Truck and unmanned aerial vehicle cooperative distribution method for urban end logistics

Abstract

The invention relates to the technical field of path planning, and discloses an urban end logistics-oriented truck and unmanned aerial vehicle collaborative distribution method, which comprises the steps of constructing a task environment model based on an actual urban distribution environment; respectively acquiring data sets and related parameters of the truck and the unmanned aerial vehicle, and constructing a truck and unmanned aerial vehicle collaborative distribution model when the unmanned aerial vehicle adopts a multi-point distribution mode; according to the task environment model and the truck and unmanned aerial vehicle collaborative distribution model, constructing an initial traffic network diagram composed of client points needing trucks or unmanned aerial vehicles to perform material distribution; an adaptive large-scale neighborhood search algorithm is adopted to carry out iterative optimization on the initial traffic network diagram to obtain an optimal traffic network diagram, and each node in the optimal traffic network diagram is a client point for carrying out distribution according to the optimal collaborative distribution scheme. According to the method, the logistics transportation distribution efficiency of truck and unmanned aerial vehicle cooperative distribution at the urban tail end is further improved.

Description

Technical Field

[0001] The present invention relates to the field of path planning technology, and in particular to a truck and drone collaborative delivery method for urban terminal logistics. Background Art

[0002] The rapid development of e-commerce has accelerated the improvement of logistics distribution methods, and the "last mile" has become the main goal of urban logistics distribution models. The continuous development of drone technology has enabled it to be widely used in various scenarios, such as terminal distribution, cold chain distribution, emergency material distribution, etc. Compared with traditional ground transportation and distribution methods, drones have the advantages of fast delivery speed, low cost and no ground traffic control. However, due to its limited endurance and load capacity, it cannot completely replace traditional transportation tools. For this reason, the truck and drone combined distribution mode has gradually become a new type of logistics distribution mode. Truck and drone combined distribution is mainly divided into three modes: truck and drone collaborative distribution, truck and drone parallel distribution, and truck support drone distribution. For urban terminal logistics distribution, its mission objectives are relatively complex, with the characteristics of many distribution types, small single batches, and high frequency. Therefore, truck and drone collaborative distribution is more suitable for scenarios such as urban terminal logistics distribution and timely distribution. However, existing technologies often simplify the application environment of truck and drone collaborative distribution, ignore customer time windows and transportation situations that may be faced during transportation, and lack consideration of drone service functions in multi-point distribution mode, thereby affecting the efficiency and cost of truck and drone collaborative distribution.

[0003] Therefore, there is an urgent need for technical improvement, namely, to develop a collaborative delivery method for trucks and drones for urban terminal logistics to meet the needs of different customers, complete the task allocation of a large number of customer points within a reasonable time and under a series of constraints, and formulate the optimal delivery routes for trucks and drones, so as to achieve good collaboration between the two. Summary of the invention

[0004] The present invention provides a truck and drone collaborative delivery method for urban terminal logistics, which fully considers the constraints such as road traffic congestion, customer demand time window and regional restrictions in urban logistics scenarios, constructs a truck and drone collaborative delivery model under the drone multi-point delivery mode, and designs an improved adaptive large-scale neighborhood search algorithm for solving it, which further reduces the delivery cost and improves the delivery efficiency, thereby overcoming the problems existing in the existing related technologies.

[0005] The present invention is achieved through the following technical solutions: A truck and drone collaborative delivery method for urban terminal logistics, comprising: Build a task environment model based on the actual urban delivery environment; Obtain the data sets and related parameters of trucks and drones respectively, and build a collaborative delivery model between trucks and drones in a multi-point delivery mode. According to the mission environment model and the truck and drone collaborative delivery model, an initial traffic network diagram consisting of customer points that require trucks or drones for material delivery is constructed; The initial traffic network graph is iteratively optimized by using an adaptive large-scale neighborhood search algorithm to obtain an optimal traffic network graph, wherein each node in the optimal traffic network graph is a customer point to be delivered by the optimal collaborative delivery solution.

[0006] As an optimization, based on the actual urban delivery environment, the specific process of building the task environment model is as follows: Set up a distribution warehouse with both trucks and drones, and identify each customer point where supplies need to be delivered; Based on the demand volume and regional restrictions of each customer point, each customer point is divided into ordinary demand points, overweight demand points, no-fly demand points and no-travel demand points, where: The common demand points are represented as customer points that can be delivered by both trucks and drones; The overweight demand point refers to a customer point whose demand is greater than the maximum load of the drone, that is, a customer point that can only be served by a truck, but the drone can be released or recovered at this customer point; The no-fly demand point refers to a customer point that is not allowed to be served by drones; The prohibited demand points are customer points that are not allowed to be served by trucks.

[0007] As an optimization, the data sets and related parameters of trucks and drones are obtained respectively, and the specific process of constructing a truck and drone collaborative delivery model under the multi-point delivery mode of drones is as follows: Get the truck and drone datasets and their parameters; Establish an objective function with the goal of minimizing the total delivery cost, wherein the total delivery cost includes the truck transportation cost, the drone transportation cost, and the cost of violating the time window constraint; Establish the constraints under the UAV multi-point delivery mode, including visit constraints, truck origin constraints, truck continuity constraints and UAV continuity constraints, truck and UAV sub-loop elimination constraints, time coordination constraints, truck and UAV time constraints, truck and UAV load constraints, truck and UAV no-go and no-fly constraints, and related variable constraints, among which, The visit constraint is to ensure that each customer point can be served by a truck or drone once; The truck origin constraint is to ensure that the truck can start from the distribution warehouse and return to the distribution warehouse after delivering all materials; The truck continuity constraint is that after a truck visits a certain customer point, it must also leave from the customer point; The drone continuity constraint is that after the drone arrives at a certain customer point, it will also leave from the customer point; The truck and drone sub-loop elimination constraints include a truck sub-loop elimination constraint and a sub-loop elimination constraint in a drone delivery multi-customer point mode, respectively. The truck sub-loop elimination constraint is to ensure that the truck satisfies the order of serving multiple customer points when the truck departs from the delivery warehouse without returning to the delivery warehouse; the sub-loop elimination constraint in the drone delivery multi-customer point mode is to ensure that the drone is released from the truck without returning to the truck, and satisfies the order of serving multiple customer points. The time coordination constraint means coordinating the time of separation of the truck and the drone at a certain customer point and the time of convergence at a certain customer point; Make customers point j At the customer point i After that, the delivery is carried out. Depending on the type of customer point, the time constraints of the truck and the drone include: the initial departure time of the truck is 0, the arrival time of the truck at the customer point is 1, and the time of the truck arriving at the customer point is 2. j The time to reach the customer point is not less than i Time plus customer points i service time plus from customer point i To customer point j Travel time, customer points i And customer points j The release point and recovery point of the drone are both when the drone arrives at the customer point j The time to reach the customer point is not less than i time plus from customer point i To customer point j Flight time, customer points i The service point and customer point of the drone j The release point and recovery point of the drone when the drone reaches the customer point j The time to reach the customer point is not less than i Time plus customer points i service time plus from customer point i To customer point j Flight time, customer points i And customer points j When both are the release point and the recovery point of the drone, the drone arrives at the customer point j The single cumulative flight time of the drone is not less than the time it takes to fly from the customer point i To customer point j Flight time, customer points i The service point and customer point of the dronej The release point and recovery point of the drone when the drone arrives at the customer point j The single cumulative flight time is not less than the time from the drone to the customer point i The single cumulative flight time plus the drone’s flight time from the customer point i To customer point j Flight time plus customer points i Service time, drone to customer point i The flight time is no longer than the maximum flight time of the drone; The truck and drone load constraints include truck to customer point j The cumulative load of the truck to the customer point is not less than i The cumulative load plus customer points i The demand, the cumulative load from the truck to the customer point is not greater than the maximum load of the truck, the customer point i It is the release point and recovery point of the drone and the customer point j The service point of the drone is when the drone arrives at the customer point j The cumulative load is not less than the customer point j Demand, customer points i The service point and customer point of the drone j The release point and recovery point of the drone when the drone arrives at the customer point j The cumulative load of the drone to the customer point is not less than i The cumulative load plus customer points i The demand and the cumulative load of the UAV to the customer point shall not exceed the maximum load of the UAV.

[0008] As an optimization, according to the task environment model and the truck and drone collaborative delivery model, the specific process of constructing an initial traffic network diagram consisting of demand points that require trucks or drones for material delivery is as follows: Acquire a connected road that can become a truck path according to the traffic road planning, and insert all the ordinary demand points and overweight demand points into the connected road in a manner with the minimum insertion cost to form the corresponding truck path; For the common demand points in the current truck path that can be served by drones, the cost difference between the common demand points being delivered by trucks or drones is calculated, and the common demand points with the largest cost difference in the truck path are added to the drone path. Then, according to the preset rules, it is determined whether the common demand points can be inserted into the drone path to construct the drone path, and the truck path is updated. Then, this step is repeated until all the common demand points in the original truck path are traversed. Insert all the no-fly demand points into the current truck path in a manner that minimizes the insertion cost, and update the arrival times of all customer points in the truck path and the drone path; All the prohibited demand points are inserted into the current drone path in a manner with the lowest insertion cost, and the arrival times of all customer points on the drone path and all recycling points on the truck path responsible for receiving the drone are updated, so as to finally form the initial traffic network diagram.

[0009] As an optimization, the specific process of obtaining a connected road that can become a truck path according to the traffic road planning, and inserting all the ordinary demand points and overweight demand points into the connected road in a way with the minimum insertion cost to form the corresponding truck path is as follows: Let the initial value of each path of the connecting road be {0, 0}; Let all the common demand points and overweight demand points be elements in the first set; Find the element with the minimum insertion cost and not inserted in the first set, insert the element into the corresponding position in the current path, determine whether the sum of the demand of the customer points in the path exceeds the maximum load of the truck after the element with the minimum insertion cost is inserted into the corresponding position in the path, if not, insert the element with the minimum insertion cost into the path, if exceeded, stop inserting the element with the minimum insertion cost into the path, reconstruct a new path, and then insert the element with the minimum insertion cost into the new path; Then return to the previous step until all elements in the first set are inserted into the corresponding path, and finally a truck path is formed.

[0010] As an optimization, the customer points k Insert customer points on the route i And customer points j The calculation formula of the insertion cost is: ; in, g and f is a random number, where the customer point j The distance to the distribution warehouse is greater than the customer point i Distance to the distribution warehouse, represents the insertion cost, Indicates that the truck is from the customer point i To customer point k The running distance, Indicates that the truck is from the customer point k To customer point j The running distance, Indicates that the truck is from the customer point iTo customer point j running distance.

[0011] As an optimization, the preset rules are: If the customer point to be inserted s The previous customer point or the next customer point is in the constructed drone path, and the customer point is calculated. s The cumulative load of the new drone path after adding the drone path and the cumulative flight time of the drone, if both meet the constraints, then the customer point s Add to the drone path, otherwise abandon the insertion and keep the customer point s In the original truck route, find the next customer point that can be served by the drone; If the customer point to be inserted s If the adjacent previous customer point and the adjacent next customer point of are both in different constructed UAV paths, consider moving the customer point s Combine the two drone paths to form a new drone path, verify the cumulative load and cumulative flight time of the drones in the new drone path, if both meet the constraints, then form a new drone path and remove the two previous independent drone paths, otherwise abandon this insertion and keep the customer point s The position in the truck’s path remains unchanged; If the customer point to be inserted s If the previous customer point and the next customer point do not exist in the constructed drone path, then the customer point s Construct a drone path separately.

[0012] As an optimization, all the no-fly demand points are inserted into the current truck path in a way that minimizes the insertion cost, and the specific process of updating the arrival time of all customer points in the truck path and the drone path is: Let all the no-fly demand points be elements in the second set; Find the element with the minimum insertion cost and not inserted in the second set; Insert the element into the corresponding position of the current truck path, and determine whether the sum of the demand of the customer points in the truck path exceeds the maximum load of the truck after the element with the minimum insertion cost is inserted into the corresponding position of the truck path. If not, insert the no-fly demand point with the minimum insertion cost into the truck path. If it exceeds, stop inserting the no-fly demand point with the minimum insertion cost into the truck path, and then find another truck path for insertion. If there is no truck path that can be inserted in the existing truck path, reconstruct a new truck path, and insert the no-fly demand point with the minimum insertion cost into the new truck path. Then update the arrival time of all customer points in the truck routes and drone routes, and return to the previous step until all the no-fly demand points are inserted; The specific process of inserting all the prohibited demand points into the current drone path in a way that minimizes the insertion cost, and updating the arrival time of all customer points on the drone path and all recycling points on the truck path responsible for receiving the drone is as follows: Let all the prohibited demand points be elements in the third set; Find an element in the third set that has the smallest insertion cost and has not been inserted; Insert the element into the corresponding position of the current drone path, and determine whether the element with the smallest insertion cost exceeds the maximum load of the drone or the cumulative flight time limit of the drone after being inserted into the corresponding position of the drone path. If it does not exceed, insert the prohibited demand point with the smallest insertion cost into the drone path. If it exceeds, stop inserting the prohibited demand point with the smallest insertion cost into the drone path, and then find another drone path for insertion. If for the prohibited demand point k , there is no UAV path that can be inserted in the existing UAV path, then a pair of customer points in a truck path is selected ( i , j ), where customer point i Must be located at the customer's point j Before, and the customer clicks i And customer points j None of them are no-fly demand points, customer points i As the release point of the drone, the customer point j As the drone recovery point, the drone is collected from the customer point i Fly to the prohibited demand point k , after delivery is completed, return to the customer point j , select a pair of truck route customer points with the minimum cost ( i , j ), and the prohibited driving demand point k Construct a new drone path; Then update the arrival time of all customer points on the drone path and all recycling points on the truck path responsible for receiving the drone, and then return to the previous step until all the prohibited demand points are inserted.

[0013] As an optimization, an adaptive large-scale neighborhood search algorithm is used to iteratively optimize the initial traffic network graph, and the specific process of obtaining the optimal traffic network graph is as follows: Designing a destruction operator and a repair operator, wherein the destruction operator refers to a type of function used to destroy the current solution, and the repair operator refers to a type of function used to repair the destroyed solution, wherein the initial weights of the selected types of the destruction operators are the same, and the initial weights of the selected types of the repair operators are the same; The type of destruction operator to be used is determined according to the roulette criterion. In each iteration, the truck selects an operator from the destruction operators related to the truck for destruction, and the drone selects an operator from the destruction operators related to the drone for destruction. The type of repair operator to be used is determined according to the roulette criterion, thereby constructing a new solution. In each iteration, the truck selects an operator from the repair operators related to the truck for repair, and the drone selects an operator from the repair operators related to the drone for repair; Different weights are assigned to operators according to the quality of the updated solution after each iteration. If the solution generated during the iteration is the current global optimal solution, the weights of the destruction operator and the repair operator corresponding to the iteration are added with the score ; If the solution generated in the current iteration is not the current global optimal solution, but is better than the current solution and is not accepted by the simulated annealing acceptance criterion, then the weights of the destruction operator and the repair operator corresponding to the current iteration are added with the score ; If the solution generated in the current iteration is not the current global optimal solution, and is worse than the current solution but can meet the simulated annealing acceptance criteria, then the weights of the destruction operator and the repair operator corresponding to the current iteration are added to the score ; If the solution generated during the iteration is not the current global optimal solution, and is worse than the current solution and does not meet the simulated annealing acceptance criteria, then the weights of the destruction operator and the repair operator corresponding to the iteration are added to the score , where the score , , , The sizes of are decreasing in sequence; After one iteration cycle, the weights of all the destruction operators and repair operators are updated, and the scores and selection times of all the destruction operators and repair operators are initialized; The second step to the fifth step are repeated until the global optimal solution converges or the set maximum number of iterations is reached, and the global optimal solution is output as the optimal traffic network diagram.

[0014] As an optimization, the destruction operators include a drone random destruction operator, a truck random destruction operator, a drone maximum cost saving destruction operator, a truck maximum cost saving destruction operator, and a drone path destruction operator, wherein, The drone random destruction operator is: Randomly remove from the currently constructed drone path customer points, and store the removed customer points in the drone's removed node list, where represents the percentage of drone customer points removed, Indicates the number of customer points served by drones in all current drone paths; The truck random damage operator is: Randomly remove from the currently constructed truck route customer points, but does not include the release point and recovery point of the drone, and stores the removed customer points in the truck's removed node list, where represents the percentage of truck customer points removed, Indicates the number of customer points served by trucks in all current truck routes released; The maximum cost saving destruction operator of the drone is: For each drone path, remove the customer point that can maximize the cost change from the drone path each time until each path removes The removed customer points are stored in the drone's removed node list. If there is only one customer point in the current drone path, the drone path is removed. represents the percentage of drone customer points removed, Indicates the number of customer points served by the drone in the current drone path; The maximum cost saving destruction operator of the truck is: For each truck path, remove the customer point that will maximize the cost change from the truck path each time until each path removes The removed customer points do not include the customer points involved in the release point and the recovery point of the drone, and the removed customer points are stored in the truck's removed node list, where represents the percentage of truck customer points removed, Indicates the number of customer points served by a truck in the current truck route; The drone path destruction operator is: Randomly remove the currently constructed drone path Paths are created, and the customer points in the removed paths are stored in the drone's removed node list. The removed customer points include the drone's release point and recovery point, where represents the percentage of drone path removal, Indicates the number of drone paths currently constructed, at each release; The repair operators include a drone random repair operator, a truck random repair operator, a drone greedy repair operator, a truck greedy repair operator, a drone regret value repair operator and a truck regret value repair operator, wherein: The drone random repair operator is: The customer points in the removed node list of the drone are randomly inserted into the currently constructed drone path. If the insertion of the customer point causes the drone path to exceed the maximum load capacity of the drone or the maximum endurance flight time of the drone, the insertion is prohibited, and a new drone path is searched for insertion. If any drone path cannot complete the insertion operation of the customer point, the customer point is inserted into an empty path to construct a new drone path, and this process is repeated until all customer points in the removed node list of the drone are reinserted into the currently constructed drone path. The truck random repair operator is: Determine the type of the customer point in the truck removed node list, and randomly insert the customer point in the truck removed node list into the currently constructed path according to the type of the customer point, wherein, If the customer point in the list of nodes removed by the truck is a common demand point, the customer point is randomly inserted into a path in the currently constructed truck path or drone path. If the insertion of the customer point causes the path to exceed the maximum load of the truck, the maximum load of the drone, or the maximum endurance flight time of the drone, the insertion is prohibited and a new path is searched for insertion. If any path cannot complete the insertion operation of the customer point, the customer point is inserted into the empty path to construct a new truck path. If the customer point in the removed node list of the truck is an overweight demand point or a no-fly demand point, the customer point is randomly inserted into the currently constructed truck path. If the insertion of the customer point causes the path to exceed the maximum load of the truck, the insertion is prohibited and a new path is searched for insertion. If any truck path cannot complete the insertion operation of the customer point, the customer point is inserted into an empty path to construct a new truck path. This process is repeated until all customer points in the node list where the truck is removed are reinserted into the currently constructed path; The greedy repair operator of the drone is: Based on the principle of minimum insertion cost, the customer points in the removed node list of the drone are inserted into the currently constructed drone path. If the insertion of the customer point into the drone path causes the drone path to exceed the maximum load capacity of the drone or the maximum endurance flight time of the drone, the insertion is prohibited, and a new drone path is found for insertion. If any drone path cannot complete the insertion operation of the customer point, a new drone path with the lowest cost is constructed for the customer point, and this process is repeated until all customer points in the removed node list of the drone are reinserted into the currently constructed drone path. The truck greedy repair operator is: Determine the type of the customer points in the truck removed node list, and insert the customer points in the truck removed node list into the currently constructed path according to the type of the customer points based on the principle of minimum insertion cost; If the customer point to be inserted is a common demand point, the optimal insertion position is found in the currently constructed truck path or drone path based on the principle of minimum insertion cost. If the insertion of the customer point causes the path to exceed the maximum load of the truck, the maximum load of the drone, or the maximum endurance flight time of the drone, the insertion of the path is prohibited, and the optimal insertion position is re-searched in other paths. If any path cannot complete the insertion operation of the customer point, the cost of adding the customer point to the empty path of the truck or the empty path of the drone is calculated respectively, and the empty path with the smaller cost is selected to insert the customer point; If the customer point to be inserted is a no-fly demand point or an overweight demand point, the optimal insertion position is found in the currently constructed truck route based on the principle of minimum insertion cost. If the insertion of the customer point causes the route to exceed the maximum load of the truck, the insertion of the route is prohibited, and the optimal insertion position is re-searched in other routes. If any truck route cannot complete the insertion operation of the customer point, a new truck route with the lowest cost is constructed for the customer point. This process is repeated until all customer points in the node list where the truck is removed are reinserted into the currently constructed path; The drone regret value repair operator is: Calculate the difference between the objective function value when each customer point in the drone removed list is inserted into the suboptimal position in all the drone paths currently constructed and the objective function value when it is at the optimal position, let the value of the difference be the regret value of each customer point, select the customer point with the largest regret value, and insert the customer point into its corresponding optimal position, wherein the optimal position refers to the customer point insertion position in the path that makes the total delivery cost the lowest under the current situation, and the suboptimal position refers to the customer point insertion position in the path that makes the total delivery cost the second lowest under the current situation. If any drone path cannot complete the insertion operation of the customer point, then construct a new drone path with the lowest cost for the customer point, and repeat this process until all customer points in the drone removed node list are reinserted into the currently constructed drone path; The truck regret value repair operator is: Determine the type of customer points in the truck removed node list. If the customer points in the truck removed node list are ordinary demand points, calculate the regret value of each customer point in the truck removed node list inserted into all currently constructed drone paths and truck paths, select the customer point with the largest regret value, and insert the customer point into its corresponding optimal position; if the customer point to be inserted is a no-fly demand point or an overweight demand point, calculate the regret value of each customer point in the truck removed node list inserted into all currently constructed truck paths, select the customer point with the largest regret value, and insert the customer point into its corresponding optimal position; if any path cannot complete the insertion operation of the customer point, construct a new truck path with the lowest cost for the customer point, and repeat this process until all customer points in the truck removed node list are reinserted into the currently constructed path.

[0015] Compared with the prior art, the present invention has the following advantages and beneficial effects: Through the above improvements, the efficiency of coordinated delivery of trucks and drones in urban terminal logistics transportation and delivery has been further improved, the cost of logistics distribution has been reduced, and its adaptability in complex urban environments has been optimized.

[0016] 1. In view of the problem that customer time windows and transportation conditions were not fully considered in the constraints of the collaborative delivery model of trucks and drones in previous studies, the present invention further adds the influence of constraints such as customer demand heterogeneity, regional restrictions, traffic congestion and customer time windows into the constraints of the model, and then optimizes the paths of trucks and drones under this multi-constraint scenario.

[0017] 2. In view of the previous studies on the coordinated delivery of trucks and drones for drone path planning, most of them studied the situation where a truck was equipped with one or more drones for delivery, and most drones only require a single delivery to serve one customer demand point. The present invention considers the multi-point delivery mode of drones, and does not require the drone to return to the original truck stop point. Compared with the single-point delivery mode of drones, the delivery cost is optimized by an average of more than 6.77%, and the highest optimization can reach 18.46%, which fully proves that multiple drone deliveries to multiple customer points can effectively utilize the carrying capacity of drones.

[0018] 3. The present invention uses an improved adaptive large neighborhood search algorithm (ALNS) to solve the constructed mixed integer programming model. Compared with the traditional large-scale neighborhood search algorithm (LNS), the distribution cost is optimized by an average of more than 7.64%, and the highest optimization can reach 18.64%, which further verifies the feasibility and effectiveness of the model and algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, constitute a part of this application, and do not constitute a limitation of the embodiments of the present invention. In the drawings: Figure 1 It is a flow chart of the truck and drone collaborative delivery method for urban terminal logistics of the present invention; Figure 2 It is a design diagram of the adaptive mechanism in the adaptive large-scale neighborhood search algorithm of the present invention; Figure 3 The truck and drone collaborative delivery environment roadmap of the present invention; Figure 4 This is a diagram illustrating the construction of the drone path of the present invention; Figure 5 This is a comparison result diagram of the R101 data set in the single-point and multi-point delivery modes of the drone according to an embodiment of the present invention; Figure 6 This is a comparison result diagram of the R102 data set in the single-point and multi-point delivery modes of the drone according to an embodiment of the present invention; Figure 7 This is a comparison result diagram of the R103 data set in the single-point and multi-point delivery modes of the drone according to an embodiment of the present invention; Figure 8 This is a comparison result diagram of the R104 data set in the single-point and multi-point delivery modes of the drone according to an embodiment of the present invention; Fig. 9 This is a comparison result diagram of the R105 data set in the single-point and multi-point delivery modes of the drone according to an embodiment of the present invention; Fig.10This is a comparison result diagram of the R106 data set in the single-point and multi-point delivery modes of the drone according to an embodiment of the present invention; Fig.11 This is a graph comparing the average delivery costs of drones at different speeds in the R101 dataset in an embodiment of the present invention; Fig.12 This is a comparison diagram of the delivery cost of the drone with a load of 10 kg in the R101 data set in an embodiment of the present invention; Fig.13 This is a comparison result diagram of the delivery cost of the UAV with a payload of 20 kg in the R101 data set in an embodiment of the present invention; Fig.14 This is a comparison diagram of the delivery cost of the UAV with a payload of 30 kg in the R101 data set in an embodiment of the present invention. DETAILED DESCRIPTION

[0020] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description are only used to explain the present invention and are not intended to limit the present invention.

[0021] At present, in terms of logistics and transportation technology, there are the following existing technologies: Prior art 1: In order to solve the distribution difficulty of the "last mile" of rural e-commerce logistics, Xiao Jianhua and others introduced the truck-UAV collaborative distribution model, and constructed a rural e-commerce "last mile" joint distribution optimization model based on trucks and drones with the goal of minimizing the distribution cost. In view of the NP-hard nature of the model, they designed a "dynamic" destruction strategy and a "parallel" repair strategy, and proposed an improved large-domain search algorithm to solve the model.

[0022] Disadvantages of prior art 1: The application scenario research of this technology for the truck and drone combination delivery mode is set in some scenes with vast areas and relatively simple environments such as rural areas. The urban logistics distribution environment is characterized by high complexity, high density and large traffic, which is completely different from the rural logistics distribution environment. This technology does not consider the impact of regional restrictions in urban logistics scenarios, and lacks consideration of customer time windows and traffic congestion, which is somewhat different from the actual delivery scenario.

[0023] Prior art 2: Murray and Chu first proposed the theory of joint delivery by trucks and drones, and established a flying partner traveling salesman problem model for the collaborative delivery problem of a truck carrying a drone. In this model, it is stipulated that the drone can only deliver to one customer demand point at a time, and the truck can only release one drone at a time at a demand node. For this model, they took the minimum delivery time as the goal, constructed a mixed integer programming model and designed a simple heuristic algorithm, which can successfully solve small-scale problems.

[0024] Disadvantages of the second prior art: This technology only studies the situation where a truck carries a drone for delivery, and stipulates that a drone can only serve one customer demand point for a single delivery. It does not fully utilize the drone's carrying capacity, and there is a considerable waste of transportation capacity. Urban terminal logistics distribution presents the characteristics of many distribution nodes, wide distribution of service objects, and complex and intertwined distribution routes. The implementation of drone single-point delivery cannot meet the needs of urban terminal logistics distribution. The use of a simple heuristic algorithm to solve the mixed integer programming model makes the algorithm's search range in the solution space too small and cannot solve large-scale problems.

[0025] In response to the above-mentioned problems existing in the prior art, this embodiment provides a truck and drone collaborative delivery method for urban terminal logistics.

[0026] Before introducing the specific technical solutions, the abbreviations and key terms are defined in advance: Truck and drone collaborative delivery mode. In this delivery method, a vehicle can carry one or more drones to deliver materials from the warehouse to demand points that need delivery services. When the vehicle arrives at a certain demand point, it can dispatch drones to serve the surrounding demand points that can be served by drones. The vehicle can either wait for the drone to return or go to the next delivery demand point to recover the drone. After the drone is recovered by the truck, it will decide whether to dispatch it again for delivery based on actual needs. The truck driver can replace the battery of the drone and load the goods in order to arrange the drone for the next delivery service. After all demand points have been delivered, the truck will return to the distribution warehouse with the drone.

[0027] Adaptive Large Neighborhood Search (ALNS) is a meta-heuristic algorithm that is mainly used to solve combinatorial optimization problems. The core idea is to destroy solutions, repair solutions, dynamically adjust weights and select. The algorithm combines local search and destroy-repair strategies. According to the historical performance of operators, the roulette criterion is used to dynamically select different destroy and repair operators to explore the solution space. The simulated annealing acceptance criterion is used to accept the algorithm solution to jump out of the local optimal solution and find a high-quality solution.

[0028] Some symbols are used in the present invention, which are explained as shown in Table 1.

[0029] Table 1 Symbol definitions and descriptions

[0030]

[0031] Table 1

[0032] Next, the method of the present invention is specifically introduced. Figure 1 As shown, it mainly includes the following steps: S1. Build a task environment model based on the actual urban delivery environment.

[0033] In some embodiments, the specific process of S1 is: S11. Set up a distribution warehouse with both trucks and drones to identify each customer point where material delivery is required; S12: Based on the demand volume and regional restrictions of each customer point, each customer point is divided into a normal demand point, an overweight demand point, a no-fly demand point and a no-travel demand point, wherein: The common demand points are represented as customer points that can be delivered by both trucks and drones; The overweight demand point refers to a customer point whose demand is greater than the maximum load of the drone, that is, a customer point that can only be served by a truck, but the drone can be released or recovered at this customer point; The no-fly demand point refers to a customer point that is not allowed to be served by drones; The prohibited demand points are customer points that are not allowed to be served by trucks.

[0034] S2. Obtain the data sets and related parameters of trucks and drones respectively, and build a collaborative delivery model between trucks and drones in a multi-point delivery mode.

[0035] In some embodiments, the specific process of S2 is: S21, obtaining data sets of trucks and drones and relevant parameters of trucks and drones; S22. Establish a truck and drone collaborative delivery model with the lowest total delivery cost as the objective function. The goal is to minimize the total delivery cost while considering the customer's time window. The cost mainly includes three parts: truck transportation cost, drone transportation cost and the cost of violating the time window constraint.

[0036] The objective function is shown in formula (1): ; (1) S23. Establish constraints under the drone multi-point delivery mode, including visit constraints, truck origin constraints, truck continuity constraints and drone continuity constraints, truck and drone sub-loop elimination constraints, time coordination constraints, truck and drone time constraints, truck and drone load constraints, truck and drone no-go and no-fly constraints, and related variable constraints, where: The access constraints are: ; (2) Formula (2) ensures that each customer point can be served once by a truck or drone.

[0037] The truck origin constraint is: ; (3)

[0038] ; (4) Among them, formulas (3) and (4) ensure that the truck can depart from the distribution warehouse and return to the distribution warehouse after delivering all materials.

[0039] The truck coherence constraint and the drone coherence constraint are: ; (5) ; (6)

[0040] Among them, formula (5) represents the truck continuity constraint, that is, after a truck visits a customer point, it must also leave from that customer point. Formula (6) represents the drone continuity constraint, that is, the drone arrives at the customer point. j You will then leave from this customer point.

[0041] The truck and drone sub-loop elimination constraints include truck sub-loop elimination constraints and drone delivery sub-loop elimination constraints in a multi-customer point mode, respectively; That is the following formula: ; (7) ; (8) Among them, formula (7) represents the truck sub-loop elimination constraint, that is, to ensure that the truck departs from the distribution warehouse and does not return to the distribution warehouse, and the order of service for multiple customer points is met. If the constraint is met, no sub-loop will be formed. Formula (8) represents the sub-loop elimination constraint in the drone delivery multi-customer point mode, that is, to ensure that the drone is released from the truck and does not return to the truck, and the order of service for multiple customer points is met. If the constraint is met, no sub-loop will be formed.

[0042] The time coordination constraint means that the time for the truck and the drone to separate at a certain customer point and to meet at a certain customer point should be coordinated; that is, the following formula: ; (9) ; (10) ; (11) ; (12) In the actual delivery process, there may be differences in the time it takes for the truck and the drone to arrive at a certain customer point, that is, the truck may arrive first or the drone may arrive first, and then the two will wait for each other. In order to facilitate the calculation of the time to reach each subsequent customer point, Formula (9) to Formula (12) coordinate the time when the truck and the drone separate at a certain customer point and meet at a certain demand point.

[0043] Make customers point j At the customer point i After that, the delivery is carried out. Depending on the type of customer point, the time constraints of the truck and the drone include: the initial departure time of the truck is 0, the arrival time of the truck at the customer point is 1, and the time of the truck arriving at the customer point is 2. j The time to reach the customer point is not less than i Time plus customer points i service time plus from customer point i To customer point j Travel time, customer points i And customer points j The release point and recovery point of the drone are both when the drone arrives at the customer point j The time to reach the customer point is not less than i time plus from customer point i To customer point j Flight time, when the customer points i The service point and customer point of the drone j The release point and recovery point of the drone when the drone reaches the customer point j The time to reach the customer point is not less than i Time plus customer points iservice time plus from customer point i To customer point j Flight time, when the customer points i And customer points j When both are the release point and the recovery point of the drone, the drone arrives at the customer point j The single cumulative flight time of the drone is not less than the time it takes to fly from the customer point i To customer point j Flight time, when the customer points i The service point and customer point of the drone j It is the release point and recovery point of the drone. j The single cumulative flight time is not less than the time from the drone to the customer point i The single cumulative flight time plus the drone’s flight time from the customer point i To customer point j Flight time plus customer points i Service time, drone to customer point i The flight time is no longer than the maximum flight time of the drone; That is the following formula: ; (13) ; (14) ; (15) ; (16) ; (17) ; (18) ; (19) The time constraints of the truck are formula (13) and formula (14). Formula (13) indicates that the initial departure time of the truck is 0, and formula (14) indicates that the truck arrives at the customer point j The time to reach the customer point is not less than i Time plus customer points i service time plus from customer point i To customer point j The travel time of a customer is i And customer points j When both are the release point and the recovery point of the drone, the drone arrives at the customer point j The time to reach the customer point is not less than i time plus from customer point i To customer point j The flight time. Formula (16) indicates that when the customer points i The service point and customer point of the dronej The release point and recovery point of the drone, when the drone arrives at the customer point j The time to reach the customer point is not less than i Time plus customer points i service time plus from customer point i To customer point j The flight time. Formula (17) indicates that when the customer points i And customer points j When both are the release point and the recovery point of the drone, the drone arrives at the customer point j The single cumulative flight time of the drone is not less than the time it takes to fly from the customer point i To customer point j The flight time. Formula (18) indicates that when the customer points i The service point and customer point of the drone j When the drone arrives at the customer point, j The single cumulative flight time is not less than the time from the drone to the customer point i The single cumulative flight time plus the drone’s flight time from the customer point i To customer point j Flight time plus customer points i The service time of the drone to the customer point is expressed in Formula (19). i The flight time is not greater than the maximum flight time of the drone.

[0044] The truck and drone load constraints are: ; (20) ;(twenty one) ;(twenty two) ;(twenty three) ;(twenty four) Among them, formula (20) and formula (21) are the truck load constraints. Formula (20) represents the truck to customer point j The cumulative load of the truck to the customer point is not less than i The cumulative load plus customer points i Formula (21) indicates that the cumulative load from the truck to the customer point is not greater than the maximum load of the truck. Formula (22) and Formula (23) indicate the actual load constraints of the drone during a single flight. Formula (22) indicates that when the customer point i It is the release point and recovery point of the drone and the customer point j When the drone is at the customer's point of service, j The cumulative load is not less than the customer point jThe demand for i The service point and customer point of the drone j When the drone arrives at the customer point, j The cumulative load of the drone to the customer point is not less than i The cumulative load plus customer points i Formula (24) represents the maximum load constraint of the UAV, that is, the cumulative load from the UAV to the customer point is not greater than the maximum load of the UAV.

[0045] The restrictions on the prohibition of driving and flying of trucks and drones are as follows: ; (25) ; (26) Among them, formula (25) represents the no-go demand points that cannot be served by trucks, and formula (26) represents the no-fly demand points that cannot be served by drones.

[0046] The variable constraints are: ; (27) ; (28)

[0047] Among them, formula (27) indicates that the decision variable is a 0-1 variable, and formula (28) indicates that other variables are continuous variables.

[0048] S3. According to the task environment model and the truck and drone collaborative delivery model, an initial traffic network diagram consisting of customer points that require trucks or drones for material delivery is constructed.

[0049] The specific process of S3 is: S31. Obtain a connected road that can become a truck path according to traffic road planning, and insert all the common demand points and overweight demand points into the connected road in a manner with minimum insertion cost to form the corresponding truck path.

[0050] Here, ordinary demand points and overweight demand points can be understood as non-prohibited demand points on the truck route.

[0051] In this embodiment, the specific process of S31 is: S311, setting the initial value of each path of the connecting roads to {0, 0}.

[0052] It should be noted here that, in the initial value, the first 0 and the second 0 represent the starting point and the end point of the path respectively.

[0053] S312: Let all the common demand points and overweight demand points be elements in the first set.

[0054] S313, find the element with the minimum insertion cost and not inserted in the first set, insert the element into the corresponding position in the current path, judge whether the sum of the demand of the customer points in the path exceeds the maximum load of the truck after the element with the minimum insertion cost is inserted into the corresponding position in the path, if not, insert the element with the minimum insertion cost into the path, if it exceeds, stop inserting the element with the minimum insertion cost into the path, reconstruct a new path, and then insert the element with the minimum insertion cost into the new path. The above process can be summarized as follows: insert all non-prohibited demand points into the truck path. Each time, select the customer point with the minimum insertion cost in the set of demand points to be inserted, insert it into the corresponding position in the path, and the initial value of each path is {0, 0}. It should be noted that when calculating the insertion cost of the truck and drone paths, the distance calculation method of the two is different. When the sum of the demand of the customer points in a path exceeds the maximum load of the truck, stop inserting and reconstruct a new path, and insert the demand points into the new path until all customer points are inserted.

[0055] The calculation will be customer points k Insert customer points on the route i And customer points j The insertion cost between , the insertion cost is calculated as: ; (29) in, g and f is a random number, , the customer point j The distance to the distribution warehouse is greater than the customer point i Distance to the distribution warehouse, represents the insertion cost, Indicates that the truck is from the customer point i To customer point k The running distance, Indicates that the truck is from the customer point k To the demand point j The running distance, Indicates that the truck is from the customer point i To customer point j The customer points here refer to normal demand points and overweight demand points.

[0056] S32. For the common demand points in the current truck path that can be served by drones, calculate the cost difference of the common demand points being delivered by trucks or drones respectively, and add the common demand points with the largest cost difference in the truck path to the drone path. Then, determine whether the common demand points can be inserted into the drone path according to preset rules to construct a drone path, and update the truck path. Then repeat this step until all common demand points in the original truck path are traversed.

[0057] That is, the process is to first insert all non-prohibited demand points into the truck path, and then calculate the cost difference between ordinary demand points served by trucks and those served by drones when constructing the drone path. Each time, the ordinary demand point with the largest cost difference in the path is added to the drone path.

[0058] From the current truck route, calculate the cost difference between the truck service and the drone service for the common demand point that can be served by the drone, that is, calculate the common demand point k The cost difference between truck service and drone service is calculated as follows: ; (30)

[0059] The cost in formula (30) includes the transportation cost of trucks and drones and the cost of violating the time window. Each time, the ordinary demand point with the largest cost difference in the path is added to the drone path, and then all the constructed truck paths are updated. This cycle is repeated until there are no ordinary demand points in the path that can be served by drones.

[0060] There are 3 preset rules in the drone path construction process: Preset rule 1: If the customer point to be inserted s The previous customer point or the next customer point is in the constructed drone path, and the customer point is calculated. s The cumulative load of the new drone path after adding the drone path and the cumulative flight time of the drone, if both meet the constraints, then the customer point s Add to the drone path, otherwise abandon the insertion and keep the customer point s In the original truck route, find the next customer point that can be served by the drone.

[0061] Preset rule 2: If the customer point to be inserted s If the adjacent previous customer point and the adjacent next customer point of are both in different constructed UAV paths, consider moving the customer point sCombine the two drone paths to form a new drone path, verify the cumulative load and cumulative flight time of the drones in the new drone path, if both meet the constraints, then form a new drone path and remove the two previous independent drone paths, otherwise abandon this insertion and keep the customer point s The position in the truck's path remains unchanged.

[0062] Preset rule 3: If the customer point to be inserted s If the previous customer point and the next customer point do not exist in the constructed drone path, then the customer point s Construct a drone path separately.

[0063] Each time a drone path is constructed, the arrival time of each customer point in the current truck path needs to be updated.

[0064] S33: insert all the no-fly demand points into the current truck path in a manner that minimizes the insertion cost, and update the arrival time of all customer points in the truck path and the drone path.

[0065] The specific process of S33 is as follows: S331, setting all the no-fly demand points as elements in the second set; S332, find the element with the minimum insertion cost and not inserted in the second set, insert the element into the corresponding position in the current truck path, determine whether the sum of the demand of the customer points in the truck path exceeds the maximum load of the truck after the element with the minimum insertion cost is inserted into the corresponding position in the truck path, if not, insert the no-fly demand point with the minimum insertion cost into the truck path, if exceeded, stop inserting the no-fly demand point with the minimum insertion cost into the truck path, and then find another truck path for insertion, if there is no truck path that can be inserted in the existing truck path, reconstruct a new truck path, and insert the no-fly demand point with the minimum insertion cost into the new truck path; S333: Update the arrival time of customer points in all truck routes and drone routes, and then return to the previous step (S332) until all the no-fly demand points are inserted.

[0066] That is, based on the path formed by S31 and S32, the no-fly demand point is inserted into the current truck path in a way that minimizes the insertion cost. If the cumulative load of the inserted new path is greater than the maximum load of the truck, the current insertion is abandoned and the next path is found for insertion. If there is no truck path that can be inserted, a new truck path is constructed for the customer point until all the no-fly demand points are inserted. After each customer point is inserted, the arrival time of all customer points in the truck path and the drone path is updated.

[0067] S34. All the prohibited demand points are inserted into the current drone path in a manner that minimizes the insertion cost, and the arrival times of all customer points on the drone path and all recycling points on the truck path responsible for receiving the drone are updated, so as to finally form the initial traffic network diagram.

[0068] The specific process of S34 is as follows: S341, setting all the prohibited driving demand points as elements in the third set; S342: Find the element with the minimum insertion cost and not inserted in the third set, insert the element into the corresponding position in the current drone path, and determine whether the element with the minimum insertion cost exceeds the maximum load of the drone or the cumulative flight time limit of the drone after being inserted into the corresponding position in the drone path. If not, insert the prohibited demand point with the minimum insertion cost into the drone path. If it exceeds, stop inserting the prohibited demand point with the minimum insertion cost into the drone path, and then find another drone path for insertion. If the prohibited demand point k , there is no UAV path that can be inserted in the existing UAV path, then a pair of customer points in a truck path is selected ( i , j ), where customer point i Must be located at the customer's point j Before, and the customer clicks i And customer points j None of them are no-fly demand points, customer points i As the release point of the drone, the customer point j As the drone recovery point, the drone is collected from the customer point i Fly to the prohibited demand point k , after delivery is completed, return to the customer point j , select a pair of truck route customer points with the minimum cost ( i , j ), and the prohibited driving demand point k Construct a new drone path; S343, updating the arrival time of all customer points on the drone path and all recycling points on the truck path responsible for receiving the drone, and then returning to the previous step (S342) until all the prohibited demand points are inserted.

[0069] That is, the prohibited demand point is inserted into the current drone path in a way that minimizes the insertion cost. Similar to S33, if the customer point to be inserted into the current drone path causes the path to exceed the maximum load of the drone or the cumulative flight time limit of the drone, the current insertion operation is abandoned and other paths are searched for for insertion. If all current drone paths cannot insert the customer point, a new drone path with the minimum cost is constructed for the prohibited demand point, and then the prohibited demand point is inserted into the new drone path.

[0070] S4, using an adaptive large-scale neighborhood search algorithm to iteratively optimize the initial traffic network graph to obtain an optimal traffic network graph, wherein each node in the optimal traffic network graph is a customer point to be delivered by the optimal collaborative delivery solution; S41. Design five types of destruction operators, namely, UAV random destruction operator, truck random destruction operator, UAV maximum cost saving destruction operator, truck maximum cost saving destruction operator and UAV path destruction operator. Each type of destruction operator has the same initial weight. The type of destruction operator to be used is determined according to the roulette criterion. In each iteration, the truck selects an operator from the destruction operators related to the truck for destruction, and the UAV selects an operator from the destruction operators related to the UAV for destruction.

[0071] The drone random destruction operator is: Randomly remove from the currently constructed drone path customer points, and store the removed customer points in the drone's removed node list, where represents the percentage of drone customer points removed, Indicates the number of customer points served by drones in all current drone routes.

[0072] The truck random damage operator is: Randomly remove from the currently constructed truck route customer points, but does not include the release point and recovery point of the drone, and stores the removed customer points in the truck's removed node list, where represents the percentage of truck customer points removed, Represents the number of customer points served by the truck in all current truck routes.

[0073] The maximum cost saving destruction operator of the drone is: For each drone path, remove the customer point that can maximize the cost change from the drone path each time until each path removes The removed customer points are stored in the drone's removed node list. If there is only one customer point in the current drone path, the drone path is removed. represents the percentage of drone customer points removed, Indicates the number of customer points served by the drone in the current drone route.

[0074] The maximum cost saving destruction operator of the truck is: For each truck path, remove the customer point that will maximize the cost change from the truck path each time until each path removes The removed customer points do not include the customer points involved in the release point and the recovery point of the drone, and the removed customer points are stored in the truck's removed node list, where represents the percentage of truck customer points removed, Indicates the number of customer points served by the truck in the current truck route.

[0075] The drone path destruction operator is: Randomly remove the currently constructed drone path Paths are created, and the customer points in the removed paths are stored in the drone's removed node list. The removed customer points include the drone's release point and recovery point, where represents the percentage of drone path removal, Indicates the number of drone paths currently constructed. This operator is designed to make up for the fact that the previous truck destruction operator cannot remove the drone release point and recovery point. When the drone path is removed, the customer points that were the original drone release point and recovery point may be removed during the destruction process, thereby promoting the search for new solutions.

[0076] S42. After being destroyed by the destruction operator, six types of repair operators are designed to construct a new solution. The six types of repair operators are: drone random repair operator, truck random repair operator, drone greedy repair operator, truck greedy repair operator, drone regret value repair operator and truck regret value repair operator. The initial weights of each type of repair operator are the same. The type of destruction operator to be used is determined according to the roulette criterion. In each iteration, the truck selects an operator from the repair operators related to the truck for repair, and the drone selects an operator from the repair operators related to the drone for repair.

[0077] The drone random repair operator is: The customer points in the removed node list of the drone are randomly inserted into the currently constructed drone path. If the insertion of the customer point causes the drone path to exceed the maximum load capacity of the drone or the maximum endurance flight time of the drone, the insertion is prohibited and a new drone path is searched for insertion. If any drone path cannot complete the insertion operation of the customer point, the customer point is inserted into an empty path to construct a new drone path, and this process is repeated until all customer points in the removed node list of the drone are reinserted into the currently constructed drone path.

[0078] The truck random repair operator is: Determine the type of the customer points in the truck removed node list, and randomly insert the customer points in the truck removed node list into the currently constructed path according to the type of the customer points; If the customer point in the list of nodes removed by the truck is a common demand point, the customer point is randomly inserted into a path in the currently constructed truck path or drone path. If the insertion of the customer point causes the path to exceed the maximum load of the truck, the maximum load of the drone, or the maximum endurance flight time of the drone, the insertion is prohibited and a new path is searched for insertion. If any path cannot complete the insertion operation of the customer point, the customer point is inserted into the empty path to construct a new truck path. If the customer point in the removed node list of the truck is an overweight demand point or a no-fly demand point, the customer point is randomly inserted into the currently constructed truck path. If the insertion of the customer point causes the path to exceed the maximum load of the truck, the insertion is prohibited and a new path is searched for insertion. If any truck path cannot complete the insertion operation of the customer point, the customer point is inserted into an empty path to construct a new truck path. This process is repeated until all customer points in the node list where the truck is removed are reinserted into the currently constructed path.

[0079] The greedy repair operator of the drone is: Based on the principle of minimum insertion cost, the customer points in the drone's removed node list are inserted into the currently constructed drone path. If the insertion of the customer point into the drone path causes the drone path to exceed the drone's maximum load capacity or the drone's maximum flight time, the insertion is prohibited and a new drone path is sought for insertion. If any drone path cannot complete the insertion operation of the customer point, a new drone path with the lowest cost is constructed for the customer point, and this process is repeated until all customer points in the drone's removed node list are reinserted into the currently constructed drone path.

[0080] The truck greedy repair operator is: Determine the type of the customer points in the truck removed node list, and insert the customer points in the truck removed node list into the currently constructed path according to the type of the customer points based on the principle of minimum insertion cost; If the customer point to be inserted is a common demand point, the optimal insertion position is found in the currently constructed truck path or drone path based on the principle of minimum insertion cost. If the insertion of the customer point causes the path to exceed the maximum load of the truck, the maximum load of the drone, or the maximum endurance flight time of the drone, the insertion of the path is prohibited, and the optimal insertion position is re-searched in other paths. If any path cannot complete the insertion operation of the customer point, the cost of adding the customer point to the empty path of the truck or the empty path of the drone is calculated respectively, and the empty path with the smaller cost is selected to insert the customer point; If the customer point to be inserted is a no-fly demand point or an overweight demand point, the optimal insertion position is found in the currently constructed truck route based on the principle of minimum insertion cost. If the insertion of the customer point causes the route to exceed the maximum load of the truck, the insertion of the route is prohibited, and the optimal insertion position is re-searched in other routes. If any truck route cannot complete the insertion operation of the customer point, a new truck route with the lowest cost is constructed for the customer point. This process is repeated until all customer points in the node list where the truck is removed are reinserted into the currently constructed path.

[0081] The drone regret value repair operator is: Calculate the difference between the objective function value when each customer point in the drone removed list is inserted into the suboptimal position in all the currently constructed drone paths and the objective function value when it is at the optimal position, let the difference be the regret value of each customer point, select the customer point with the largest regret value, and insert the customer point into its corresponding optimal position, wherein the optimal position refers to the customer point insertion position in the path that makes the total delivery cost the lowest under the current situation, and the suboptimal position refers to the customer point insertion position in the path that makes the total delivery cost the second lowest under the current situation. If any drone path cannot complete the insertion operation of the customer point, a new drone path with the lowest cost is constructed for the customer point, and repeat this process until all customer points in the drone removed node list are reinserted into the currently constructed drone path.

[0082] The truck regret value repair operator is: Determine the type of customer points in the truck removed node list. If the customer points in the truck removed node list are ordinary demand points, calculate the regret value of each customer point in the truck removed node list inserted into all currently constructed drone paths and truck paths, select the customer point with the largest regret value, and insert the customer point into its corresponding optimal position; if the customer point to be inserted is a no-fly demand point or an overweight demand point, calculate the regret value of each customer point in the truck removed node list inserted into all currently constructed truck paths, select the customer point with the largest regret value, and insert the customer point into its corresponding optimal position; if any path cannot complete the insertion operation of the customer point, construct a new truck path with the lowest cost for the customer point, and repeat this process until all customer points in the truck removed node list are reinserted into the currently constructed path.

[0083] S43, Adaptive mechanism design. Figure 2 As shown. Different weights are assigned to operators according to the quality of the updated solution after each iteration. If the solution generated during the iteration is the current global optimal solution, the weights of the destruction operator and the repair operator corresponding to the iteration are both added with the score. ; If the solution generated in the current iteration is not the current global optimal solution, but is better than the current solution and is not accepted by the simulated annealing acceptance criterion, then the weights of the destruction operator and the repair operator corresponding to the current iteration are added with the score ; If the solution generated in the current iteration is not the current global optimal solution, and is worse than the current solution but can meet the simulated annealing acceptance criteria, then the weights of the destruction operator and the repair operator corresponding to the current iteration are added to the score ; If the solution generated during the iteration is not the current global optimal solution, and is worse than the current solution and does not meet the simulated annealing acceptance criteria, then the weights of the destruction operator and the repair operator corresponding to the iteration are added to the score , where the score , , , The size of decreases in turn. As for the specific value, it needs to be set according to the actual situation. The simulated annealing acceptance criterion is mainly set to prevent falling into the local optimum. The probability of accepting an inferior solution is ,in, is the cost of the current inferior solution, is the cost of the current optimal solution, and the temperature is change, is the cooling parameter. After each iteration, the weights of all destruction operators and repair operators are updated, and the scores and selection times of all destruction operators and repair operators are initialized. Formula (31) is the weight update formula.

[0084] ; (31) in, Indicates j The operator in the bonus cycle i The weight of is the influencing factor, controlling the speed of weight change. For operator i The score, For operator i The number of times selected.

[0085] The solution here refers to the constructed truck path and drone path, and the global optimal solution is the optimal solution in all iterations so far.

[0086] Next, the method of the present invention is described through specific experimental simulations. Figure 3 and Figure 4 shown.

[0087] In the embodiment of the present invention, the test example in the document "Solomon M M. Algorithms for the vehicle routing and scheduling problems with time window constraints [J]. Operations research, 1987, 35 (2): 254-265" is adapted to meet the needs of the embodiment. The adaptation strategy mainly includes multiplying the coordinates of each customer point by 0.1, the unit is km, and the time window of each customer point is also multiplied by 0.1 and rounded up, the unit is min, and then a simulation experiment analysis is performed based on the adapted test example. The data of the simulation test includes 6 data sets R101, R102, R103, R104, R105 and R106, and 10, 20, 30, 40 and 50 customer points are taken from each data set for simulation test.

[0088] In order to facilitate quantitative analysis, the embodiments of the present invention are based on the following assumptions: (1) The locations and demand of all customer points are known; (2) Drones have load limits and flight time limits; (3) All drones are homogeneous; (4) All customer points delivered by drones meet the drone load constraints; (5) The time required to load supplies and replace batteries is negligible; (6) Drones can serve multiple customer locations in a single delivery; (7) We will not consider the material demand points that cannot be delivered by drones or trucks; (8) The locations for drone release and recovery are all accessible by trucks; (9) The speed of a drone is not affected by the weight of its load, while the speed of a truck is affected by road congestion; (10) The demand of customer points cannot be split.

[0089] The specific sub-steps of step S1 include: S11. Set up a Trucks and The drone will be sent to warehouse D. Deliver materials to each customer point; S12. Set normal demand points, which are customer points that can be served by both trucks and drones. Set overweight demand points, which are customer points whose demand is greater than the maximum load of drones, that is, customer points that can only be served by trucks, but drones can be released or recovered at these points; set no-fly demand points, which are customer points that are not allowed to be served by drones; set no-travel demand points, which are customer points that are not allowed to be served by trucks.

[0090] In the embodiment of the present invention, the road congestion impact parameter is set, and the specific method is as follows: Considering the problem of urban road congestion, trucks cannot always run at the theoretical operating speed when driving on urban roads, so the road congestion impact parameter is introduced. This parameter refers to the road congestion index, which is a conceptual index value that comprehensively reflects the smoothness or congestion of the road network. Formula (32) is the calculation formula for the actual driving speed of trucks on the road.

[0091] ; (32) in, Refers to the theoretical speed of the truck. Refers to trucks passing through the road ( i , j ) section, in order to facilitate calculation, this embodiment sets the parameter between (0, 1), and the smaller the value, the more congested the road. Specific parameter examples are shown in Table 2.

[0092] Table 2 Examples of road congestion impact parameters

[0093] The number 6 indicates a no-fly demand point, so trucks will not go to this customer point for delivery. Therefore, the parameters between this customer point and other customer points are all 0, which means that there is no traffic between the two points.

[0094] Furthermore, the specific sub-steps of step S2 include: S21. Obtain the data set and related parameters of the truck and drone.

[0095] The model parameters related to the truck and the UAV in the embodiment of the present invention are shown in Table 3.

[0096] Table 3 Model parameters

[0097] Then proceed to implement the subsequent steps.

[0098] In S4, the embodiment of the present invention sets the proportion of each type of customer points, and the specific method is: Customer points in the restricted area account for 30% of the total customer points, specifically, no-fly demand points account for 15%, no-travel demand points account for 15%, and customer points in the non-restricted area account for 40% of overweight demand points and 60% of ordinary demand points.

[0099] The embodiment of the present invention sets the relevant parameters of the score addition of each operator in the ALNS algorithm, the percentage of damage degree of trucks and drones, the change ratio of operator weights, and the simulated annealing acceptance criterion. The specific method is: Truck and drone customer point removal percentage and Both are set to 0.4, the percentage of drone path removal Set to 0.4, the weighted scoring of the destruction operator and the repair operator when different solutions are obtained is set to: the score of the new global optimal solution , the score of the solution that is better than the current solution and does not meet the simulated annealing acceptance criteria , the score of the solution obtained that is worse than the current solution but passes the simulated annealing acceptance criterion , the score of the solution obtained that is worse than the current solution and does not pass the simulated annealing acceptance criteria , weight update ratio , set the maximum number of iterations to 100, the number of iterations in the scoring cycle to 20, and adjust the weights of each operator after each scoring cycle, and initialize the scores and selection times of each operator. , is the initial solution cost, the temperature drop parameter .

[0100] The embodiment of the present invention obtains the simulation results of the comparison between the adaptive large neighborhood search (ALNS) algorithm and the large-scale neighborhood search (LNS) algorithm: The traditional LNS algorithm and the ALNS algorithm designed by the present invention are used to solve the truck and drone collaborative delivery model. Each test case is solved 10 times to obtain the optimal value. The specific results are compared in Table 4. The LNS algorithm selects one from the existing destruction operator and repair operator each time, and then destroys and repairs the current solution to obtain a new solution. Based on LNS, ALNS allows multiple destruction and repair operators to be used in the same search to obtain the neighborhood of the current solution.

[0101] Table 4 Simulation comparison between LNS algorithm and ALNS algorithm

[0102] In Table 4, Gap represents the optimization percentage of the objective function value of the ALNS algorithm compared with the objective function value of the LNS algorithm in each case. It can be seen from the table that the ALNS algorithm is significantly better than the LNS algorithm, with the lowest average optimization percentage being 7.64% and the highest optimization percentage being 18.64%.

[0103] The embodiment of the present invention obtains the simulation results of the comparison between the single-point delivery mode and the multi-point delivery mode of the drone: Table 5 Comparison of different delivery modes

[0104] In Table 5, Gap represents the percentage of operating cost savings of the multi-point delivery model compared to the single-point delivery model, where the operating cost includes the delivery cost and the fixed cost of the drone. It can be seen from the table that in the multi-point delivery model, the number of drones used is less than that in the single-point delivery model, because drones can deliver to multiple customer points in a single flight, so even if the same number of customer points are served, the number of drones used is also less. At the same time, it can be found that the average optimization percentage of operating costs of drones using multi-point delivery mode compared to single-point delivery mode is at least 6.77% and can reach up to 18.46%. If the fixed cost of drones increases, it will be better to use drone multi-point delivery mode.

[0105] For easier observation, the operating cost data in the above table is plotted into a bar chart as shown below: Figure 5-Figure 10 As shown, the broken line represents the relationship between the number of drones used in the two delivery modes under different data.

[0106] The embodiment of the present invention performs key parameter sensitivity analysis on the obtained simulation results: Taking R101 as an example, 20 customer points were selected to test the change trend of delivery cost under different drone flight speeds and endurance. The test data results are shown in Table 6. In order to observe the data change trend more intuitively, the delivery cost and average delivery cost under different flight speeds with the same load in Table 6 are plotted into a line graph as shown in the figure below: Figures 11 to 14 shown.

[0107] Table 6 Comparison of different payload, speed and endurance of UAVs

[0108] According to Table 6 and Figures 11 to 14 It can be found that: (1) Under the same drone load capacity, as the drone speed increases, the drone's service range will also increase accordingly, and more customer points will be allocated to drone services, so the delivery cost will first decrease. However, when the drone's service range reaches a threshold, the customer points served by drones and trucks will gradually stabilize, so the delivery cost will remain basically unchanged.

[0109] (2) When the drone's endurance and speed are relatively low, increasing the drone's maximum load capacity will not effectively reduce the delivery cost. This is because the drone's service coverage is relatively small, and more customer points are delivered by trucks. Simply increasing the drone's maximum load capacity will not change the number of customer points served by the drone, so the delivery cost remains basically unchanged. However, when the drone's endurance and speed are gradually increased from a relatively low value, the delivery cost shows a trend of gradually decreasing first and then stabilizing.

[0110] (3) When the speed of the drone is high, even if the current drone's endurance is low, its delivery cost is at a low level. This is because the current drone's service coverage is expanded due to its high speed, and more customer points will be arranged for drone delivery, thereby reducing delivery costs. At the same time, when the speed of the drone is high, the delivery cost remains basically unchanged or is within a smaller fluctuation range as the drone's endurance increases. The reason is that when most customer points are within the drone's service delivery range, the customer points served by trucks and drones will tend to be stable.

[0111] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A truck and drone collaborative delivery method for urban terminal logistics, characterized in that: include: Build a task environment model based on the actual urban delivery environment; Obtain the data sets and related parameters of trucks and drones respectively, and build a collaborative delivery model between trucks and drones in a multi-point delivery mode. According to the mission environment model and the truck and drone collaborative delivery model, an initial traffic network diagram consisting of customer points that require trucks or drones for material delivery is constructed; The initial traffic network graph is iteratively optimized by using an adaptive large-scale neighborhood search algorithm to obtain an optimal traffic network graph, wherein each node in the optimal traffic network graph is a customer point to be delivered by the optimal collaborative delivery solution.

2. The method of truck and drone collaborative delivery for urban terminal logistics according to claim 1 is characterized in that: Based on the actual urban distribution environment, the specific process of building the task environment model is as follows: Set up a distribution warehouse with both trucks and drones, and identify each customer point where supplies need to be delivered; Based on the demand volume and regional restrictions of each customer point, each customer point is divided into ordinary demand points, overweight demand points, no-fly demand points and no-travel demand points, where: The common demand points are represented as customer points that can be delivered by both trucks and drones; The overweight demand point refers to a customer point whose demand is greater than the maximum load of the drone, that is, a customer point that can only be served by a truck, but the drone can be released or recovered at this customer point; The no-fly demand point refers to a customer point that does not allow drone service; The prohibited demand points are customer points that are not allowed to be served by trucks.

3. The method of truck and drone collaborative delivery for urban terminal logistics according to claim 1 is characterized in that: The specific process of obtaining the data sets and related parameters of trucks and drones respectively and constructing a truck and drone collaborative delivery model in which drones adopt a multi-point delivery mode is as follows: Get the data sets of trucks and drones and the relevant parameters of trucks and drones; Establish an objective function with the goal of minimizing the total delivery cost, wherein the total delivery cost includes the truck transportation cost, the drone transportation cost, and the cost of violating the time window constraint; Establish constraints under the drone multi-point delivery mode, including visit constraints, truck origin constraints, truck continuity constraints and drone continuity constraints, truck and drone sub-loop elimination constraints, time coordination constraints, truck and drone time constraints, truck and drone load constraints, truck and drone no-drive and no-fly constraints, and related variable constraints.

4. The method of truck and drone collaborative delivery for urban terminal logistics according to claim 2 is characterized in that: According to the task environment model and the truck and drone collaborative delivery model, the specific process of constructing an initial traffic network diagram consisting of demand points that require trucks or drones for material delivery is as follows: Acquire a connected road that can become a truck path according to the traffic road planning, and insert all the ordinary demand points and overweight demand points into the connected road in a manner with the minimum insertion cost to form the corresponding truck path; For the common demand points in the current truck path that can be served by drones, the cost difference between the common demand points being delivered by trucks or drones is calculated, and the common demand points with the largest cost difference in the truck path are added to the drone path. Then, according to the preset rules, it is determined whether the common demand points can be inserted into the drone path to construct the drone path, and the truck path is updated. Then, this step is repeated until all the common demand points in the original truck path are traversed. Insert all the no-fly demand points into the current truck path in a manner that minimizes the insertion cost, and update the arrival times of all customer points in the truck path and the drone path; All the prohibited demand points are inserted into the current drone path in a manner with the lowest insertion cost, and the arrival times of all customer points on the drone path and all recycling points on the truck path responsible for receiving the drone are updated, so as to finally form the initial traffic network diagram.

5. The method of truck and drone collaborative delivery for urban terminal logistics according to claim 4 is characterized in that: The specific process of obtaining a connecting road that can become a truck path according to traffic road planning, and inserting all the ordinary demand points and overweight demand points into the connecting road in a manner with the minimum insertion cost to form the corresponding truck path is as follows: Let the initial value of each path of the connecting road be {0, 0}; Let all the common demand points and overweight demand points be elements in the first set; Find the element with the minimum insertion cost and not inserted in the first set, insert the element into the corresponding position in the current path, determine whether the sum of the demand of the customer points in the path exceeds the maximum load of the truck after the element with the minimum insertion cost is inserted into the corresponding position in the path, if not, insert the element with the minimum insertion cost into the path, if exceeded, stop inserting the element with the minimum insertion cost into the path, reconstruct a new path, and then insert the element with the minimum insertion cost into the new path; Then return to the previous step until all elements in the first set are inserted into the corresponding path, and finally form a truck path; Among them, the customer points k Insert customer points on the route i And customer points j The calculation formula of the insertion cost is: ； in, g and f is a random number, where the customer point j The distance to the distribution warehouse is greater than the customer point i Distance to the distribution warehouse, represents the insertion cost, Indicates that the truck is from the customer point i To customer point k The running distance, Indicates that the truck is from the customer point k To customer point j The running distance, Indicates that the truck is from the customer point i To customer point j running distance.

6. The method of truck and drone coordinated delivery for urban terminal logistics according to claim 4 is characterized in that: The preset rules are: If the customer point to be inserted s The previous customer point or the next customer point is in the constructed drone path, and the customer point is calculated. s The cumulative load of the new drone path after adding the drone path and the cumulative flight time of the drone, if both meet the constraints, then the customer point s Add to the drone path, otherwise abandon the insertion and keep the customer point s Find the next customer point that can be served by the drone on the original truck route; If the customer point to be inserted s If the adjacent previous customer point and the adjacent next customer point of are both in different constructed UAV paths, consider moving the customer point s Combine the two drone paths to form a new drone path, verify the cumulative load and cumulative flight time of the drones in the new drone path, if both meet the constraints, then form a new drone path and remove the two previous independent drone paths, otherwise abandon this insertion and keep the customer point s The position in the truck’s path remains unchanged; If the customer point to be inserted s If the previous customer point and the next customer point do not exist in the constructed drone path, then the customer point s Construct a drone path separately.

7. The method of truck and drone coordinated delivery for urban terminal logistics according to claim 4 is characterized in that: The specific process of inserting all the no-fly demand points into the current truck path in a way that minimizes the insertion cost, and updating the arrival time of all customer points in the truck path and the drone path is as follows: Let all the no-fly demand points be elements in the second set; Find the element with the smallest insertion cost and not inserted in the second set, insert the element into the corresponding position in the current truck path, and determine whether the sum of the demand of the customer points in the truck path exceeds the maximum load of the truck after the element with the smallest insertion cost is inserted into the corresponding position in the truck path. If not, insert the no-fly demand point with the smallest insertion cost into the truck path. If it exceeds, stop inserting the no-fly demand point with the smallest insertion cost into the truck path, and then find another truck path for insertion. If there is no truck path that can be inserted in the existing truck path, reconstruct a new truck path and insert the no-fly demand point with the smallest insertion cost into the new truck path; then update the arrival time of the customer points in all truck paths and drone paths, and then return to the previous step until all the no-fly demand points are inserted.

8. The method of truck and drone coordinated delivery for urban terminal logistics according to claim 4 is characterized in that: The specific process of inserting all the prohibited demand points into the current drone path in a way that minimizes the insertion cost, and updating the arrival time of all customer points on the drone path and all recycling points on the truck path responsible for receiving the drone is as follows: Let all the prohibited demand points be elements in the third set; Find the element with the minimum insertion cost and not inserted in the third set, insert the element into the corresponding position in the current drone path, and determine whether the element with the minimum insertion cost exceeds the maximum load of the drone or the cumulative flight time limit of the drone after being inserted into the corresponding position in the drone path. If it does not exceed, insert the prohibited demand point with the minimum insertion cost into the drone path. If it exceeds, stop inserting the prohibited demand point with the minimum insertion cost into the drone path, and then find another drone path for insertion. If for the prohibited demand point k , there is no UAV path that can be inserted in the existing UAV path, then a pair of customer points in a truck path is selected ( i , j ), where customer point i Must be located at the customer's point j Before, and the customer clicks i And customer points j None of them are no-fly demand points, customer points i As the release point of the drone, the customer point j As the drone recovery point, the drone is collected from the customer point i Fly to the prohibited demand point k , after delivery is completed, return to the customer point j , select a pair of truck route customer points with the minimum cost ( i , j ), and the prohibited driving demand point k Construct a new drone path; Then update the arrival time of all customer points on the drone path and all recycling points on the truck path responsible for receiving the drone, and then return to the previous step until all the prohibited demand points are inserted.

9. The method of truck and drone collaborative delivery for urban terminal logistics according to claim 1 is characterized in that: The specific process of iteratively optimizing the initial traffic network graph by using an adaptive large-scale neighborhood search algorithm to obtain the optimal traffic network graph is as follows: Designing a destruction operator and a repair operator, wherein the destruction operator refers to a type of function used to destroy the current solution, and the repair operator refers to a type of function used to repair the destroyed solution, wherein the initial weights of the selected types of the destruction operators are the same, and the initial weights of the selected types of the repair operators are the same; The type of destruction operator to be used is determined according to the roulette criterion. In each iteration, the truck selects an operator from the destruction operators related to the truck for destruction, and the drone selects an operator from the destruction operators related to the drone for destruction. The type of repair operator to be used is determined according to the roulette criterion, thereby constructing a new solution. In each iteration, the truck selects an operator from the repair operators related to the truck for repair, and the drone selects an operator from the repair operators related to the drone for repair; Different weights are assigned to operators according to the quality of the updated solution after each iteration. If the solution generated during the iteration is the current global optimal solution, the weights of the destruction operator and the repair operator corresponding to the iteration are added with the score ; If the solution generated in the current iteration is not the current global optimal solution, but is better than the current solution and is not accepted by the simulated annealing acceptance criterion, then the weights of the destruction operator and the repair operator corresponding to the current iteration are added with the score ; If the solution generated in the current iteration is not the current global optimal solution, and is worse than the current solution but can meet the simulated annealing acceptance criteria, then the weights of the destruction operator and the repair operator corresponding to the current iteration are added to the score ; If the solution generated during the iteration is not the current global optimal solution, and is worse than the current solution and does not meet the simulated annealing acceptance criteria, then the weights of the destruction operator and the repair operator corresponding to the iteration are added to the score , where the score , , , The sizes of are decreasing in sequence; After one iteration cycle, the weights of all the destruction operators and repair operators are updated, and the scores and selection times of all the destruction operators and repair operators are initialized; The second step to the fifth step are repeated until the global optimal solution converges or the set maximum number of iterations is reached, and the global optimal solution is output as the optimal traffic network diagram.

10. The method of truck and drone coordinated delivery for urban terminal logistics according to claim 9, characterized in that: The destruction operators include a drone random destruction operator, a truck random destruction operator, a drone maximum cost saving destruction operator, a truck maximum cost saving destruction operator and a drone path destruction operator, wherein: The drone random destruction operator is: Randomly remove from the currently constructed drone path customer points, and store the removed customer points in the drone's removed node list, where represents the percentage of drone customer points removed, Indicates the number of customer points served by drones in all current drone paths; The truck random damage operator is: Randomly remove from the currently constructed truck route customer points, but does not include the release point and recovery point of the drone, and stores the removed customer points in the truck's removed node list, where represents the percentage of truck customer points removed, Indicates the number of customer points served by the truck in all current truck routes; The maximum cost saving destruction operator of the drone is: For each drone path, remove the customer point that can maximize the cost change from the drone path each time until each path removes The removed customer points are stored in the drone's removed node list. If there is only one customer point in the current drone path, the drone path is removed. represents the percentage of drone customer points removed, Indicates the number of customer points served by the drone in the current drone path; The maximum cost saving destruction operator of the truck is: For each truck path, remove the customer point that will maximize the cost change from the truck path each time until each path removes The removed customer points do not include the customer points involved in the release point and the recovery point of the drone, and the removed customer points are stored in the truck's removed node list, where represents the percentage of truck customer points removed, Indicates the number of customer points served by a truck in the current truck route; The drone path destruction operator is: Randomly remove the currently constructed drone path Paths are created, and the customer points in the removed paths are stored in the drone's removed node list. The removed customer points include the drone's release point and recovery point, where represents the percentage of drone path removal, Indicates the number of drone paths currently being constructed.

11. The method of truck and drone coordinated delivery for urban terminal logistics according to claim 9, characterized in that: The repair operators include a drone random repair operator, a truck random repair operator, a drone greedy repair operator, a truck greedy repair operator, a drone regret value repair operator and a truck regret value repair operator, wherein: The drone random repair operator is: The customer points in the removed node list of the drone are randomly inserted into the currently constructed drone path. If the insertion of the customer point causes the drone path to exceed the maximum load capacity of the drone or the maximum endurance flight time of the drone, the insertion is prohibited, and a new drone path is searched for insertion. If any drone path cannot complete the insertion operation of the customer point, the customer point is inserted into an empty path to construct a new drone path, and this process is repeated until all customer points in the removed node list of the drone are reinserted into the currently constructed drone path. The truck random repair operator is: Determine the type of the customer points in the truck removed node list, and randomly insert the customer points in the truck removed node list into the currently constructed path according to the type of the customer points; If the customer point in the list of nodes removed by the truck is a common demand point, the customer point is randomly inserted into a path in the currently constructed truck path or drone path. If the insertion of the customer point causes the path to exceed the maximum load of the truck, the maximum load of the drone, or the maximum endurance flight time of the drone, the insertion is prohibited and a new path is searched for insertion. If any path cannot complete the insertion operation of the customer point, the customer point is inserted into the empty path to construct a new truck path. If the customer point in the removed node list of the truck is an overweight demand point or a no-fly demand point, the customer point is randomly inserted into the currently constructed truck path. If the insertion of the customer point causes the path to exceed the maximum load of the truck, the insertion is prohibited and a new path is searched for insertion. If any truck path cannot complete the insertion operation of the customer point, the customer point is inserted into an empty path to construct a new truck path. This process is repeated until all customer points in the node list where the truck is removed are reinserted into the currently constructed path; The greedy repair operator of the drone is: Based on the principle of minimum insertion cost, the customer points in the removed node list of the drone are inserted into the currently constructed drone path. If the insertion of the customer point into the drone path causes the drone path to exceed the maximum load capacity of the drone or the maximum endurance flight time of the drone, the insertion is prohibited, and a new drone path is found for insertion. If any drone path cannot complete the insertion operation of the customer point, a new drone path with the lowest cost is constructed for the customer point, and this process is repeated until all customer points in the removed node list of the drone are reinserted into the currently constructed drone path. The truck greedy repair operator is: Determine the type of the customer points in the truck removed node list, and insert the customer points in the truck removed node list into the currently constructed path according to the type of the customer points based on the principle of minimum insertion cost; If the customer point to be inserted is a common demand point, the optimal insertion position is found in the currently constructed truck path or drone path based on the principle of minimum insertion cost. If the insertion of the customer point causes the path to exceed the maximum load of the truck, the maximum load of the drone, or the maximum endurance flight time of the drone, the insertion of the path is prohibited, and the optimal insertion position is re-searched in other paths. If any path cannot complete the insertion operation of the customer point, the cost of adding the customer point to the empty path of the truck or the empty path of the drone is calculated respectively, and the empty path with the smaller cost is selected to insert the customer point; If the customer point to be inserted is a no-fly demand point or an overweight demand point, the optimal insertion position is found in the currently constructed truck route based on the principle of minimum insertion cost. If the insertion of the customer point causes the route to exceed the maximum load of the truck, the insertion of the route is prohibited, and the optimal insertion position is re-searched in other routes. If any truck route cannot complete the insertion operation of the customer point, a new truck route with the lowest cost is constructed for the customer point. This process is repeated until all customer points in the node list where the truck is removed are reinserted into the currently constructed path; The drone regret value repair operator is: Calculate the difference between the objective function value when each customer point in the drone removed list is inserted into the suboptimal position in all the drone paths currently constructed and the objective function value when it is at the optimal position, let the difference be the regret value of each customer point, select the customer point with the largest regret value, and insert the customer point into its corresponding optimal position, wherein the optimal position refers to the customer point insertion position in the path that makes the total delivery cost the lowest under the current situation, and the suboptimal position refers to the customer point insertion position in the path that makes the total delivery cost the second lowest under the current situation. If any drone path cannot complete the insertion operation of the customer point, then build a new drone path with the lowest cost for the customer point, and repeat this process until all customer points in the drone removed node list are reinserted into the drone path currently constructed; The truck regret value repair operator is: Determine the type of customer points in the truck removed node list. If the customer points in the truck removed node list are ordinary demand points, calculate the regret value of each customer point in the truck removed node list inserted into all currently constructed drone paths and truck paths, select the customer point with the largest regret value, and insert the customer point into its corresponding optimal position; if the customer point to be inserted is a no-fly demand point or an overweight demand point, calculate the regret value of each customer point in the truck removed node list inserted into all currently constructed truck paths, select the customer point with the largest regret value, and insert the customer point into its corresponding optimal position; if any path cannot complete the insertion operation of the customer point, construct a new truck path with the lowest cost for the customer point, and repeat this process until all customer points in the truck removed node list are reinserted into the currently constructed path.

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