty set, O is an empty set, go to step 6, otherwise, set the number of clusters K=K+1, and go to step 3; Step 6: Delete the empty set, output the cluster center and the customer points in each cluster.

[0049] Phase 2: Step 1 Based on the results generated in the first phase, the cluster center is used as the temporary stop point for trucks and the launch point for drones, and the greedy algorithm is used to form the initial solution s0 for the truck and drone routes; Step 2: The initial routes of trucks and drones are optimized using 2-exchange exchange to generate solution s1. If f(s1) < f(s0), let the current solution s = s1; otherwise, let the current solution be s = s0, let the historical optimal solution s′ = s1, determine the initial temperature t0, let the current temperature t = t0, and determine the neighborhood structure n p ={n1,n2,...,n pmax}; Step 3: Determine whether the maximum number of iterations is met. If so, go to step 8; otherwise, set the current optimal solution s c =s, go to step 4; Step 4: Determine whether the sampling stability criterion is met. If so, go to step 6; otherwise, go to step 5; Step 5: Randomly generate p value, select the pth neighborhood structure of s, and randomly exchange the new truck route and drone route, which is the solution s2. If min{1,exp[-(f(s2)-f(s)) / t]}≥randrom[0,1], then let s=s2, go to step 6; otherwise, go to step 3; Step 6: If f(s)<f(s c ), then let s c =s, go to step 3, otherwise keep s c No change, go to step 3; Step 7: If f(s)<f(s′), then let s′=s c , go to step 8, otherwise p=(p / p max )+1, go to step 8; Step 8: Cool down Go to step 3; Step 9: Output the current optimal solution.

[0050] Figure 3 It is a coding diagram of a two-stage algorithm for truck-UAV collaborative delivery under contactless delivery according to the present invention. The feasible solution includes truck routes and UAV routes, which affect each other's arrival time at the customer, thereby generating penalty costs. Collaborative optimization of the overall routes of trucks and UAVs requires encoding their routes first: Depot represents the warehouse, and the temporary stop of the truck is generated by clustering using the improved K-Means algorithm in the first stage. In the coding, the warehouse is coded with the number 0, and multiple sub-regions are marked as ak, representing the centers of each sub-region; assuming that partition b contains customer points numbered 1-7, and partition k contains customer points numbered 8 to 10, the UAV routes in this area are generated respectively, and the cluster center in the UAV route is numbered 0.

[0051] Figure 4This is a schematic diagram of the exchange of a two-stage algorithm for truck-UAV collaborative delivery based on contactless delivery in the present invention. According to the neighborhood structure of the solution, the truck path determines the exchange mode according to the randomly generated probability - forward exchange and reverse exchange. Assuming that the truck subpath r_1 (0-abcdefgh-0) is taken as an example, cut1 is selected as a, cut2 is selected as f, crosslen is 2. If forward exchange is selected, the transformed truck subpath is (0-ghfdecba-0); if reverse exchange is selected, the transformed truck subpath is (0-fhgdeacb-0); the drone path uses 2-opt and 2-exchange exchange operators with equal probability to generate new solutions. Assume that a drone subpath r_2 (0-1-2-3-4-5-0) in the sub-region contained in the truck subpath r_1 is taken as an example. Cut3 is selected as 1 and cut4 is selected as 4. If 2-opt exchange is selected, the new drone subpath generated is (0-4-3-2-1-5-0). If 2-exchange exchange operator is selected, the new drone subpath generated is (0-4-2-3-1-5-0).

[0052] Further, the following situation is used as an example to illustrate:

[0053] Taking C101 / 201, R101 / 201, and RC101 / 201 as examples, 10, 15, 25, 35, 50, 70, and 100 customer points are selected respectively to generate different calculation examples, which contain information such as the location coordinates of each point, demand, service time, and time window.

[0054] (1) First, the improved K-means algorithm is used to cluster the case set to obtain the corresponding temporary truck stops and the customers included in the corresponding sub-regions, ensuring that the drone can complete the delivery task for all customer points in the region. The calculation formula is:

[0055]

[0056] In the formula Represents a truck stop i The distance between internal customer points r and v; R represents the clustering radius; N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including stop i, i.e., the drone launch point), L D Indicates the maximum range / maximum flight radius of the drone.

[0057] (2) According to a truck-drone collaborative delivery model based on contactless delivery according to the present invention, the fitness function is to minimize the total delivery cost, and the calculation formula is as follows:

[0058] minZ=F1+F2+F3

[0059]

[0060] Wherein, the truck delivery cost is F1, the drone delivery cost is F2, and the time penalty cost is F3.

[0061] (3) The maximum range of the drone is set to 30 km; the unit fixed costs of the truck and drone are 30 yuan and 3 yuan respectively, the mileage costs are 1.25 yuan / km and 0.15 yuan / km, and the speeds are 40 km / h and 60 km / h respectively; the unit waiting cost and unit delay cost are 0.2 yuan and 0.5 yuan respectively. The initial temperature of the variable neighborhood simulated annealing (SAVN) is t0 = 5000, The maximum number of iterations is 5000. The fitness of the generated path is calculated based on the location coordinates, demand, service time, and time window of each point in the example, and it is iterated to continuously obtain a feasible solution.

Claims

1. A truck-drone collaborative delivery model and two-stage algorithm based on contactless delivery are used to achieve contactless delivery in the logistics delivery link, improve delivery quality, and reduce delivery costs, including the following: The truck delivery cost F1 includes the operating cost of each truck and the delivery cost per unit distance of the truck; the drone delivery cost F2 includes the operating cost of each drone and the delivery cost per unit distance of the drone. Time penalty cost F3. During the delivery process, customers accept a certain degree of early arrival and late arrival. If the delivery arrives outside the time window, the early arrival or late arrival fee will be increased accordingly. If the delivery arrives within the customer's expected time window, that is, within the time window, the time penalty cost is 0. In order to avoid loss of generality, the following assumptions need to be made to construct the model of the present invention: (1) Each customer can only be visited once; (2) The drone is subject to mileage and load constraints; (3) The drone is launched by a truck parked at the stop and can visit multiple customers after a single launch. After completing the delivery mission, the drone must return to the launching truck parked at the origin; (4) The drone's flight time is fixed and constant, and its flight time is not affected by flight speed and cargo capacity; at the same time, loading and unloading time has no effect on the overall situation, and the drone can continue to deliver after replacing the battery or charging on the truck; (5) The truck has sufficient fuel supply for one trip, but it has capacity constraints; (6) The speed of the truck and the drone is constant, and each mileage is measured using Euclidean distance. The two-stage algorithm is an improved K-means algorithm and a variable domain simulated annealing algorithm. In the first stage, the improved K-means algorithm is used to cluster the temporary stops of trucks, the number of customers and customer points in each sub-area; in the second stage, the variable domain simulated annealing algorithm is used to solve the optimal path for trucks and drones under the minimum total cost.

2. A truck-drone collaborative delivery model and two-stage algorithm based on contactless delivery as claimed in claim 1, characterized in that Truck delivery cost F1, drone delivery cost F2. Truck delivery cost F1 and drone delivery cost F2 mainly include their respective fixed costs and unit distance delivery costs, and the calculation formula is: Where d ij represents the distance between truck stops i and j, represents the distance between customer points r and v within truck stop i, N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including stop i, i.e., the drone launch point), C T ,C D They are the fixed costs of using trucks and drones, C vT ,C vD They represent the unit transportation costs of trucks and drones, M represents the set of trucks, and H represents the set of drones. When it is 1, it means that truck m travels from temporary stop i to j, otherwise, it is 0. indicates that UAV h flies from customer point r to customer point v, otherwise, it is 0. To meet the relevant assumptions, the truck and drone paths have corresponding constraints, which are as follows: (1) Each truck departs from the warehouse and returns to the warehouse, and traverses all stops only once, while ensuring that the flow of the truck line remains balanced. The calculation formula is: Where N m represents the set of truck stops (including the starting warehouse 0), M represents the set of trucks, When it is 1, it means that truck m travels from temporary stop i to j, otherwise, it is equal to 0. When it is 1, it means that truck m visits temporary stop i, otherwise, it is 0. (2) Each drone must take off and return at the same temporary stop, and ensure that each customer point in each zone is served only once, maintaining the flow balance of the drone service route. In addition, the cumulative distance of each drone's single flight must be controlled within the range of its maximum endurance, calculated as follows: In the formula Represents a truck stop i The distance between the inner customer points r and v, N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including stop i, i.e., the drone launch point), L D It is represented by the maximum cruising range / maximum flight radius of the drone, H is the set of drones, indicates that UAV h flies from customer point r to customer point v, otherwise, it is 0. (3) The total demand of each temporary stop is equal to the cumulative value of the demand of all customer points in its coverage area. At the same time, the weight of the cargo loaded on each truck must be kept within the maximum load limit, and the total weight of the items that each drone can carry in a single flight must not exceed its maximum load capacity. Using the load balance constraints of trucks and drones, the calculation formula for eliminating sub-loops is: Where N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including the stop i, i.e., the drone launch point), M represents the truck set, H represents the drone set, represents the demand of customer r at truck stop i, q i The demand for truck stop i, Q T , Q D Represent the maximum load of trucks and drones, When it is 1, it means that truck m travels from temporary stop i to j, otherwise, it is equal to 0. indicates that UAV h flies from customer point r to customer point v, otherwise, it is 0.

3. A truck-drone collaborative delivery model and two-stage algorithm based on contactless delivery as claimed in claim 1, characterized in that Time penalty cost F3, the cost incurred when the drone delivery service is not delivered within the time expected by the customer: waiting cost will be incurred when the drone arrives earlier than the customer's time window When arriving later than the customer's time window, a late arrival cost will be incurred The penalty cost is 0 when delivering within the customer's time window, and the calculation formula is: Where N c represents the logistics distribution customer set, H represents the drone set, C1, C2 represent the unit waiting cost and unit delay cost, [a r ,b r ] represents the delivery time window for customer r, a r is the earliest time that customer r expects the goods to be delivered, b r is the latest time that customer r expects the goods to be delivered. Indicates the time when the drone arrives at the customer point. Each truck needs to wait at the stop for the drone to complete the delivery task at the current point and return. Therefore, its waiting time is equivalent to the longest time required for the drone on the truck to complete all deliveries at the stop. For a truck, the time to arrive at each node should not be earlier than the sum of the time it arrived at the previous node, the waiting time at the node, and the driving time from the node to the next node. Correspondingly, the time a drone arrives at any customer point must be no earlier than the time it arrived at the previous customer point, the service time at the customer point, the waiting time, and the flight time from the customer point to the next customer point. Regarding the time relationship, the time the drone arrives at the customer point and the time the truck arrives at the temporary stop need to be coordinated with each other; and both the arrival time of the truck and the arrival time of the drone should be strictly greater than 0. The calculation formula is: Where N c represents the set of logistics distribution customers, N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including the stop i, i.e., the drone launch point), M represents the truck set, H represents the drone set,, When it is 1, it means that truck m travels from temporary stop i to j, otherwise, it is equal to 0. is to indicate that the drone h flies from the customer point r to the customer point v, otherwise, it is 0. When it is 1, it means that truck m visits temporary stop i, otherwise, it is 0. Indicates the time when the truck arrives at the temporary stop. Indicates the time when the drone arrives at the customer point, Represent the waiting time of trucks and drones, Represents the driving or flying time of the truck and the drone, Indicates the delivery time of the drone, represents the customer's service time, and W represents an integer that is always large enough.

4. A truck-drone collaborative delivery model and two-stage algorithm based on contactless delivery as claimed in claim 1, characterized in that Two-stage algorithm. In the first stage, the improved K-Means algorithm is used to cluster the customers in the region. The traditional K-Means clustering algorithm gives a cluster value in advance. The value not only affects the clustering effect, but also may affect the subsequent route planning. In addition, due to the complexity of truck-drone collaborative delivery, after clustering according to the given K value, the distance between some customers and their cluster center exceeds the maximum flight distance of the drone, which makes the established delivery plan unfeasible. Therefore, a custom clustering radius R is added to the traditional K-Means clustering algorithm. The improved K-Means clustering algorithm can adaptively determine the number of clusters. The truck’s stop point is the center point of each clustering category. The clustering radius must not exceed the maximum flight radius of the drone. At the same time, the drone must be able to fly to the customer point in each area. The calculation formula is: In the formula Represents a truck stop i The distance between internal customer points r and v; R represents the clustering radius; N m represents the set of truck stops (including the starting warehouse 0), represents the set of customer points r contained in the truck stop i (including stop i, i.e., the drone launch point), L D Indicates the maximum range / maximum flight radius of the drone. In the second stage, the simulated annealing algorithm with variable neighborhood is used to solve the paths of trucks and drones. The simulated annealing algorithm (SA) is inspired by the thermodynamic annealing process. It starts at a higher initial temperature and follows the Metropolis sampling stability criterion. It randomly searches in the neighborhood structure of the solution space and allows a suboptimal solution that is worse than the current solution to be accepted with a certain probability. In order to further enhance the comprehensiveness and search ability of the algorithm, the variable neighborhood search algorithm (VNS) is combined to more comprehensively explore the solution space by dynamically adjusting the search neighborhood range, thereby improving the efficiency of finding a better solution. First, the neighborhood structure of the solution is generated, and then the greedy algorithm is used to generate the initial feasible solution, which is optimized by the variable neighborhood simulated annealing algorithm (SAVN) to minimize the total cost. The key to the variable neighborhood simulated annealing algorithm (SAVN) is to construct the neighborhood structure of the solution. First, select a subpath r1 of the truck route, p = 1, and randomly generate two tangent points and exchange subpath lengths - cut1, cut2, crosslen. The crosslen length is randomly generated within (1, min (p, length (r1)) to satisfy the exchange length is less than the subpath length. At the same time, for a sub-drone path r2 contained in the region i of the subpath r1, randomly generate cut3 and cut4, which satisfy the exchange length is less than the length of the drone path r2 excluding the endpoints on both sides, n i ={i,cut3,cut4},n d ={n i ,n j , ...} is the neighborhood structure of the feasible solution of the drone path of all partitions contained in the sub-path r1, generating the sub-neighborhood structure n p ={cut1,cut2,crosslen,n d }, let p = p + 1, and loop to generate the neighborhood structure n of this subpath p ={n1,n2,...,n pmax }, the calculation formula is as follows: 1<cut1,cut2<length(r1)-2 cut1+crosslen<length(r1)-2 cut2+crosslen<length(r1)-2 1<cut3,cut4<length(r2)-2 p<length(r1).

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