A rural area truck-unmanned aerial vehicle cooperative distribution path optimization method

Abstract

This invention provides a route optimization method for truck-drone collaborative delivery in rural areas. It relates to the field of route planning technology. The method includes: constructing a delivery network comprising delivery centers, ground delivery points, and flight delivery points; dividing customer nodes into multiple delivery clusters; selecting a cluster center for each cluster as the truck's stopping point and the drone's take-off and landing starting point; establishing an integer programming model with the objective of minimizing delivery costs and waiting time costs; solving the integer programming model using a two-layer interactive optimization algorithm; dynamically determining the optimal connection point between the truck's next stopping point and the drone's current path using the golden section method, minimizing the time difference between the truck and the drone reaching that point; and outputting the optimal collaborative delivery route for the truck and drone, including the truck's driving path, the drone's flight path, and the location information of each dynamically connected point.

Description

Technical Field

[0001] This invention relates to the field of route planning technology, and in particular to a route optimization method for truck-drone collaborative delivery in rural areas. Background Technology

[0002] With the development of rural revitalization and the low-altitude economy, drone delivery has become an important way to break through the bottleneck of last-mile logistics in rural areas. However, rural customers are sparsely distributed, the terrain is complex, and the road network is not perfect. Traditional truck delivery is inefficient, and the payload and range of a single drone are limited. Against this backdrop, truck-drone collaborative delivery has become the mainstream solution. By using trucks as mobile base stations to transport drones to suitable locations for release, complementary advantages are achieved, effectively reducing the cost of last-mile delivery.

[0003] Existing methods typically pre-set fixed take-off and landing stations or allow temporary stops at discrete nodes, making it difficult to achieve fine-grained spatiotemporal coordination in continuous rural road networks. This coarse-grained connection mechanism leads to significant waiting times when trucks and drones meet at non-pre-set locations, especially in complex rural road networks where terrain obstacles and poor road connectivity often prevent pre-set stations from covering the optimal meeting point. This results in delivery efficiency losses and energy waste, severely limiting the practical application of collaborative delivery systems in rural last-mile logistics. Summary of the Invention

[0004] Therefore, it is necessary to provide a route optimization method for truck-drone collaborative delivery in rural areas to address the aforementioned technical problems.

[0005] The following technical solution is adopted in this specification: This manual provides a route optimization method for truck-drone collaborative delivery in rural areas, including: Construct a delivery network for the target rural area. The delivery network includes multiple delivery customer nodes, which are divided into several delivery clusters. The cluster center of each delivery cluster serves as the truck parking location and the drone take-off location. A delivery route optimization model is constructed with the goal of minimizing delivery costs and waiting time costs within the delivery network. An improved two-layer interactive optimization algorithm is used to solve the delivery route optimization model, obtaining a truck-drone collaborative delivery route. The improved two-layer interactive optimization algorithm includes outer-layer optimization, inner-layer optimization, and dynamic connection point optimization. During each iteration: The outer layer optimization uses a genetic algorithm to optimize the truck delivery routes in order to determine the order in which trucks stop at the cluster centers; Under the constraint of the order in which trucks stop at each cluster center determined by the outer optimization, the inner optimization uses the dung beetle algorithm to plan the delivery path of the drone from the take-off and landing point of each cluster center to visit all customer nodes in the corresponding delivery cluster. The dynamic connection point optimization uses the truck travel path between adjacent cluster centers determined by the outer layer optimization as the search interval, and divides the initial search interval to generate candidate connection points; obtains the time difference between the time it takes for the truck to travel from the current cluster center to the candidate connection point and the time it takes for the drone to return from the current delivery location to the candidate connection point, and selects the candidate connection point that minimizes the time difference as the optimal dynamic connection point.

[0006] Furthermore, the step of segmenting the initial search interval to generate candidate connection points specifically includes: The truck driving path segment between the adjacent first cluster center and second cluster center determined by the outer layer optimization is used as the search interval; and the search interval is divided based on the golden ratio of 0.618 to generate initial candidate connection points; The first time difference is the difference between the time it takes for the truck to travel from the center of the first cluster to the initial candidate connection point and the time it takes for the drone to return from the current delivery location to the initial candidate connection point. The time difference between the time it takes for the truck to travel from the first cluster center to the second cluster center and the time it takes for the drone to return from the current delivery location to the second cluster center is used as the second time difference; Compare the first time difference with the second time difference, and take the interval with the smaller time difference as the new search interval; Repeat the steps of segmentation, time difference comparison, and interval update until the length of the search interval is less than the preset precision threshold to obtain the optimal dynamic connection point.

[0007] Furthermore, the outer layer optimization is based on a genetic algorithm to optimize the truck delivery routes to determine the order in which trucks stop at each cluster center, specifically including: Step 1. After encoding the order in which trucks visit each cluster center using integer encoding, a genetic population is generated using a combination of random initialization and nearest neighbor heuristics. The genetic population consists of multiple genetic individuals, each representing a truck delivery route: R ={ r 0, r 1, ..., rn},in r 0 is the warehouse delivery start number. r 1~ rn The cluster centers are numbered from the 1st cluster center to the nth cluster center; Step 2. Use the reciprocal of the delivery cost corresponding to the truck delivery route as the fitness function of the improved genetic algorithm, and obtain the fitness value of all genetic individuals in the genetic population according to the fitness function; Step 3. Based on the fitness value, perform selection, crossover, mutation, and local search optimization operations on the genetic population to generate new genetic individuals; Step 4. Obtain the fitness value of the new individual based on the fitness function, and perform dynamic parameter adjustment and population maintenance: If the optimal path does not improve within the first preset iteration number of generations, dynamically increase the mutation probability to the preset target mutation probability value to enhance the search capability; after each preset second iteration number of generations, randomly inject several new genetic individuals into the genetic population to maintain the population's search capability and diversity; at the same time, adopt an elite retention mechanism to retain the genetic individual with the best fitness value in the genetic population to the next generation; Step 5. When the preset termination condition of the improved genetic algorithm is met, output the order in which the trucks stop at the center of each cluster; otherwise, return to Step 2.

[0008] Furthermore, the process of performing selection, crossover, mutation, and local search optimization operations on the genetic population based on fitness values ​​to generate new genetic individuals specifically includes: The selection operation employs an elite roulette wheel strategy, which obtains the selection probability of each genetic individual in the current genetic population based on its fitness value, and then generates new genetic individuals based on the selection probability. in, Indicates genetic individual The probability of choosing; Indicates genetic individual fitness value; This represents the total number of genetic individuals in the current genetic population. In each selection operation, a preset proportion of elite genetic individuals are additionally retained in the genetic population for the next iteration. Elite genetic individuals are those whose selection probability is greater than a preset selection probability threshold. The crossover operation employs an adaptive partial mapping crossover strategy to generate new genetic individuals. This strategy executes the crossover operation with a first crossover probability when the current iteration count of the improved genetic algorithm is within a preset iteration start range, thereby enhancing the diversity and search capability of the genetic population. When the current iteration count of the improved genetic algorithm is within a preset iteration convergence range, the crossover operation is executed with a second crossover probability to maintain the propagation of excellent solutions. The first crossover probability is greater than the second crossover probability. The mutation operation generates a new genetic individual by randomly swapping the two cluster centers in a genetic individual that are not located at the warehouse delivery origin. The local search optimization operation generates new genetic individuals through the 2-opt local search strategy.

[0009] Furthermore, under the constraint of the truck stopping order at each cluster center determined by the outer layer optimization, the inner layer optimization plans the delivery path of the drone from the take-off and landing point of each cluster center to visit all customer nodes within the corresponding delivery cluster using the dung beetle algorithm. Specifically, this includes: Step 1. Randomly initialize the dung beetle population. X ={ x 1, x 2, ..., xn}, x 1~ xn Here, represents the 1st to nth dung beetle individuals, and each dung beetle individual represents a feasible path for a drone's access order; and the maximum number of iterations for the improved dung beetle algorithm is set. Tmax Rolling step size factor α and local search probability ; Step 2. Use the path cost of feasible paths in the drone visit order as the fitness function for the improved dung beetle algorithm: in, and They represent the first The and the first Individual dung beetle; and They represent respectively; Represents an infinite number; This means that if the drone's path exceeds the range or payload constraints, a penalty term is introduced. The penalty term is positive only when the path violates the constraints, and 0 otherwise. This indicates the total flight distance along the current path. Indicates the maximum flight distance; This indicates the total weight of the current delivery task. This represents the total maximum load capacity; Step 3. Simulate the dung beetle's ball-rolling behavior by randomly swapping the positions of two nodes in the path to achieve a global search: in, Indicates the formation of a new path; Indicates the original path, and These represent the original paths. The positions of the two nodes in the text; Represents the commutation operator; if Then accept the new solution. ; Step 4. Simulate dung beetle dance behavior and use the 2-opt algorithm to reverse the path subsequence to achieve local search optimization: Xdance =Re verse ( X , s , t ) in, s and t These represent the selected path subsequences. The position of the ending node in the path; Reverse() represents the reverse operator, which selects a continuous subsequence in the path and reverses its order. If so, then update the path; Step 5. Simulate dung beetle foraging behavior, randomly reconstruct path segments, and update the path using a greedy algorithm: Xf =Re build ( X , k ) in, Indicates the formation of a new path; Indicates the original path, and These represent the original paths. The positions of the two nodes in Re; build () indicates the original path X Randomly select a length of k The fragments are randomly arranged to generate a new path, and the path is updated according to a greedy criterion: if Then accept the new solution. ; Step 6. After foraging, all dung beetles will move. Sort all dung beetles in ascending order of their fitness values, and select the top [number] fitness values ​​to form an elite group for breeding operations. ,in ; Step 7. Simulate dung beetle reproductive behavior and target elite groups. The individual dung beetle in the process or The operator is perturbed to obtain new individuals that form a child set. Replace the worst-fit dung beetle individuals in the current dung beetle population with the generated offspring: in, Indicates the first New dung beetle individuals reproduced in the next iteration; This represents the total number of dung beetle individuals in the current dung beetle population; Step 8: In each iteration, simulate dung beetle rolling, dancing, foraging, and reproductive behaviors to generate a new population and record the current best dung beetle individual. When the best dung beetle individual does not improve for several consecutive generations or reaches the preset maximum number of iterations, terminate the iteration and output the optimal access path for the drone to the customer nodes within the delivery cluster.

[0010] Furthermore, the construction of the delivery route optimization model specifically includes: The optimization objective of the delivery route optimization model is to minimize the delivery cost and waiting time cost within the delivery network. in, This indicates the delivery cost of the truck; This indicates the delivery cost of the drone; This represents the waiting time cost for the truck while waiting for the drone; This refers to the collection of ground delivery points where trucks are responsible for delivery. Indicates that the truck comes from the node To the node Path cost; Indicates that the truck comes from the node To the node The decision variable is set to 1 during delivery and 0 otherwise. This refers to the collection of delivery points where drones are responsible for delivery. Indicates that the drone comes from the node To the node Path cost; Indicates that the drone comes from the node To the node The decision variable is set to 1 during delivery and 0 otherwise. This represents the unit time cost of a truck waiting for a drone; Indicates the truck is at the node Waiting time for the drone; The delivery route optimization model is constrained by truck route-related constraints, drone route-related constraints, drone payload and range constraints, and truck-drone collaboration constraints; among them, Truck routing constraints are used to ensure that trucks depart from and return to the distribution center, traffic balance, that each transfer point is visited only once, and to eliminate sub-loops: in, Indicates that the truck comes from the node Returning to the decision variables of the distribution center, This indicates that the truck departs from the distribution center and heads to the node. Decision variables; Indicates that the truck comes from the node To the node The decision variable is set to 1 during delivery and 0 otherwise. This indicates the node where the truck is accessed. Auxiliary order variables for sequential order; This indicates the node where the truck is accessed. Auxiliary order variables for sequential order; This represents the total number of nodes in the set D of ground delivery points handled by the trucks, excluding the distribution centers. Represents an infinite number; Drone path constraints are used to ensure that all flight delivery points are visited, traffic is balanced, and drones take off only from transit points and land at dynamic connection points: in, and These represent the drones starting from the nodes. j To the node and from node i To the node Decision variables; Indicates that the truck comes from the node To the node Decision variables; and These represent the nodes accessed by the drone. and nodes Auxiliary order variables for sequential order; This represents the total number of nodes in the set of delivery points handled by the drone, excluding the starting point. This indicates that the drone is responsible for delivering goods from the designated delivery point. Represents a set of dynamic connection points; Unmanned aerial vehicle (UAV) payload and range constraints are used to limit the single flight distance from the maximum range and the payload from the maximum payload capacity. in, Indicates drone node To the node The remaining flight range; This indicates the maximum flight distance of a single drone flight; Indicates that the truck comes from the node To the node Euclidean distance; Represents client node Demand; This indicates the maximum payload capacity of the drone; Represents a node from the set D of ground delivery points. Nodes in the set of flight delivery points F Euclidean distance; This indicates the maximum flight distance of a single drone flight; Truck-drone coordination constraints are used to ensure that the drone's takeoff time coincides with the truck's arrival time at the transfer point, and that the time difference between the truck's and the drone's arrival at the dynamic connection point does not exceed a preset threshold. in, and These represent the nodes reached by the drone. and nodes Time; This indicates the average speed of the drone; Indicates that the drone comes from the node To the node Manhattan distance; Indicates at node Service hours; and These represent the nodes where the trucks arrived. and nodes Time; Indicates that the truck comes from the node To the node Euclidean distance; This indicates the average speed of the truck; and These represent the arrival nodes for the truck and the drone, respectively. Time; and These represent the arrival nodes for the truck and the drone, respectively. Time; This indicates the tolerance range for time difference at the connection point.

[0011] Furthermore, the multiple delivery customer nodes are divided into several delivery clusters, specifically including: Initial clustering of multiple delivery customer nodes was performed using the HDBSCAN algorithm; For clusters in the HDBSCAN clustering results where the number of nodes exceeds a preset threshold or the spatial distribution span exceeds the service radius of the drone, the K-means algorithm is used for recursive subdivision until the subdivided clusters meet the preset size constraints, thus obtaining several delivery clusters.

[0012] This specification provides a route optimization device for truck-drone collaborative delivery in rural areas, including: The delivery network modeling module is used to construct the delivery network for the target rural area. The delivery network includes multiple delivery customer nodes, which are divided into several delivery clusters. The cluster center of each delivery cluster serves as the truck parking location and the drone take-off location. The model building module is used to build a delivery route optimization model with the goal of minimizing delivery costs and waiting time costs within the delivery network. The model optimization module is used to solve the delivery route optimization model through an improved two-layer interactive optimization algorithm to obtain the truck-drone collaborative delivery route. The improved two-layer interactive optimization algorithm includes outer-layer optimization, inner-layer optimization, and dynamic connection point optimization. During each iteration: The outer layer optimization uses a genetic algorithm to optimize the truck delivery routes in order to determine the order in which trucks stop at the cluster centers; Under the constraint of the order in which trucks stop at each cluster center determined by the outer optimization, the inner optimization uses the dung beetle algorithm to plan the delivery path of the drone from the take-off and landing point of each cluster center to visit all customer nodes in the corresponding delivery cluster. The dynamic connection point optimization uses the truck travel path between adjacent cluster centers determined by the outer layer optimization as the search interval, and divides the initial search interval to generate candidate connection points; obtains the time difference between the time it takes for the truck to travel from the current cluster center to the candidate connection point and the time it takes for the drone to return from the current delivery location to the candidate connection point, and selects the candidate connection point that minimizes the time difference as the optimal dynamic connection point.

[0013] This specification provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned route optimization method for truck-drone collaborative delivery in rural areas.

[0014] This specification provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-described route optimization method for truck-drone collaborative delivery in rural areas.

[0015] The above-mentioned technical solutions adopted in this specification can achieve the following beneficial effects: This invention uses the actual driving paths of trucks between adjacent cluster centers determined by outer-layer optimization as a continuous search interval. Candidate connection points are dynamically generated, and the driving time of a truck from the current cluster center to a candidate point is matched with the flight time of a drone returning from its delivery location. The point with the smallest time difference is selected as the optimal rendezvous position. This dynamic connection point optimization, combined with outer-layer and inner-layer optimization, forms a closed-loop iteration. In each iteration: the outer-layer genetic algorithm globally optimizes the driving paths of trucks between delivery clusters, the inner-layer dung beetle algorithm finely plans the delivery routes of drones within clusters, and the dynamic connection points are updated according to real-time path status, enabling coordinated optimization of truck inter-cluster paths, drone intra-cluster paths, and connection point positions. This global-local-connection three-dimensional collaborative architecture can dynamically adapt to the characteristics of dispersed customer nodes, complex road networks, and varied terrain in rural areas, avoiding the path adjustment lag caused by fixed connection points, improving the efficiency of collaborative delivery, and preventing energy waste. Attached Figure Description

[0016] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0017] Figure 1 This document provides a flowchart illustrating a route optimization method for truck-drone collaborative delivery in rural areas. Figure 2 This manual provides a static connection diagram of a truck and a drone. Figure 3 This manual provides a schematic diagram of the dynamic connection between a truck and a drone. Figure 4 This is a flowchart illustrating a two-layer interactive algorithm provided in this specification; Figure 5 This document provides a schematic diagram of an HDBSCAN density hierarchical clustering tree. Figure 6A flowchart illustrating an improved clustering algorithm provided in this specification; Figure 7 This is a schematic diagram of a cross-operation provided in this specification; Figure 8 This is a schematic diagram of a mutation operation provided in this specification; Figure 9 A schematic diagram of an improved dung beetle algorithm provided in this specification; Figure 10 This document provides a comparative diagram of the total costs of four algorithms at different scales. Figure 11 This manual provides a schematic diagram of the distribution of customer nodes in Changqingqiao Town, Qingyang City. Figure 12 This is a schematic diagram illustrating a static collaborative delivery result using a truck-drone. Figure 13 This is a schematic diagram illustrating the dynamic collaborative delivery result of a truck and drone, as provided in this specification. Figure 14 This document provides a cost comparison diagram of two collaborative methods. Figure 15 This manual provides a cost comparison diagram of three delivery modes under different driving radii. Figure 16 This specification provides a structural diagram of a route optimization device for truck-drone collaborative delivery in rural areas. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this specification clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in this specification without creative effort are within the scope of protection of this application.

[0019] The technical solution provided by this invention can be applied to route optimization scenarios for truck-drone collaborative delivery in rural areas. Especially against the backdrop of rapid development of the low-altitude economy, drone delivery, as a new mode of transportation, shows great potential in addressing the shortcomings of last-mile logistics in rural areas. With the rapid development of e-commerce, last-mile delivery has gradually become a crucial factor restricting logistics efficiency. Compared to urban areas, rural and remote areas face challenges such as sparse customer distribution, complex road network structures, and high transportation costs. While traditional truck delivery can guarantee a large carrying capacity, it is often inefficient when dealing with scattered and fragmented orders. Drones, with their advantages of high speed, obstacle avoidance, and high mobility, are expected to compensate for the flexibility shortcomings of truck delivery. The truck-drone collaborative delivery model has become an innovative path and is gradually becoming an effective strategy to solve the last-mile dilemma in rural areas. In recent years, dynamic connection strategies have gradually become a research hotspot, aiming to flexibly determine the take-off and landing positions of drones based on real-time status, achieving dynamic route adjustment and efficient collaboration. However, spatiotemporal synchronization and global optimization in large-scale rural environments still present challenges; dynamic connection and real-time optimization are future research directions. Such studies typically pre-define take-off and landing sites for drones in the network or allow temporary parking at non-customer nodes, but they are still insufficient for fine-grained coupling at rendezvous points in continuous road spaces.

[0020] Based on the aforementioned research background, this invention proposes a path planning method that integrates dynamic connection and two-layer interactive optimization for truck-drone collaborative delivery in rural areas. In the outer layer, a genetic algorithm is used to optimize the global delivery path for trucks; in the inner layer, an improved dung beetle optimization algorithm is used to assign intra-cluster task paths to drones, and the golden section method is combined to accurately determine the dynamic connection position between trucks and drones, thereby improving delivery efficiency. Simulations under various scales and distribution scenarios verify the effectiveness of the proposed method in reducing total cost, decreasing waiting time, and improving task completion rate, demonstrating significant advantages over fixed connection modes.

[0021] The following is combined with Figures 1-15 This invention describes a route optimization method for truck-drone collaborative delivery in rural areas.

[0022] Figure 1 This is one of the flowcharts illustrating the route optimization method for truck-drone collaborative delivery in rural areas provided by the present invention, such as... Figure 1 As shown, the method includes the following: S1. Construct a delivery network for the target rural area. The delivery network includes multiple delivery customer nodes, which are divided into several delivery clusters. The cluster center of each delivery cluster serves as the truck parking location and the drone take-off location.

[0023] S2. With the goal of minimizing delivery costs and waiting time costs within the delivery network, construct a delivery route optimization model.

[0024] S3. The delivery path optimization model is solved by an improved two-layer interactive optimization algorithm to obtain the truck-drone collaborative delivery path. The improved two-layer interactive optimization algorithm includes outer layer optimization, inner layer optimization, and dynamic connection point optimization. In each iteration: the outer layer optimization optimizes the truck delivery path based on a genetic algorithm to determine the order in which the trucks stop at each cluster center; the inner layer optimization, under the constraint of the order in which the trucks stop at each cluster center determined by the outer layer optimization, plans the delivery path of the drone from the take-off and landing point of each cluster center to visit all customer nodes in the corresponding delivery cluster using the dung beetle algorithm; the dynamic connection point optimization uses the truck driving path between adjacent cluster centers determined by the outer layer optimization as the search interval, and divides the initial search interval to generate candidate connection points; the time difference between the time it takes for the truck to travel from the current cluster center to the candidate connection point and the time difference between the time it takes for the drone to return from the current delivery location to the candidate connection point is obtained, and the candidate connection point that minimizes the time difference is selected as the optimal dynamic connection point.

[0025] Based on the above Figure 1 The illustrated embodiment, for example, describes the delivery network in step S1 above: Considering the problem of collaborative delivery between drones and trucks in rural areas, in the delivery network G={N,A}, N is the set of nodes and A is the set of arcs. There are three different types of nodes in N, including central warehouse node O, drone delivery point F and transfer point P; drone delivery point F is the customer node to which drones are responsible for delivery, because drones can cross terrain obstacles and shorten delivery time, and are usually used in areas with poor roads; transfer point P is suitable for customer nodes delivered by trucks, and is generally located in areas with good road conditions. In the collaborative delivery mode of trucks and drones in rural areas, the truck is responsible for transporting the drone to the transfer point, and the drone takes off from the transfer point to deliver to customer nodes in areas with poor roads. During this process, the truck does not wait for the drone at the original transfer point, but continues to the next customer node. After completing their respective delivery tasks, they meet on the way. After meeting, the drone immediately changes its battery to ensure the endurance of the drone for the next flight. The assumptions of this problem are as follows: (1) the drone can serve multiple delivery points after takeoff; (2) the maximum load capacity and maximum range of the truck are negligible compared with the maximum load and range limit of the drone; (3) the location and demand of each customer node are known. This invention considers dynamic collaborative delivery between trucks and drones, and requires the study of two scenarios. Figure 2 This specification provides a static connection diagram of a truck and a drone, such as... Figure 2 As shown, after the truck releases the drone at the transfer point, it waits in place. After the drone completes its delivery, it rejoins the truck at the transfer point and heads to the next customer node. Figure 3 This specification provides a schematic diagram of the dynamic connection between a truck and a drone, such as... Figure 3As shown, after the truck releases the drone at the transfer point, both complete their respective delivery tasks and dynamically connect on the way to the next delivery point.

[0026] Based on the above Figure 1 The illustrated embodiment, for example, describes the model construction in step S2 above: For example, based on the different characteristics of trucks and drones, the objective of this invention is to minimize the delivery cost and time cost of the entire system. The objective function can be established as follows: (1) in, This refers to the collection of ground delivery points where trucks are responsible for delivery. m ground delivery points; Indicates that the truck comes from the node To the node Path cost; Indicates that the truck comes from the node To the node The decision variable is set to 1 during delivery and 0 otherwise. This refers to the collection of delivery points where drones are responsible for delivery. Indicates that the drone comes from the node To the node Path cost; Indicates that the drone comes from the node To the node The decision variable is set to 1 during delivery and 0 otherwise. This represents the unit time cost of a truck waiting for a drone; Indicates the truck is at the node Waiting time for the drone.

[0027] For example, the objective function consists of three terms: the first is the delivery cost of the truck, the second is the delivery cost of the drone, and the third is the waiting time cost of the truck waiting for the drone. Based on this problem, the constraints are as follows:

[0028] (1) Truck routing constraints, where constraint (2) indicates that the truck departs from and returns to the distribution center, constraint (3) indicates the truck flow balance constraint, constraint (4) indicates that all truck stops are visited only once, constraints (5) and (6) are for eliminating sub-loops using the MTZ method for trucks, and constraints (7) and (8) are supplementary constraints of the Big M method, used to strengthen the directionality and order validity of the path: in, Indicates that the truck comes from the node Returning to the decision variables of the distribution center, This indicates that the truck departs from the distribution center and heads to the node. Decision variables; Indicates that the truck comes from the node To the node The decision variable is set to 1 during delivery and 0 otherwise. This indicates the node where the truck is accessed. Auxiliary order variables for sequential order; This indicates the node where the truck is accessed. Auxiliary order variables for sequential order; This represents the total number of nodes in the set D of ground delivery points handled by the trucks, excluding the distribution centers. It represents an infinite number.

[0029] (2) UAV path-related constraints, where constraint (9) indicates that all flight delivery points must be visited only once, constraint (10) is the flow balance constraint for UAVs, constraints (11) and (12) indicate that UAVs can only take off from transit points and land at dynamic connection points, and constraints (13) and (14) are the UAV MTZ method sub-loop elimination constraints: in, and These represent the drones starting from the nodes. j To the node and from node i To the node Decision variables; Indicates that the truck comes from the node To the node Decision variables; and These represent the nodes accessed by the drone. and nodes Auxiliary order variables for sequential order; This represents the total number of nodes in the set of delivery points handled by the drone, excluding the starting point. This indicates that drones are responsible for delivering goods to designated delivery points. k flight deliveries; Represents a set of dynamic connection points. There are h connection points.

[0030] (3) Unmanned Aerial Vehicle (UAV) payload and range constraints, where constraint (15) represents the maximum flight distance the UAV can fly after each launch from the truck; constraint (16) represents the constraint that the UAV's remaining flight distance is sufficient to return to the truck. Constraint (17) ensures that the UAV cannot repeatedly access the same client node, and constraint (18) is the single payload limit for the UAV. Constraint (19) is the single range limit for the UAV.

[0031] in, Indicates drone node To the node The remaining flight range; This indicates the maximum flight distance of a single drone flight; Indicates that the truck comes from the node To the node Euclidean distance; Represents client node Demand; This indicates the maximum payload capacity of the drone; Represents a node from the set D of ground delivery points. Nodes in the set of flight delivery points F Euclidean distance; This indicates the maximum flight distance of a single drone flight.

[0032] (4) Truck-Drone Coordination Constraints, where constraint (20) is the truck time progression constraint, ensuring that the truck's arrival time from i to j satisfies the sum of travel and service times. Constraint (21) is the drone time progression constraint, ensuring that the drone's arrival time from i to j satisfies the sum of flight and service times. Constraints (22) and (23) ensure that the drone's takeoff time is consistent with the truck's arrival time at the transfer point. Constraints (24) and (25) ensure that, among all candidate connection points, the time difference between the truck and drone arrival times does not exceed a threshold.

[0033] in, and These represent the nodes reached by the drone. and nodes Time; This indicates the average speed of the drone; Indicates that the drone comes from the node To the node Manhattan distance; Indicates at node Service hours; and These represent the nodes where the trucks arrived. and nodes Time; Indicates that the truck comes from the node To the node Euclidean distance; This indicates the average speed of the truck; and These represent the arrival nodes for the truck and the drone, respectively. Time; and These represent the arrival nodes for the truck and the drone, respectively. Time; This indicates the tolerance range for time difference at the connection point.

[0034] Based on the above Figure 1 The illustrated embodiment, for example, describes the model solving in step S3 above: In the truck-drone path coordination optimization problem, if only the static connection between the truck and the drone at the customer node is considered, and the drone path can be modeled as a TSP problem, the static model can be accurately solved using optimization solvers such as Gurobi to obtain the global optimum. However, after introducing a dynamic connection mechanism, nonlinearity, nested calculations, and complex dynamic synchronization constraints appear in the model, making it difficult to transform the problem into a standard linear programming model and impossible to solve accurately using Gurobi directly. Therefore, this invention designs a two-layer interactive heuristic algorithm. Figure 4 This is a flowchart illustrating a two-layer interactive algorithm provided in this specification, such as... Figure 4 As shown, while the outer genetic algorithm optimizes the truck path, the inner layer introduces an improved dung beetle algorithm and the golden section method to dynamically optimize the UAV path and connection points, thus achieving a solution under complex constraints.

[0035] In truck-drone collaborative delivery systems, the rational division of service areas is a prerequisite for efficient scheduling and route optimization. By constructing a transfer point-cluster point structure, a task division basis is provided for the collaborative route planning model. To this end, this invention introduces a clustering algorithm to preprocess delivery customer nodes. By employing an improved clustering method, geographically adjacent customer nodes are divided into several delivery clusters. Each cluster automatically selects a cluster center point, which not only constitutes a key stop target in the truck route but also forms the starting point for drone route planning.

[0036] Traditional K-means algorithm requires specifying the number of clusters K beforehand, and the choice of K value has a significant impact on the clustering results. Furthermore, the K-means algorithm is highly sensitive to outliers and noise points, easily leading to distorted clustering results. To improve the adaptability of clustering on irregularly distributed customer node sets, this invention proposes an improved clustering method that integrates HDBSCAN and K-means. This method mainly includes the following steps:

[0037] Step 1: Preliminary density clustering based on HDBSCAN. A minimum spanning tree is constructed using the cross-distance, and a density hierarchical clustering tree is generated accordingly, automatically identifying highly stable cluster structures and edge noise points. This process avoids subjective setting of the number of clusters and improves adaptability to complex spatial distributions. The cross-distance between any two points p and q is defined as:

[0038] Where corek(p) represents the distance from point p to its k-th nearest neighbor, reflecting the local density; d(p,q) represents the Euclidean distance between points p and q; and MRD represents the maximum value of the three, used to construct the "inter-distance graph".

[0039] Figure 5This document provides a schematic diagram of an HDBSCAN density-based hierarchical clustering tree, such as... Figure 5 As shown in the figure, each vertical structure represents the survival period of a candidate cluster under different density thresholds λ, and the color represents the cluster's point size. Structures with colored borders are the stable clusters ultimately selected by HDBSCAN, indicating clustering structures that remain stable during density evolution. A total of 10 stable clusters were extracted from the figure; other structures not selected were discarded as noise points due to insufficient point count or instability. This structure diagram effectively demonstrates the advantage of HDBSCAN in automatically extracting the optimal cluster partitioning based on density stability without requiring a preset number of clusters.

[0040] Step 2: K-means recursive intra-cluster subdivision. Although the HDBSCAN algorithm is effective in handling heterogeneous density distributions, it can still lead to uneven point distribution within clusters and affect subsequent path design when there are locally very large clusters. Therefore, the K-Means algorithm is further introduced to subdivide large clusters. After each round of subdivision, the sub-clusters are assigned new cluster numbers, and the original label array is updated, achieving hierarchical cluster partitioning. This recursive subdivision strategy enables dynamic adaptation of clustering, allowing the granularity to be adjusted according to point density and intra-cluster structure, avoiding the formation of excessively large clusters that lead to difficulties in path optimization or excessive scheduling load.

[0041] Step 3: Cluster Center Extraction. To ensure that the subsequent path model can directly call the representative point of each cluster as a transit node, this invention extracts the customer node closest to its geometric center from each cluster as the cluster center. This strategy avoids the geometric center offset problem caused by taking the average and ensures that the extracted point is a valid customer node in the original data.

[0042] This invention combines HDBSCAN's automatic clustering and noise identification capabilities with K-Means' intra-cluster structure optimization capabilities to achieve a hierarchical clustering process from density-driven to structure-controlled. This effectively overcomes the limitations of traditional clustering methods, ensuring that the shape and size of each cluster meet actual requirements while maintaining clustering accuracy and stability. Figure 6 This is a flowchart illustrating an improved clustering algorithm provided in this specification.

[0043] Based on the above Figure 1 The illustrated embodiment, for example, describes the outer truck path optimization algorithm in step S3 above: To optimize the collaborative path optimization model established in this invention, a two-layer interactive optimization algorithm is designed. The outer layer uses a genetic algorithm to optimize the truck delivery path, while the inner layer uses an improved dung beetle algorithm to optimize the drone delivery path. The two algorithms iteratively optimize through information exchange at dynamic connection points, giving full play to the global search capability of the genetic algorithm and the local optimization advantage of the dung beetle algorithm, and gradually approaching the global optimal solution. The GA algorithm and DBO algorithm are nested and interact, and the golden ratio 0.618 rule is introduced to dynamically calculate the optimal meeting point of the truck and drone, so as to achieve synchronous collaborative delivery.

[0044] The outer optimization algorithm uses a genetic algorithm with an improved elite-preserving strategy to determine the optimal path for the truck. The specific implementation steps are as follows: Step 1. Encoding Method and Population Initialization. The truck access order is represented by integer encoding, with individuals defined as R = {r0, r1...rn}, where r0 = 0 represents the starting warehouse, and the rest are cluster center numbers. To improve the initial quality of the population, a combination of random initialization and nearest neighbor heuristics is used to generate the initial population. Random initialization ensures path diversity by randomly shuffling all customer nodes; while the nearest neighbor initialization strategy starts from the starting point and connects sequentially to the nearest unvisited customer node, quickly constructing a feasible path with good local structure, providing excellent guidance for the algorithm. This strategy not only improves the average fitness of the population but also significantly accelerates early convergence. The initial population is generated by setting the population size, maximum number of iterations, selection probability, crossover probability, and mutation probability.

[0045] Step 2. Establish the fitness function. The objective function established in this invention is to minimize the delivery cost. Therefore, its reciprocal is taken as the fitness function to screen the quality of chromosomes in the population.

[0046] Step 3. Genetic Operator Operations. Perform a series of operations such as selection, crossover, and mutation according to the genetic strategy, and calculate the fitness function.

[0047] A. The selection operation adopts an elite roulette strategy, and the selection probability is calculated based on fitness. Individuals with higher fitness have a greater probability of being selected. At the same time, in each selection operation, an additional proportion of elite individuals are reserved to directly enter the next population to ensure that high-quality genes continue to exist in the population. The probability of an individual being selected is proportional to its fitness, and its probability calculation is shown in Equation (27): in, Indicates genetic individual The probability of choosing; Indicates genetic individual fitness value; This represents the total number of genetic individuals in the current genetic population. In each selection operation, a preset proportion of elite genetic individuals are additionally retained in the genetic population for the next iteration step. Elite genetic individuals are those whose selection probability is greater than a preset selection probability threshold.

[0048] B. The crossover operation employs Adaptive Partial Mapping Crossover (A-PMX) to generate new individuals. This strategy automatically increases the crossover probability in the early stages of the genetic algorithm's operation to enhance population diversity and search capability; however, it decreases the crossover probability as the algorithm stabilizes to maintain the stable transmission of excellent solutions. Figure 7 This is a diagram illustrating a cross-operation process provided in this specification, such as... Figure 7 As shown, in the specific crossover process, the fixed warehouse point is used as the starting point. Path segments are randomly selected from the parent individuals for exchange, and the remaining path segments are recombined according to the center order, thereby improving the algorithm's global exploration ability and convergence stability. It selects crossover points from the parent genes, exchanges their order, and generates new offspring individuals. In the crossover process, the fixed warehouse point is used as the starting point, and the order of other cluster centers is exchanged to generate new individuals.

[0049] C. Mutation operations generate new individuals by exchanging values ​​at certain positions in a gene. Mutation operations can enhance the diversity of algorithms and avoid getting trapped in local optima. Figure 8 This is a schematic diagram of a mutation operation provided in this specification, such as... Figure 8 As shown, during the mutation process, the two cluster centers at the non-starting position of the truck path will randomly swap.

[0050] D. Local Search Optimization. To further improve the quality of the solution and the smoothness of the path, a 2-opt local search strategy is applied to the best individual in each generation. Specifically, two edges are randomly selected and swapped. If the path length decreases, the updated solution is retained, effectively avoiding path redundancy.

[0051] E. Dynamic parameter adjustment and population maintenance. To avoid premature convergence, the following strategies are designed: if the optimal path does not improve for 100 consecutive generations, the mutation probability is dynamically increased to 0.2 to enhance the search capability; a small number of new individuals are randomly injected every 50 generations to maintain the population's search capability and diversity; an elite retention mechanism is used to retain a number of the best individuals in each generation to directly enter the next generation.

[0052] The outer layer genetic algorithm continuously optimizes the truck path population and passes each candidate truck path to the inner layer module for fitness evaluation. The inner layer dung beetle algorithm optimizes the drone path and dynamic connection points: for each truck path scheme given by the outer layer, the improved dung beetle algorithm plans the corresponding drone delivery route and dynamic connection points. After each iteration of the outer layer provides a truck path, the improved dung beetle algorithm optimizes the drone path and the dynamic connection point positions.

[0053] Based on the above Figure 1 The illustrated embodiment, for example, describes the inner-layer UAV path planning algorithm in step S3 above: The improved inner-layer dung beetle algorithm aims to complete customer node delivery tasks after the truck launches the drone at the current transfer point. It simulates the global search capability and local development mechanism of the dung beetle during navigation and scrolling, and minimizes and optimizes the flight sequence and path length of the drone. The dung beetle optimization algorithm simulates various behaviors of the dung beetle in the drone path planning to gradually optimize the delivery path of the drone.

[0054] Existing dung beetle algorithms suffer from poor global search and mutation capabilities. To enhance the performance of the DBO algorithm in path optimization problems, this invention employs an improved dung beetle algorithm. This improvement introduces adaptive mutation to adjust the position updates of the dung beetle population and integrates 2-opt local search. It simulates rolling balls using node swapping, dance calibration using path reversal, and foraging behavior using fragment reconstruction, and constructs a composite fitness function by combining path cost and penalty terms. This strategy effectively improves the algorithm's local search capability and feasible solution rate, making it suitable for constrained path optimization scenarios. Figure 9 This document provides a flowchart illustrating an improved dung beetle algorithm. Figure 9 As shown, the specific steps are as follows:

[0055] Step 1. Randomly initialize the population Each individual represents a feasible path for a drone's access sequence, and a maximum number of iterations is set. Rolling step size factor Local search probability .

[0056] Step 2. The fitness function uses path cost as the evaluation criterion, as follows: Where P is a penalty term introduced if the path exceeds the range or load constraints. The penalty term is positive only when the path violates the constraints, and is 0 otherwise. Its definition is as follows: in: This represents the total flight distance along the current path. This represents the total load capacity of the current mission.

[0057] Step 3. Global search: Simulate the behavior of a dung beetle pushing a dung ball. First, randomly select two nodes in the path. Exchange positions to form a new path : Represents the commutation operator, if ,but Accept the new interpretation.

[0058] Step 4. Local search: Simulate the dung beetle's dance-like behavior to adjust its rolling direction and select a sub-path within the main path. The 2-opt algorithm is used to optimize the search within the neighborhood: The reverse operator refers to selecting a continuous subsequence in the path and reversing its order. If so, then update the path.

[0059] Step 5. Foraging behavior: Simulate dung beetles abandoning dung balls midway in search of new food. Randomly select a path of length... The fragments are randomly arranged to generate a new path.

[0060] This means reordering the data to form a new sequence, and then updating the path using a greedy algorithm. .

[0061] Step 6. Fitness Update and Elite Selection: After completing foraging behavior, all dung beetle individuals have moved according to environmental information. The fitness of all individuals is then ranked in ascending order, and the top-performing individuals are selected. The best-fit individuals constitute an elite set. ,in This is for use in the next stage of breeding operations.

[0062] Step 7. Reproductive behavior: This step simulates the process by which dung beetles reproduce new individuals using existing resources after foraging. This strategy ensures that superior genes are preserved while introducing new search paths. For elite groups Individual execution or The operator is perturbed to obtain new individuals that form a child set. Replace the worst-fit individuals in the current population with the generated offspring: In each iteration, the above operation is performed on all individuals to update and obtain the optimal individual. If there is no improvement after several consecutive iterations or the maximum number of iterations is reached, the process terminates and the optimal path is output.

[0063] Through the above steps, the DBO algorithm maintains its global search capability while designing a local perturbation strategy and structural adjustment mechanism for the path sequence problem, effectively avoiding getting trapped in local optima. At the same time, it uses a penalty function to handle feasibility constraints, ensuring that the final path meets the range and load limits.

[0064] Based on the above Figure 1 The illustrated embodiment, for example, describes the dynamic connection optimization algorithm of step S3 above: To ensure efficient connection between trucks and drones after completing their respective tasks without waiting, the location of their dynamic connection point must be precisely determined, minimizing the time difference between their arrival at that point. The golden ratio method, an efficient approach for solving one-dimensional unimodal optimization problems in continuous space, is used to determine the optimal rendezvous ratio between the truck's next stop and the drone's current path, minimizing the time difference between them. This allows for a precise rendezvous point between the two. The basic principle is to progressively narrow the search interval using the golden ratio. Specifically, the interval between the truck's next stop and the drone's current client node is repeatedly divided by ratios of 0.618 and 0.382. The side with the smaller time difference is selected to further narrow the search range. Through a finite number of iterations, the truck and drone arrive almost simultaneously, eliminating waiting time. They then move forward sequentially and meet at a suitable location, completing the dynamic connection. This enables the drone to replenish cargo and replace batteries mid-journey, reflecting the truck's role as a resupply station for the drone.

[0065] This process essentially involves a nonlinear, non-convex optimization problem with continuous variables. It eliminates the need to enumerate multiple possible connection points, significantly improving computational efficiency while ensuring the real-time performance and accuracy of the truck-drone connection. The golden ratio method is used to calculate the dynamic connection point between the truck and the drone. The pseudocode for the program design is shown in Table 1. Table 1. Pseudocode for calculating the connection point using the golden ratio method. In summary, the information feedback mechanism of the interactive algorithm lies in the inner algorithm's calculation of the total delivery cost for each truck path individual provided by the outer genetic algorithm, taking into account truck mileage, drone mileage, and waiting time costs. This total cost is then fed back to the outer layer as the individual's fitness value. If a path fails to meet range or load constraints during drone delivery, the system assigns a punitive fitness, reducing its probability of being selected. Based on the feedback fitness information, the outer genetic algorithm performs population update operations, continuously optimizing the truck path sequence through operators such as selection, crossover, and mutation. This mechanism achieves collaborative optimization of truck paths, drone paths, and dynamic connection points, prompting the population to iteratively converge towards a better solution set, ultimately obtaining an optimal path scheme with the minimum overall cost.

[0066] Furthermore, this application also provides specific case analyses in its embodiments. These case analyses are described below:

[0067] To verify the rationality and effectiveness of the proposed two-layer interaction algorithm, the Solomn dataset was used for analysis. Python was used to call Gurobi to accurately solve cases of different scales, and the results were compared with the interaction algorithm proposed in this invention for the static connection process of truck-drone systems. Following the approach of existing scholars, relaxation conditions were set: the drone has no endurance or load capacity limitations, and one drone can complete the delivery to all customer nodes within the cluster. The drone problem was also transformed into a standard TSP problem for solution, thereby finding the shortest path. The calculation results of the two algorithms for the paths of customer nodes of different scales are shown in Table 2.

[0068] Table 2 Comparison between the two-layer interactive algorithm and the exact solution Experimental results show that the proposed GA and DBO two-layer interactive algorithm has good feasibility and optimization performance for three types of scenarios: regular, clustered, and random distribution. In small-scale regular distribution scenarios, the solution obtained by the algorithm is almost identical to the exact solution, with the gap value of most instances being less than ±1%, and the algorithm outperforming the exact solution in some problems. This indicates that the algorithm can fully explore the solution space and obtain high-quality solutions under regular structures. In class-to-class scenarios, the path structure is more complex, but the algorithm still maintains high stability, with the average gap value within the range, and the optimal solution improvement of some instances exceeding 25%. This fully demonstrates that the proposed algorithm has good generalization ability and adaptability to complex delivery structures. In particular, in the RC1-80 and RC1-100 problem sets, the solution obtained by Gurobi is of poor quality, while the algorithm of this invention can still obtain solutions with lower costs and better paths, with gap values ​​reaching -23.88% and -27.94%, respectively. This shows that in large-scale, irregular customer node distribution scenarios, the two-layer interactive optimization strategy proposed in this invention can overcome the performance bottleneck of exact solution and obtain more practically meaningful solutions. In summary, the GA+DBO collaborative algorithm demonstrates strong problem-solving capabilities and practical value in complex environments, making it an efficient optimization method suitable for complex logistics scheduling problems.

[0069] To further verify the solution effect and superiority of the proposed "two-layer interactive optimization algorithm", this invention selects classic heuristic algorithms such as Genetic Algorithm (GA), Ant Colony Algorithm (ACO), and Particle Swarm Optimization (PSO) for comparative testing under the same experimental environment, and compares the solutions for the static collaborative delivery model. Figure 10 This document provides a comparative diagram of the total cost of four algorithms at different scales. The solution results are shown in Table 3. The data in the table show that GA+DBO consistently achieves the lowest total cost in instances of all scales, and its path optimization capabilities are superior in both truck path and drone path dimensions.

[0070] Table 3. Comparison of total costs of four algorithms at different scales. By comparing the above algorithms, the GA+DBO algorithm performs best in terms of total truck path length, total drone path length, and total cost at all scales. Its advantages become more obvious as the number of customer nodes increases. This trend shows that the two-layer interaction algorithm exhibits good scalability and global search capability in large-scale problems, which can effectively improve the quality of solutions and control total cost.

[0071] However, by introducing a dynamic connection mechanism, trucks and drones no longer need to wait at transfer points but can dynamically meet along the path. Calculating these dynamic connection points involves continuous variables and time synchronization, and its core complexity lies in the real-time optimization of these points. The Gurobi exact solution algorithm is suitable for solving linear programming problems, rather than continuous searches embedded with the golden ratio. Therefore, although the Gurobi optimizer can be used to verify the model accuracy and the solution quality of heuristic algorithms in static collaborative scenarios, dynamic collaborative problems exhibit significant nonlinearity, continuity, and nesting, making them unsolvable by solvers. Heuristic algorithms, on the other hand, demonstrate stronger structural adaptability and solution space exploration capabilities in such problems, thus becoming a reasonable choice for dynamic collaborative optimization.

[0072] To further verify the practicality of the proposed two-layer interactive dynamic collaborative path planning algorithm, a rural area in Gansu Province was selected for analysis of the dynamic collaborative mode of truck-drone systems. Qingyang City in Gansu Province successfully applied for a national urban air traffic management pilot project. Ningxian Hesheng Industrial Park has formed a closed-loop industrial chain and is equipped with a large-scale warehousing and logistics park. Huachi Nanliang General Aviation Airport can serve as a test base for medium and large-sized drones to conduct test flights. Furthermore, Qingyang has fewer airspace restrictions, and a dedicated railway line from Changqing Bridge to Xifeng Industrial Park passes through the city, which is conducive to the rapid integration of drone delivery services with the existing logistics system. Therefore, this region was chosen for analysis due to its representativeness. The relevant data for each customer node are shown in Table 4. Figure 11 This specification provides a schematic diagram of the distribution of customer nodes in Changqingqiao Town, Qingyang City. Figure 11 As shown, the distribution center is the Changqingqiao Warehousing and Logistics Park.

[0073] Table 4. Location and Demand of Each Customer Node The algorithm was implemented using Python programming. The experimental environment was an Intel Core i5-1035G1 CPU @ 1.00GHz or 1.19GHz processor with 8GB of memory. The algorithm parameters are set as shown in Table 5. Figure 12 This is a schematic diagram illustrating a static collaborative delivery result using a truck-drone, as provided in this specification. Figure 12 As shown, the truck is responsible for accessing the client node at the cluster center and launching the drone at that point. The drone visits the client node within the cluster and eventually returns to the origin to meet up with the truck. Throughout the process, the truck waits in place for the drone to return. Figure 13 This is a schematic diagram illustrating the dynamic collaborative delivery result of a truck and drone, as provided in this specification. Figure 13As shown, after the truck launches the drone at the connection point, it does not wait in place but moves to the next customer node. The drone simultaneously visits the customer nodes in the cluster, calculates the dynamic connection points along the way based on the speed difference between the two, completes the drone's mid-journey resupply, and finally returns to the distribution center after traversing all customer nodes in sequence.

[0074] Table 5 Algorithm Parameter Values To verify the stability and adaptability of the proposed truck-drone dynamic collaborative delivery model under different operating parameters, this invention conducts sensitivity analysis from the perspectives of the number of customer nodes and drone range, and compares the results with the cost of truck-only delivery and static collaborative delivery strategies to verify the superiority of the algorithm.

[0075] To evaluate the benefits of dynamic collaborative delivery, the algorithm proposed in this invention was used to compare and solve cases of different scales, recording the changes in costs. By changing the number of delivery customer nodes, the cost of the two collaborative delivery strategies was examined as the scale of demand increased. Five delivery scenarios with 25, 30, 35, 40, and 47 customer nodes were selected for testing, simulating delivery demand gradually increasing from a small scale to a large scale. The results are shown in Table 6.

[0076] Table 6. Cost Comparison of Two Collaboration Methods Figure 14 This document provides a cost comparison diagram of two collaborative methods, as shown below. Figure 14 As shown, the total delivery cost of both collaborative delivery strategies increases with the number of customer nodes from 25 to 47. This is because the increased scale of delivery demand inevitably leads to longer routes and higher operating costs. However, the rate of cost increase differs significantly between the different strategies. In the static collaborative approach, the waiting time for trucks to wait for drones accumulates significantly with the increase in the number of customer nodes, forming a waiting time cost. In contrast, the dynamic collaborative strategy, by synchronizing trucks and drones, eliminates the waiting time cost of trucks because the tolerance range for the time difference at the connection point is extremely small. When the number of customer nodes is small (e.g., 25 points), the cost of both methods decreases by 28.6%; as the number of customer nodes further increases to 47, the cost decreases by 32.3%. Therefore, when customer nodes are widely distributed and numerous, the dynamic collaborative model can significantly reduce the total cost. Thus, in actual delivery, if the number of customer nodes is large and dispersed, the truck-drone dynamic collaborative strategy is more economically advantageous.

[0077] To explore the impact of drone maximum range on collaborative delivery effectiveness, this section fixes other parameters and only adjusts the drone's endurance for sensitivity analysis. Four typical maximum single-trip range radii of 5km, 10km, 15km, and 20km are selected to test the path costs of three delivery methods under different range constraints. These range radii cover the range of current mainstream delivery drones, from low to high battery performance. The experimental scenario uses the aforementioned maximum customer node distribution to ensure comparison of the differences in range between strategies for the same delivery task. Finally, the relationship between the total cost of each strategy and the drone's range is shown in Table 7.

[0078] Table 7 Comparison of route costs for three delivery methods under different driving radii. Figure 15 This instruction manual provides a cost comparison diagram for three delivery modes under different driving radii. Figure 15 This study illustrates the changing trends in route costs for three delivery strategies as the drone's flight range increases from 5km to 20km. Only truck delivery remains unaffected by changes in drone flight range and can serve as a benchmark. The trends show that the route costs for both collaborative delivery models decrease significantly with increasing drone flight range. This indicates that drone flight range has a substantial impact on collaborative delivery models; a longer flight range means that drones can replace trucks to handle more delivery tasks, thereby effectively reducing overall delivery costs.

[0079] When the drone's range is only 5km, the advantages of collaborative delivery are significantly limited. Due to the small service range of drones, they need to frequently stop and take off during delivery. In this scenario, although the dynamic collaborative mode can reduce truck waiting to some extent, its overall cost-saving ability is limited. When the drone's range increases to 15km or more, the dynamic collaborative mode avoids the idling and stagnation problems caused by trucks waiting for drones in static collaboration, and has higher scheduling efficiency and execution flexibility.

[0080] In summary, to address the high cost and low efficiency of last-mile delivery in rural areas, this invention studies a truck-drone collaborative delivery path optimization problem considering dynamic connection points and time synchronization. An integer programming model is established with the objective of minimizing delivery cost and waiting time cost. A two-layer interactive optimization algorithm based on a dynamic connection mechanism is designed. The outer layer uses an improved genetic algorithm (GA) to determine the truck route, while the inner layer uses an improved dung beetle algorithm (DBO) to optimize the drone path. The dynamic connection point between the truck and drone is determined using the golden section method, achieving precise synchronous collaboration between the two. The effectiveness and feasibility of the algorithm are verified by comparing the results with those obtained using the Solom dataset and the Gurobi dataset. A delivery case study in a rural area of ​​Qingyang City, Gansu Province, shows that the proposed dynamic collaborative model achieves a maximum cost reduction of 32.26% compared to the static collaborative strategy across various scales; the dynamic model also reduces costs by 35.0% compared to truck-only delivery, with particularly significant advantages in scenarios with a wide distribution and large number of customer nodes. Sensitivity analysis further revealed that the drone's flight range and the size of customer nodes significantly impacted delivery costs. The longer the drone's flight range and the larger the customer node size, the more pronounced the economic advantages of the dynamic collaboration model. The dynamic collaboration model demonstrated superior cost performance and stronger adaptability across different flight ranges. Especially at longer flight ranges, this model maximized the drone's coverage and maneuverability, significantly reducing overall delivery costs. In contrast, while the static collaboration model offered some cost reduction in high-range scenarios, its path flexibility and scheduling efficiency were inferior to the dynamic strategy due to its fixed connection mechanism. Therefore, in actual delivery processes, intelligent collaboration mechanisms with dynamic connection capabilities should be prioritized to improve the economy and reliability of logistics systems in complex environments.

[0081] This invention addresses the optimization of truck-drone collaborative delivery routes in rural areas. It systematically constructs a route optimization model considering dynamic connection points and time synchronization constraints, and proposes a two-layer optimization framework based on the interactive collaboration of a genetic algorithm and an improved dung beetle algorithm. By using clustering preprocessing to divide delivery areas and introducing the golden section method to determine dynamic meeting points, it comprehensively achieves synchronized optimization of trucks and drones in the spatiotemporal dimensions. The main conclusions of this invention are as follows:

[0082] (1) This invention addresses the challenges of dispersed customer nodes and complex terrain in rural areas by introducing a dynamic connection mechanism to construct a more practical model that better suits rural scenarios. Compared to traditional static collaboration strategies, the proposed dynamic collaboration model can effectively reduce total delivery costs. In simulations of different scales, the dynamic strategy achieved an average cost reduction of 30.6% compared to the static strategy, with a maximum reduction of 32.3%.

[0083] (2) Under different flight range conditions, the total cost of the dynamic collaborative strategy is lower than that of the static strategy, and its cost advantage becomes more and more obvious as the flight range increases. When the flight range is 20km, the cost of the dynamic mode is reduced by 35.0% compared with the truck delivery alone, demonstrating its high adaptability and economy to the high-performance UAV environment.

[0084] (3) In terms of operational efficiency, the dynamic mode eliminates the problem of trucks waiting idly. Even under the condition of limited range, it can avoid unnecessary stagnation time through flexible connection, thereby effectively reducing time loss.

[0085] (4) Sensitivity analysis shows that when the UAV has a long range and the customer node density is high, the dynamic collaborative strategy has a stronger advantage in terms of cost control and path efficiency, and has a realistic foundation and development potential for promotion and application in typical environments such as mountainous areas, hilly areas and remote rural areas.

[0086] This invention studies the dynamic collaborative delivery problem of trucks and drones in rural areas, constructing a path optimization model and proposing a corresponding solution method. Considering the weak infrastructure and continuously increasing policy support in rural areas, collaborative delivery has broad application prospects in this region. Future research can be further extended to complex terrain scenarios such as mountainous areas, combining 3D path planning with real terrain data to improve the model's practicality and promotional value.

[0087] The following describes the route optimization device for truck-drone collaborative delivery in rural areas provided by the present invention. The route optimization device for truck-drone collaborative delivery in rural areas described below and the route optimization method for truck-drone collaborative delivery in rural areas described above can be referred to in correspondence with each other.

[0088] Figure 16 A schematic diagram of a route optimization device for truck-drone collaborative delivery in rural areas provided by the present invention is shown below. For example, please refer to... Figure 16 As shown, the route optimization device for truck-drone collaborative delivery in rural areas may include: The delivery network modeling module is used to construct the delivery network for the target rural area. The delivery network includes multiple delivery customer nodes, which are divided into several delivery clusters. The cluster center of each delivery cluster serves as the truck parking location and the drone take-off location. The model building module is used to build a delivery route optimization model with the goal of minimizing delivery costs and waiting time costs within the delivery network. The model optimization module is used to solve the delivery route optimization model through an improved two-layer interactive optimization algorithm to obtain the truck-drone collaborative delivery route. The improved two-layer interactive optimization algorithm includes outer-layer optimization, inner-layer optimization, and dynamic connection point optimization. During each iteration: The outer layer optimization uses a genetic algorithm to optimize the truck delivery routes in order to determine the order in which trucks stop at the cluster centers; Under the constraint of the order in which trucks stop at each cluster center determined by the outer optimization, the inner optimization uses the dung beetle algorithm to plan the delivery path of the drone from the take-off and landing point of each cluster center to visit all customer nodes in the corresponding delivery cluster. The dynamic connection point optimization uses the truck travel path between adjacent cluster centers determined by the outer layer optimization as the search interval, and divides the initial search interval to generate candidate connection points; obtains the time difference between the time it takes for the truck to travel from the current cluster center to the candidate connection point and the time it takes for the drone to return from the current delivery location to the candidate connection point, and selects the candidate connection point that minimizes the time difference as the optimal dynamic connection point.

[0089] Specific limitations regarding the route optimization device for truck-drone collaborative delivery in rural areas can be found in the above-mentioned limitations on route optimization for truck-drone collaborative delivery in rural areas, and will not be repeated here. Each module in the aforementioned route optimization device for truck-drone collaborative delivery in rural areas can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0090] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0091] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A route optimization method for truck-drone collaborative delivery in rural areas, characterized in that, include: Construct a delivery network for the target rural area. The delivery network includes multiple delivery customer nodes, which are divided into several delivery clusters. The cluster center of each delivery cluster serves as the truck parking location and the drone take-off location. A delivery route optimization model is constructed with the goal of minimizing delivery costs and waiting time costs within the delivery network. An improved two-layer interactive optimization algorithm is used to solve the delivery route optimization model, obtaining a truck-drone collaborative delivery route. The improved two-layer interactive optimization algorithm includes outer-layer optimization, inner-layer optimization, and dynamic connection point optimization. During each iteration: The outer layer optimization uses a genetic algorithm to optimize the truck delivery routes in order to determine the order in which trucks stop at the cluster centers; Under the constraint of the order in which trucks stop at each cluster center determined by the outer optimization, the inner optimization uses the dung beetle algorithm to plan the delivery path of the drone from the take-off and landing point of each cluster center to visit all customer nodes in the corresponding delivery cluster. The dynamic connection point optimization uses the truck travel path between adjacent cluster centers determined by the outer layer optimization as the search interval, and divides the initial search interval to generate candidate connection points; obtains the time difference between the time it takes for the truck to travel from the current cluster center to the candidate connection point and the time it takes for the drone to return from the current delivery location to the candidate connection point, and selects the candidate connection point that minimizes the time difference as the optimal dynamic connection point.

2. The route optimization method for truck-drone collaborative delivery in rural areas as described in claim 1, characterized in that, The step of segmenting the initial search interval to generate candidate connection points specifically includes: The truck driving path segment between the adjacent first cluster center and second cluster center determined by the outer layer optimization is used as the search interval; and the search interval is divided based on the golden ratio of 0.618 to generate initial candidate connection points; The first time difference is the difference between the time it takes for the truck to travel from the center of the first cluster to the initial candidate connection point and the time it takes for the drone to return from the current delivery location to the initial candidate connection point. The time difference between the time it takes for the truck to travel from the first cluster center to the second cluster center and the time it takes for the drone to return from the current delivery location to the second cluster center is used as the second time difference; Compare the first time difference with the second time difference, and take the interval with the smaller time difference as the new search interval; Repeat the steps of segmentation, time difference comparison, and interval update until the length of the search interval is less than the preset precision threshold to obtain the optimal dynamic connection point.

3. The route optimization method for truck-drone collaborative delivery in rural areas as described in claim 1, characterized in that, The outer layer optimization is based on a genetic algorithm to optimize the truck delivery routes to determine the order in which trucks stop at each cluster center, specifically including: Step 1. After encoding the order in which trucks visit each cluster center using integer encoding, a genetic population is generated using a combination of random initialization and nearest neighbor heuristics. The genetic population consists of multiple genetic individuals, each representing a truck delivery route: R ={ r 0, r 1, ..., rn },in r 0 is the warehouse delivery start number. r 1~ rn The cluster centers are numbered from the 1st cluster center to the nth cluster center; Step 2. Use the reciprocal of the delivery cost corresponding to the truck delivery route as the fitness function of the improved genetic algorithm, and obtain the fitness value of all genetic individuals in the genetic population according to the fitness function; Step 3. Based on the fitness value, perform selection, crossover, mutation, and local search optimization operations on the genetic population to generate new genetic individuals; Step 4. Obtain the fitness value of the new individual based on the fitness function, and perform dynamic parameter adjustment and population maintenance: If the optimal path does not improve within the first preset iteration number of generations, dynamically increase the mutation probability to the preset target mutation probability value to enhance the search capability; after each preset second iteration number of generations, randomly inject several new genetic individuals into the genetic population to maintain the population's search capability and diversity; at the same time, adopt an elite retention mechanism to retain the genetic individual with the best fitness value in the genetic population to the next generation; Step 5. When the preset termination condition of the improved genetic algorithm is met, output the order in which the trucks stop at the center of each cluster; otherwise, return to Step 2.

4. The route optimization method for truck-drone collaborative delivery in rural areas as described in claim 3, characterized in that, The process of generating new genetic individuals by performing selection, crossover, mutation, and local search optimization operations on the genetic population based on fitness values ​​specifically includes: The selection operation employs an elite roulette wheel strategy, which obtains the selection probability of each genetic individual in the current genetic population based on its fitness value, and then generates new genetic individuals based on the selection probability. in, Indicates genetic individual The probability of choosing; Indicates genetic individual fitness value; This represents the total number of genetic individuals in the current genetic population. In each selection operation, a preset proportion of elite genetic individuals are additionally retained in the genetic population for the next iteration. Elite genetic individuals are those whose selection probability is greater than a preset selection probability threshold. The crossover operation employs an adaptive partial mapping crossover strategy to generate new genetic individuals. This strategy executes the crossover operation with a first crossover probability when the current iteration count of the improved genetic algorithm is within a preset iteration start range, thereby enhancing the diversity and search capability of the genetic population. When the current iteration count of the improved genetic algorithm is within a preset iteration convergence range, the crossover operation is executed with a second crossover probability to maintain the propagation of excellent solutions. The first crossover probability is greater than the second crossover probability. The mutation operation generates a new genetic individual by randomly swapping the two cluster centers in a genetic individual that are not located at the warehouse delivery origin. The local search optimization operation generates new genetic individuals through the 2-opt local search strategy.

5. The route optimization method for truck-drone collaborative delivery in rural areas as described in claim 1, characterized in that, The inner-layer optimization, constrained by the truck stopping order at each cluster center determined by the outer-layer optimization, uses the dung beetle algorithm to plan the delivery path for the drone to depart from the take-off and landing point of each cluster center and visit all customer nodes within the corresponding delivery cluster. Specifically, this includes: Step 1. Randomly initialize the dung beetle population. X ={ x 1, x 2, ..., xn }, x 1~ xn Here, represents the 1st to nth dung beetle individuals, and each dung beetle individual represents a feasible path for a drone's access order; and the maximum number of iterations for the improved dung beetle algorithm is set. Tmax Rolling step size factor α and local search probability ; Step 2. Use the path cost of feasible paths in the drone visit order as the fitness function for the improved dung beetle algorithm: in, and They represent the first The and the first Individual dung beetle; and They represent respectively; Represents an infinite number; This indicates that if the drone's path exceeds the range or payload constraints, a penalty term is introduced. The penalty term is positive only when the path violates the constraints, and 0 otherwise. This indicates the total flight distance along the current path. Indicates the maximum flight distance; This indicates the total weight of the current delivery task. This represents the total maximum load capacity; Step 3. Simulate the dung beetle's ball-rolling behavior by randomly swapping the positions of two nodes in the path to achieve a global search: in, Indicates the formation of a new path; Indicates the original path, and These represent the original paths. The positions of the two nodes in the text; Represents the commutation operator; if Then accept the new solution. ; Step 4. Simulate dung beetle dance behavior and use the 2-opt algorithm to reverse the path subsequence to achieve local search optimization: Xdance =Re verse ( X , s , t ) in, s and t These represent the selected path subsequences. The position of the ending node in the path; Reverse() represents the reverse operator, which selects a continuous subsequence in the path and reverses its order. If so, then update the path; Step 5. Simulate dung beetle foraging behavior, randomly reconstruct path segments, and update the path using a greedy algorithm: Xf =Re build ( X , k ) in, Indicates the formation of a new path; Indicates the original path, and These represent the original paths. The positions of the two nodes in Re; build () indicates the original path X Randomly select a length of k The fragments are randomly arranged to generate a new path, and the path is updated according to a greedy criterion: if Then accept the new solution. ; Step 6. After foraging, all dung beetles will move. Sort all dung beetles in ascending order of their fitness values, and select the top [number] fitness values ​​to form an elite group for breeding operations. ,in ; Step 7. Simulate dung beetle reproductive behavior and target elite groups. The individual dung beetle in the process or The operator is perturbed to obtain new individuals that form a child set. Replace the worst-fit dung beetle individuals in the current dung beetle population with the generated offspring: in, Indicates the first New dung beetle individuals reproduced in the next iteration; This represents the total number of dung beetle individuals in the current dung beetle population; Step 8: In each iteration, simulate dung beetle rolling, dancing, foraging, and reproductive behaviors to generate a new population and record the current best dung beetle individual. When the best dung beetle individual does not improve for several consecutive generations or reaches the preset maximum number of iterations, terminate the iteration and output the optimal access path for the drone to the customer nodes within the delivery cluster.

6. The route optimization method for truck-drone collaborative delivery in rural areas as described in claim 1, characterized in that, The construction of the delivery route optimization model specifically includes: The optimization objective of the delivery route optimization model is to minimize the delivery cost and waiting time cost within the delivery network. in, This indicates the delivery cost of the truck; This indicates the delivery cost of the drone; This represents the waiting time cost for the truck while waiting for the drone; This refers to the collection of ground delivery points where trucks are responsible for delivery. Indicates that the truck comes from the node To the node Path cost; Indicates that the truck comes from the node To the node The decision variable is set to 1 during delivery and 0 otherwise. This refers to the collection of delivery points where drones are responsible for delivery. Indicates that the drone comes from the node To the node Path cost; Indicates that the drone comes from the node To the node The decision variable is set to 1 during delivery and 0 otherwise. This represents the unit time cost of a truck waiting for a drone; Indicates the truck is at the node Waiting time for the drone; The delivery route optimization model is constrained by truck route-related constraints, drone route-related constraints, drone payload and range constraints, and truck-drone collaboration constraints; among them, Truck routing constraints are used to ensure that trucks depart from and return to the distribution center, traffic balance, that each transfer point is visited only once, and to eliminate sub-loops: in, Indicates that the truck comes from the node Returning to the decision variables of the distribution center, This indicates that the truck departs from the distribution center and heads to the node. Decision variables; Indicates that the truck comes from the node To the node The decision variable is set to 1 during delivery and 0 otherwise. This indicates the node where the truck is accessed. Auxiliary order variables for sequential order; This indicates the node where the truck is accessed. Auxiliary order variables for sequential order; This represents the total number of nodes in the set D of ground delivery points handled by the trucks, excluding the distribution centers. Represents an infinite number; Drone path constraints are used to ensure that all flight delivery points are visited, traffic is balanced, and drones take off only from transit points and land at dynamic connection points: in, and These represent the drones starting from the nodes. j To the node and from node i To the node Decision variables; Indicates that the truck comes from the node To the node Decision variables; and These represent the nodes accessed by the drone. and nodes Auxiliary order variables for sequential order; This represents the total number of nodes in the set of delivery points handled by the drone, excluding the starting point. This indicates that the drone is responsible for delivering goods from the designated delivery point. Represents a set of dynamic connection points; Unmanned aerial vehicle (UAV) payload and range constraints are used to limit the single flight distance from the maximum range and the payload from the maximum payload capacity. in, Indicates drone node To the node The remaining flight range; This indicates the maximum flight distance of a single drone flight; Indicates that the truck comes from the node To the node Euclidean distance; Represents client node Demand; This indicates the maximum payload capacity of the drone; Represents a node from the set D of ground delivery points. Nodes in the set of flight delivery points F Euclidean distance; This indicates the maximum flight distance of a single drone flight; Truck-drone coordination constraints are used to ensure that the drone's takeoff time coincides with the truck's arrival time at the transfer point, and that the time difference between the truck's and the drone's arrival at the dynamic connection point does not exceed a preset threshold. in, and These represent the nodes reached by the drone. and nodes Time; This indicates the average speed of the drone; Indicates that the drone comes from the node To the node Manhattan distance; Indicates at node Service hours; and These represent the nodes where the trucks arrived. and nodes Time; Indicates that the truck comes from the node To the node Euclidean distance; This indicates the average speed of the truck; and These represent the arrival nodes for the truck and the drone, respectively. Time; and These represent the arrival nodes for the truck and the drone, respectively. Time; This indicates the tolerance range for time difference at the connection point.

7. The route optimization method for truck-drone collaborative delivery in rural areas as described in claim 1, characterized in that, The multiple delivery customer nodes are divided into several delivery clusters, specifically including: Initial clustering of multiple delivery customer nodes was performed using the HDBSCAN algorithm; For clusters in the HDBSCAN clustering results where the number of nodes exceeds a preset threshold or the spatial distribution span exceeds the service radius of the drone, the K-means algorithm is used for recursive subdivision until the subdivided clusters meet the preset size constraints, thus obtaining several delivery clusters.

8. A route optimization device for truck-drone collaborative delivery in rural areas, characterized in that, include: The delivery network modeling module is used to construct the delivery network for the target rural area. The delivery network includes multiple delivery customer nodes, which are divided into several delivery clusters. The cluster center of each delivery cluster serves as the truck parking location and the drone take-off location. The model building module is used to build a delivery route optimization model with the goal of minimizing delivery costs and waiting time costs within the delivery network. The model optimization module is used to solve the delivery route optimization model through an improved two-layer interactive optimization algorithm to obtain the truck-drone collaborative delivery route. The improved two-layer interactive optimization algorithm includes outer-layer optimization, inner-layer optimization, and dynamic connection point optimization. During each iteration: The outer layer optimization uses a genetic algorithm to optimize the truck delivery routes in order to determine the order in which trucks stop at the cluster centers; Under the constraint of the order in which trucks stop at each cluster center determined by the outer optimization, the inner optimization uses the dung beetle algorithm to plan the delivery path of the drone from the take-off and landing point of each cluster center to visit all customer nodes in the corresponding delivery cluster. The dynamic connection point optimization uses the truck travel path between adjacent cluster centers determined by the outer layer optimization as the search interval, and divides the initial search interval to generate candidate connection points; obtains the time difference between the time it takes for the truck to travel from the current cluster center to the candidate connection point and the time it takes for the drone to return from the current delivery location to the candidate connection point, and selects the candidate connection point that minimizes the time difference as the optimal dynamic connection point.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the route optimization method for truck-drone collaborative delivery in rural areas as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the route optimization method for truck-drone collaborative delivery in rural areas as described in any one of claims 1 to 7.

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