Unmanned aerial vehicle and vehicle joint distribution path optimization method and device and medium

Abstract

The application relates to a method and device for optimizing a combined delivery path of a UAV and a vehicle and a medium, wherein the method comprises the following steps: S1, acquiring the positions of all delivery points and delivery goods demands; S2, constructing a constraint condition combination; S3, regarding the delivery center and all delivery points as nodes and randomly generating a node sequence; S4, based on the current node sequence, combining the constraint conditions, defining the delivery attributes of each node as a vehicle delivery node, a UAV delivery node or a stop point, and based on the delivery attributes of each node, combining the sequence of the nodes to generate a vehicle path and one or more UAV paths; S5, generating a total delivery time based on the obtained vehicle path and all UAV paths; and S6, after updating the node sequence by using an optimization algorithm, repeating steps S3 to S5 multiple times, and generating a delivery scheme of the vehicle path and all UAV paths with the shortest total delivery time. Compared with the prior art, the application can improve the optimization speed.

Description

Technical Field

[0001] This invention relates to the field of logistics and distribution, and in particular to a method, apparatus and medium for optimizing delivery routes using drones and vehicles. Background Technology

[0002] In recent years, the development of drone technology has become a hot topic in the high-tech field both domestically and internationally. As a disruptive technology, drones have been widely applied in military, civilian, and commercial sectors. The Chinese government attaches great importance to the development of drone technology, providing policy support and market guarantees for the drone industry. In 2018, the "New Generation Artificial Intelligence Development Plan" was issued, which mentioned that drone technology has very broad application prospects in smart cities, agriculture, logistics and distribution, and other fields. At the same time, the "Unmanned Aerial Vehicle System Development Plan" released by the National Aeronautics and Space Administration clarified the development direction and goals of drone technology for the next five years, including improving drone autonomous flight, strengthening application scenario research and construction, and strengthening drone talent training. In addition, the government has also introduced a series of policies, such as allowing civilian drones to increase their flight altitude and providing tax incentives for drone-related enterprises, further promoting the development of the drone industry.

[0003] Drones have been widely used in various fields, such as agriculture, environmental protection, security, aviation, logistics, and delivery. The use of drones has improved the efficiency of many traditional tasks, especially in emergency rescue missions requiring efficient operation and rapid response. For example, drones can provide aerial monitoring and rescue in natural disasters such as fires and floods, reducing casualties and property damage.

[0004] With the development of the internet and e-commerce, logistics and delivery have become a crucial sector. As market competition intensifies and consumer demand continues to grow, bottlenecks in logistics and delivery are becoming increasingly apparent. The application of drones in logistics and delivery can solve these bottlenecks, enabling rapid and accurate delivery with relatively low operating costs, while also reducing traffic congestion and environmental pollution.

[0005] The main advantages of drones in logistics delivery are speed and flexibility. Drones can complete the delivery of goods in a short time, avoiding problems such as wasted human resources and traffic congestion. In addition, drones can also complete the transportation and delivery of goods in some special environments, such as mountainous areas, islands, and some adverse weather conditions.

[0006] Currently, the application of drones in logistics delivery is still in its early stages. However, major logistics companies and e-commerce platforms have begun related pilot programs and trials. As a new type of transportation tool in logistics delivery, drones have advantages such as low cost, easy operation, low environmental requirements, and strong survivability, and have great potential in logistics transportation applications, capable of undertaking more delivery tasks. However, due to their small size, they also have disadvantages such as small payload, short flight distance, and greater susceptibility to weather conditions. In contrast, traditional delivery vehicles have advantages such as large capacity, long-distance delivery capability, high safety and stability, and mature related delivery technologies. The joint delivery of drones and vehicles can fully leverage their respective advantages, and large logistics companies such as Amazon, UPS, and JD.com are vigorously developing new drone delivery models.

[0007] Following sudden events such as earthquakes and flash floods, damaged roads and residential areas restrict vehicle delivery. Drones, however, offer advantages such as terrain-independent flight, high operational efficiency, and relatively low cost, enabling them to quickly reach disaster areas or emergency rescue sites. This shortens material transportation time, improves emergency response speed, and provides an efficient and convenient means of transporting emergency supplies. Furthermore, drones can improve the speed and accuracy of material delivery, avoid the risk of personnel entering dangerous areas, and enhance transportation safety. With the continuous development and widespread adoption of drone technology, research into drone-vehicle joint delivery models will be of great significance in ensuring the timely, efficient, and contactless delivery of large quantities of supplies.

[0008] To construct a reasonable model, researchers attempted to start with classic routing problems, such as the Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP), assuming that vehicles and drones cooperate to complete the delivery tasks for all customers.

[0009] (1) Traveling Salesman Problem In 2015, Murray and Chu proposed two models for the Flight Assistant Traveling Salesman Problem (FSTSP) and the Parallel Unmanned Aerial Vehicle Scheduling Traveling Salesman Problem (PDSTSP). These were among the earliest and most influential papers published in this field, providing a reference for a large number of subsequent studies.

[0010] In FSTSP (Full-Time Straight-Linear Programming), vehicles and drones require coordinated control and joint operation. To avoid the drawbacks of using the Big M method for constraints during modeling, Boccia et al. proposed a new integer linear programming (ILP) model for FSTSP and solved the problem with 20 customer nodes based on column generation. Murray and Raj addressed the mFSTSP problem with a single vehicle and multiple drones, using a three-stage heuristic algorithm to analyze the impact of different drone battery sizes, payloads, flight distances, and flight phases on the total completion time of joint delivery, concluding that additional drones may lead to diminishing marginal returns.

[0011] In PDSTSP, vehicles and drones do not cooperate; each independently completes its delivery task. Based on the PDSTSP model built by Murray, Saleu et al. proposed a two-step iterative heuristic algorithm, which was tested using a large-scale case study of 229 customer locations. DellAmico et al. combined a local search algorithm to solve the PDSTSP problem, aiming to minimize the total time spent serving all customers, and validated the model's effectiveness in small- to medium-scale cases using data from Murray and Saleu. Ham et al. extended PDSTSP to a scenario with multiple vehicles, multiple drones, and multiple warehouses, considering that drones could simultaneously pick up or deliver goods at warehouses or customer locations, aiming to minimize the completion time of all tasks. Drones launched from vehicles could be retrieved from different vehicles.

[0012] Agatz et al. termed this path problem the Drone Traveling Salesman Problem (TSP-D), constructing a mixed-integer model with the goal of minimizing delivery costs. They solved the problem using a two-stage heuristic algorithm based on local search and dynamic programming, employing routing followed by clustering. Bouman et al. improved the traditional dynamic programming algorithm for the TSP problem and optimized it with the 𝐴* algorithm, making it suitable for solving large-scale TSP-D problems. Ha et al. addressed the TSP-D problem for a single truck and a single drone, aiming to minimize the total delivery cost and the penalty cost of the truck waiting for the drone. They proposed a greedy stochastic adaptive search algorithm that first clusters and then routes, by dividing the optimal TSP path into TSP-D paths. Kitjacharoenchai et al. extended TSP-D to a joint delivery problem involving multiple trucks and drones, allowing drones to land on different vehicles. They designed an insertion-based heuristic algorithm to solve large-scale cases and compared the results with those for single-truck delivery and single-drone single-vehicle delivery. Mario et al. proposed that to maximize the use of drones for package delivery, trucks could not only launch and receive drones at fixed nodes but also launch and retrieve drones along the delivery route. Some engineers have proposed a mixed-integer linear programming formula to decompose the TSP-D model into two decision-making stages. The first stage selects and sorts the service nodes of the vehicles, and the second stage schedules the drones for the truck routes and the remaining nodes. A Benders-type decomposition algorithm is designed to solve large-scale instances.

[0013] (2) Vehicle routing problem When considering the limitations of delivery involving more drones and vehicles, TSP expands to VRP. To improve the efficiency of joint delivery, Savuran and Karakaya proposed a new variant, MoDVRP, which assumes that vehicles travel in a straight line with a large number of customer points distributed along both sides of the route, and that drones deliver to as many customer points as possible after departure. Dorling considered the relationship between drone flight distance and payload, constructed an integer linear model of VRPs, verified that the energy consumption of drones and payload are linearly related, and applied simulated annealing algorithm to solve the model, concluding that energy consumption and delivery time cannot be optimal simultaneously.

[0014] Regarding the limitations of drones, Wang et al. considered the drone vehicle routing problem (VRP-D) under the constraint of endurance limitations, proposing that drones can be launched and received from trucks at warehouses or any customer location, and analyzed the delivery results under several worst-case scenarios. The results showed that the worst-case outcome depends on the number of drones on each truck and the relative speed between the drones and the vehicle. Sacramento et al. addressed the difficulty of solving large-scale instances in joint delivery by proposing an adaptive large-scale neighborhood search metaheuristic algorithm, while also performing sensitivity analysis on drone-related parameters. Scherme et al., based on mixed-integer linear programming, introduced an efficient inequality set (VIEQ) to solve the drone allocation and scheduling problem (DASP), finding the optimal allocation and scheduling of drones given existing vehicle routes. The results showed that the proposed model can effectively solve the VRP-D problem. Wang and Sheu applied joint delivery in urban logistics, transforming the arc-based problem model in VRP-D into a path-based model, and developed a branch-and-price method to find high-quality exact solutions. Kuo et al. extended the VRP-D mathematical formula of Sacramento et al., and developed a model of UAV vehicle path problem with customer time window (VRPTWD) to explore this cooperation, taking into account the time window constraints of different customers. They also proposed a simple and effective variable neighborhood search (VNS) algorithm to solve the VRPTWD problem.

[0015] In addition, some researchers have started with another variant of the two-level vehicle routing problem, using a two-layer path planning approach. Drones deliver goods within a certain range, centered on nodes along the vehicle path. Some scholars have applied the 2E-CLRP model to demonstrate how to utilize vehicle-mounted drones for intelligence gathering, reconnaissance, and surveillance tasks. The first layer of this problem is equivalent to solving a partial loop travel problem, where the vehicle only needs to select some stopping points to launch and recover the drone. The second layer is equivalent to solving a single-loop vehicle routing problem, where the drone needs to visit all target points in the shortest possible time, constrained by its endurance. Some scholars have proposed a new two-layer vehicle-mounted drone cooperative routing problem, 2E-GUCRP, assuming that the vehicle cannot remain stationary. Building upon 2E-VRP, this paper proposes that the vehicle not only handles package delivery but also acts as a mobile warehouse for the drone. The drone can launch multiple packages from the vehicle, return to the vehicle after delivery, and analyze the energy consumption process of the drone when transporting multiple packages. The 2E-VRP-TM, a two-tier vehicle routing problem with time windows and mobile satellites, is introduced to minimize operating costs. In the first tier, vehicles depart from distribution centers (DCs) to deliver packages to customers with time windows. When vehicles are parked at customer locations for drone launches and recoveries, they are treated as mobile satellites.

[0016] In particular, Chinese patent CN 113139678A discloses a method for optimizing the delivery route of a drone-vehicle joint delivery system. This method defines some delivery points as stopping points, allowing the drone and vehicle to be simultaneously located at these points for relaunch, thereby increasing the drone's reachability and expanding the spatial range of feasible solutions. However, this prior art has the following drawbacks: 1. It divides the vehicle's delivery route into sub-chains, which need to be optimized step by step according to the launch rounds of the drone, resulting in low optimization efficiency.

[0017] 2. It employs a three-stage model, accumulating the single-path planning of drones and vehicles, and then performing overall optimization. Therefore, in addition to the main objective, there are two sub-objectives to construct a joint delivery route. Thus, the existence of these two sub-objectives actually affects the probability of finding the optimal solution.

[0018] 3. It is impossible to achieve modular expansion of constraints. Summary of the Invention

[0019] The purpose of this invention is to provide a method, apparatus, and medium for optimizing delivery routes using drones and vehicles in order to solve the problems existing in the prior art.

[0020] The objective of this invention can be achieved through the following technical solutions: A method for optimizing delivery routes using drones and vehicles includes: Step S1: Obtain the location of all delivery points and the delivery needs; Step S2: Construct one or more combinations of constraints; Step S3: Treat the distribution center and all delivery points as nodes, and randomly generate a node sequence, wherein the first and last nodes in the node sequence are both distribution centers, and the remaining delivery points are randomly ordered between the first and last nodes; Step S4: Based on the current node sequence and all constraints, define the delivery attributes of each node as vehicle delivery node, drone delivery node, or docking point, and generate vehicle routes and one or more drone routes based on the delivery attributes of each node and the order of the nodes. Step S5: Generate the total delivery time based on the obtained vehicle routes and all drone routes; Step S6: After updating the node sequence using the optimization algorithm, repeat steps S3 to S5 multiple times, and generate a delivery plan by combining the vehicle route with the shortest total delivery time and all drone routes.

[0021] The combination of constraints includes at least the maximum payload constraint of the UAV, the maximum range constraint of the UAV, and the cooperative constraint of the UAV. Step S4 includes: Step S4-1: Define the delivery attributes of the first and last nodes in the node sequence as docking points, and select the first node in the node sequence as the first node; Step S4-2: Traverse from the current first node to the next node, and select the second node based on the maximum payload constraint and the maximum range constraint of the UAV; Step S4-3: Define the delivery attribute of the current second node as a docking point, and define the delivery attribute of all nodes between the first and second nodes that have not defined delivery attributes as drone delivery nodes; Step S4-4: Traverse from the current second node onwards, and select the third node based on the UAV cooperative constraints; Step S4-5: Define the nodes with undefined delivery attributes between the second and third nodes, as well as the third node, as vehicle delivery nodes; Step S4-6: Determine if there are still nodes with undefined delivery attributes. If yes, then make the third node the new first node and return to step S4-2; otherwise, execute step S4-7. Steps S4-8: Based on the delivery attributes of each node and the order of the nodes, generate vehicle routes and one or more drone routes.

[0022] Step S4-2 includes: Step S4-2-1: Select the next node with undefined delivery attributes after the current first node as the target node; Step S4-2-2: Determine whether all of the following conditions are true: The total distance from the first node through each node with undefined delivery attributes to the target node is less than the drone's maximum range. The total weight of goods delivered from the first node through each node with undefined delivery attributes to the target node is less than the maximum payload of the drone. If yes, then proceed to step S4-2-3; otherwise, proceed to step S4-2-4. Step S4-2-3: Take the next node of the current target node as the target node, and return to step S4-2-2; Step S4-2-4: Determine whether the current target node is the next node with undefined delivery attributes after the first node. If yes, then the current target node is taken as the second node; otherwise, the node preceding the current target node is taken as the second node.

[0023] Specifically, step S4-2-3 is as follows: determine whether the current target node is the second to last node in the node sequence. If it is, then take the current target node as the second node and execute step S4-3. Otherwise, take the next node of the current target node as the target node and return to step S4-2-2.

[0024] Step S4-4 includes: Step S4-4-1: Initialize the candidate node set to an empty set, and select the next node of the current second node as the target node; Step S4-4-2: Calculate the first time of the drone flight from the first node through each node with the delivery attribute of drone delivery node to the second node, and calculate the second time of the vehicle travel from the first node through each node with the undefined delivery attribute after the second node to the target node and then to the current target node. Step S4-4-3: Calculate whether the ratio of the second duration to the first duration falls within the first ratio range; Step S4-4-5: Determine whether the ratio of the second duration to the first duration is less than the left boundary of the first ratio interval. If yes, select the next node of the current target node as the target node and return to step S4-4-2. Otherwise, execute step S4-4-6. Step S4-4-6: Determine whether the ratio of the second duration to the first duration is within the first ratio range. If yes, add the current target node to the candidate node set, select the next node of the current target node as the target node, and return to step S4-4-2. Otherwise, execute step S4-4-7. Step S4-4-7: Determine whether the candidate node set is empty. If it is, proceed to step S4-6. Otherwise, select the node in the candidate node set that is closest to the midpoint of the first proportional interval as the third node.

[0025] Step S4-4-6 specifically includes: Step S4-4-6-1: Determine whether the ratio of the second duration to the first duration is within the first ratio range. If yes, proceed to step S4-4-6-2; otherwise, proceed to step S4-4-7. Step S4-4-6-2: Add the current target node to the candidate node set, and determine whether the current target node is the second to last node in the node sequence. If it is, proceed to step S4-4-7; otherwise, the next node of the current target node is taken as the target node, and return to step S4-4-2. The total delivery time is: in: The time when the vehicle arrives at the distribution center. Let k be the time when the drone arrives at the distribution center after its kth launch. To take the larger function, n is the number of nodes.

[0026] The optimization algorithm is the simulated annealing algorithm.

[0027] A device for optimizing delivery routes using drones and vehicles includes a memory, a processor, and a program stored in the memory, wherein the processor executes the program to implement the method described above.

[0028] A storage medium having a program stored thereon, which, when executed, implements the method described above.

[0029] Compared with the prior art, the present invention has the following beneficial effects: 1. This approach directly operates on the entire node sequence and generates a complete vehicle and drone path plan in one go, avoiding the computational complexity and efficiency losses associated with segmented optimization. Furthermore, the optimization objective is solely to minimize the total delivery time, abandoning the structure of multiple sub-objectives found in existing technologies. This eliminates interference between sub-objectives, allowing the optimization algorithm to search for the global optimum more directly and efficiently, and explicitly decoupling constraint combination from path generation. Different constraints can be flexibly integrated during the optimization process without altering the core optimization flow, providing a clear modular interface for adding new constraints later.

[0030] 2. The design identifies at least several core constraints, including the maximum payload of the UAV, the maximum range of the UAV, and the cooperative constraints of the UAV, and integrates them into an automated node attribute partitioning process. This design allows each type of constraint to be calculated and verified independently, realizing modular management of constraint conditions. A set of defined rules is used to transform a random node sequence into a unique feasible delivery solution that meets multiple constraints, thereby realizing single-layer optimization logic, greatly improving the optimization speed, and providing high-quality initial solutions or neighborhood solutions for subsequent optimization iterations.

[0031] 3. Ensure that the physical limitations of drones are strictly followed when planning drone delivery segments. By gradually testing and verifying cumulative distance and weight, the farthest node that a single drone flight can cover can be accurately determined, thus ensuring that each generated drone sub-path is actually feasible and improving the effectiveness and safety of the solution.

[0032] 4. Special handling for node sequence boundaries has been added, making the algorithm logic more rigorous and complete. It can correctly handle the special case where the drone has great potential and may cover almost all subsequent nodes until the end of the sequence, thus enhancing the algorithm's robustness and ability to handle various scenarios. 5. On the one hand, by introducing the ratio of the first duration to the second duration and setting a reasonable first ratio range, this mechanism aims to match drones and vehicles with similar work rhythms. This helps reduce the idle time of vehicles or drones waiting for the other party, thereby improving the overall collaborative efficiency of joint delivery. On the other hand, by screening candidate nodes whose ratios fall within a reasonable range and selecting the node closest to the midpoint of the range as the third node, this strategy tends to assign vehicles a delivery segment that matches the time consumption of the drone delivery segment that has just been completed. This promotes load balancing between the two types of transportation capacity and is conducive to further shortening the total completion time. Attached Figure Description

[0033] Figure 1 This is a schematic diagram of the main steps of the method of the present invention; Figure 2This is a diagram illustrating the delivery route; Figure 3 This is a schematic diagram of the optimization results of the present invention in the C-100 example; Figure 4 This is a schematic diagram of the optimization results of the present invention in the R-100 example; Figure 5 This is a schematic diagram of the optimization results of the present invention in the RC-100 example. Detailed Implementation

[0034] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0035] A method for optimizing delivery routes using drones and vehicles. In drone-vehicle joint delivery, drones and vehicles collaborate multiple times, with each drone launching from the vehicle. After completing a delivery to a customer's location, the drone needs to return to the vehicle for refueling, battery replacement, and to decide whether to carry cargo and launch again. The vehicle acts as both a resupply station and warehouse for the drones, while also fulfilling its own delivery tasks. Both drones and vehicles work together, based on customer distribution, to serve all customers.

[0036] Based on existing problems, this application expands the delivery capabilities of drones, enabling them to serve multiple customers after a single launch, provided they meet their payload and range requirements. For special nodes that drones cannot serve, the availability of drones is determined based on node type, increasing the number of selectable docking points and improving the efficiency of drone-vehicle collaboration. Furthermore, the goal is to maximize the number of customers served along the joint drone-vehicle delivery route, thereby improving drone utilization efficiency. Therefore, this paper makes the following assumptions: (1) The locations and demand of the distribution center and customer points are known, and the demand of the distribution center is 0; (2) All customer locations must be served, regardless of the time window restrictions of the customer locations; (3) The maximum payload and maximum endurance of the UAV are known; (4) Under the given constraints, a single launch of a UAV can serve multiple customer locations; (5) The vehicle's load capacity and range are not taken into account; (6) The vehicle must arrive at the docking point before the drone, and the drone must not hover at the docking point; (7) After each delivery, the drone must return to the vehicle to pick up the goods and replace the battery; (8) The pickup and battery replacement time for passenger drones is not taken into account; (9) The vehicle carries sufficient power for the drone.

[0037] Based on the above issues, the parameters used in the model building process are as follows.

[0038] — Node set, ,in, n For the number of customer points, The time indicates the distribution center; —A collection of customer needs ; —A set of customer locations that exceed the maximum payload limit of drones; these customer locations are referred to as "excessive priority locations". —A set of customer points whose distance from all other nodes exceeds the maximum flight time limit of the drone; these customer points are referred to as "extremely far points". —Customer collection points for drone delivery The subscript indicates the launch round of the drone; —The first drone The second launch will involve drone delivery to customer assembly points. —A collection point for customers of vehicle delivery services; —Meet at the stop. ; —A collection of drone launch sites; —A collection of drone recycling points; —Number of drone launches ; —Total number of customer locations; ——No. The number of customer points delivered by the drone on each launch; ——No. The number of customer points for each launch and vehicle delivery; --node The demand for goods; --node To the node Euclidean distance; —Maximum payload capacity of the drone; —Maximum flight time of the drone; —The average flight speed of the drone; —The average speed of the vehicle; —Road impedance coefficient; --Customer nodes delivered by drones Service hours; —By vehicle delivery customer nodes Service hours; —Vehicle arrives at the node At the moment, the initial ; —The first drone Second launch arrival node At the moment, the initial ; —A sufficiently large positive number; —Total time to return to the distribution center after serving all customer nodes; —Take 1, node If it is a stop point, then use 0; .

[0039] like Figure 1 As shown, the method of this application includes: Step S1: Obtain the location of all delivery points and the delivery needs; Step S2: Construct one or more combinations of constraints; The combination of constraints must include at least the maximum payload constraint of the UAV, the maximum range constraint of the UAV, and the cooperative constraint of the UAV. In other embodiments, the combination of constraints includes special point path constraints, UAV constraints, vehicle constraints, path cooperation constraints, and other constraints, wherein the maximum payload constraint and the maximum range constraint of the UAV belong to UAV constraints, and the UAV cooperation constraint belongs to path cooperation constraints.

[0040] Specifically, as follows: For special point route constraints, these special points are marked, and all marked points can only be delivered by vehicles. The super-weighted point, while meeting the drone's endurance limitations, can serve as the endpoint, or docking point, for a single delivery mission, supporting drone recovery. It's important to note that the inflow and outflow at this special point are not necessarily conserved; the drone can be launched from and recovered at any of these points.

[0041] (1) (2) (3) (4) (5) Formulas (1) and (2) indicate that the vehicle must go to the super-point and the super-far point; Formulas (3) and (4) indicate that the drone cannot go to the super-far point; Formula (5) indicates that if the drone flies to the super-point, the vehicle must go to the super-point.

[0042] Regarding the constraints of drones, in the joint delivery of drones and vehicles, under the condition of meeting the maximum payload and maximum flight time of drones, drones can give full play to their advantages of speed and efficiency and serve as the main delivery tool in task allocation. While completing their own delivery tasks, vehicles provide support for drones. Each launch and recovery is carried out on the vehicle. Drones only need to return to the vehicle for power replacement and cargo replenishment, without having to go to the delivery center again.

[0043] (6) (7) (8) (9) (10) (11) (12) (13) Formulas (6) and (7) indicate that the drone will definitely go to the customer delivered by the drone; Formula (8) indicates that the flow of drones entering and leaving all nodes is conserved; Formula (9) indicates that the drone will serve at least one customer each time it launches; Formula (10) indicates that the weight of the customer package that the drone can carry in one launch cannot exceed its maximum payload; Formula (11) indicates that the flight time of the drone in one launch cannot exceed its maximum endurance; Formulas (12) and (13) indicate that for each launch, the time when the drone arrives at the next node is the time when it arrives at the previous node plus the drone service time at that point and the drone flight time between the two nodes.

[0044] Regarding vehicle constraints, without considering the collaboration between the vehicle and the drone, the vehicle path approximates a traveling salesman's path. However, at each stop, the vehicle needs to complete the launch and recovery of the drone while providing services at that stop. To support the drone's flight, the vehicle needs to wait for the drone to return at the recovery point.

[0045] (14) (15) (16) (17) (18) Formulas (14) and (15) indicate that for customers delivered by vehicles, the vehicles will definitely go there; Formula (16) indicates that the flow of vehicles entering and leaving all nodes is conserved; Formulas (17) and (18) indicate that the time when a vehicle arrives at the next customer point is the time when it arrives at the previous point (non-recycling point) plus the vehicle service time at that point and the vehicle travel time between the two nodes.

[0046] Regarding collaborative constraints, including path collaboration constraints and docking point collaboration constraints, path collaboration is key in joint drone and vehicle delivery. For each customer point, reasonable task allocation is essential to improve delivery efficiency while fulfilling customer service needs. For delivery centers, whether drones are carried in and out by vehicles depends on specific task allocations. Drones can be launched and retrieved independently at the delivery center, but will not be launched again after retrieval. Furthermore, drones need to recharge after completing delivery tasks. However, current legal regulations regarding drones are not yet comprehensive, and hovering flight may be subject to various uncertainties (weather, signal, human factors, etc.). For safety reasons, drones cannot hover and wait at docking points; therefore, vehicles must arrive before the drones reach the docking points.

[0047] (19) (20) (twenty one) (twenty two) (twenty three) Formulas (19) and (20) indicate that drones and vehicles need to serve all customer nodes, and only one drone or vehicle can go to each customer node; Formulas (21) and (22) indicate that drones and vehicles can enter and exit the distribution center independently, or vehicles can carry drones to enter and exit together; Formula (23) indicates that the vehicle must arrive before the drone lands.

[0048] Docks are unique nodes in drone-vehicle joint delivery. They can be any customer location or distribution center. Drones and vehicles interact and collaborate at docks to launch or retrieve drones. Since drones cannot hover at docks, vehicles must wait at the retrieval point for the drone to return.

[0049] (twenty four) (25) (26) (27) (28) Formula (24) indicates that for a launch node, the drone and vehicle must leave once; Formula (25) indicates that for a recovery node, the drone and vehicle must enter once; Formulas (26) and (27) indicate that if the vehicle recovers the drone at the previous customer point, the time when the vehicle arrives at the next customer point is the greater of the time when the vehicle arrives at the recovery node plus the vehicle service time at that point and the time when the drone arrives at the recovery node, plus the vehicle travel time between the two nodes; Formula (28) indicates that for the case where the launch and recovery of the drone are at the same customer node, except for this case, the arrival time of the drone at other launch nodes is the time when the vehicle arrives at that point.

[0050] For other constraints (29) (30) (31) (32) Formulas (29) to (30) represent the range of values ​​for the parameters.

[0051] Step S3: Treat the distribution center and all delivery points as nodes, and randomly generate a node sequence. The first and last nodes in the node sequence are both distribution centers, and the remaining delivery points are randomly ordered between the first and last nodes. For example, given the following node sequence: {0,5,2,7,8,6,4,9,1,10,9,3,0}, its corresponding delivery path is as follows: Figure 2 As shown.

[0052] Step S4: Based on the current node sequence and all constraints, define the delivery attributes of each node as vehicle delivery node, drone delivery node, or docking point, and generate vehicle routes and one or more drone routes based on the delivery attributes of each node and the order of the nodes. Step S4 includes: Step S4-1: Define the delivery attributes of the first and last nodes in the node sequence as docking points, and select the first node in the node sequence as the first node; Step S4-2: Traverse from the current first node, and select the second node based on the drone's maximum payload constraint and maximum range constraint, including: Step S4-2-1: Select the next node with undefined delivery attributes after the current first node as the target node; Step S4-2-2: Determine whether all of the following conditions are true: The total distance from the first node through each node with undefined delivery attributes to the target node is less than the drone's maximum range. The total weight of goods delivered from the first node through each node with undefined delivery attributes to the target node is less than the maximum payload of the drone. If yes, then proceed to step S4-2-3; otherwise, proceed to step S4-2-4. Step S4-2-3: Take the next node of the current target node as the target node and return to step S4-2-2. Specifically, determine whether the current target node is the second to last node in the node sequence. If it is, take the current target node as the second node and execute step S4-3. Otherwise, take the next node of the current target node as the target node and return to step S4-2-2.

[0053] Step S4-2-4: Determine whether the current target node is the next node with undefined delivery attributes after the first node. If yes, then the current target node is taken as the second node; otherwise, the node preceding the current target node is taken as the second node.

[0054] Step S4-3: Define the delivery attribute of the current second node as a docking point, and define the delivery attribute of all nodes between the first and second nodes that have not defined delivery attributes as drone delivery nodes; Step S4-4: Traverse from the current second node onwards, selecting the third node based on UAV cooperative constraints, including: Step S4-4-1: Initialize the candidate node set to an empty set, and select the next node of the current second node as the target node; Step S4-4-2: Calculate the first time of the drone flight from the first node through each node with the delivery attribute of drone delivery node to the second node, and calculate the second time of the vehicle travel from the first node through each node with the undefined delivery attribute after the second node to the target node and then to the current target node. Step S4-4-3: Calculate whether the ratio of the second duration to the first duration falls within the first ratio range; Step S4-4-5: Determine whether the ratio of the second duration to the first duration is less than the left boundary of the first ratio interval. If yes, select the next node of the current target node as the target node and return to step S4-4-2. Otherwise, execute step S4-4-6. Step S4-4-6: Determine whether the ratio of the second duration to the first duration is within the first ratio range. If yes, add the current target node to the candidate node set, select the next node of the current target node as the target node, and return to step S4-4-2. Otherwise, execute step S4-4-7. Step S4-4-6 specifically includes: Step S4-4-6-1: Determine whether the ratio of the second duration to the first duration is within the first ratio range. If yes, proceed to step S4-4-6-2; otherwise, proceed to step S4-4-7. Step S4-4-6-2: Add the current target node to the candidate node set, and determine whether the current target node is the second to last node in the node sequence. If it is, proceed to step S4-4-7; otherwise, the next node of the current target node is taken as the target node, and return to step S4-4-2. Step S4-4-7: Determine whether the candidate node set is empty. If it is, proceed to step S4-6. Otherwise, select the node in the candidate node set that is closest to the midpoint of the first proportional interval as the third node.

[0055] Step S4-5: Define the nodes with undefined delivery attributes between the second and third nodes, as well as the third node, as vehicle delivery nodes; Step S4-6: Determine if there are still nodes with undefined delivery attributes. If yes, then make the third node the new first node and return to step S4-2; otherwise, execute step S4-7. Steps S4-8: Based on the delivery attributes of each node and the order of the nodes, generate vehicle routes and one or more drone routes.

[0056] Step S5: Generate the total delivery time based on the obtained vehicle routes and all drone routes; Step S6: After updating the node sequence using the optimization algorithm, repeat steps S3 to S5 multiple times, and generate a delivery plan by combining the vehicle route with the shortest total delivery time and all drone routes.

[0057] The total delivery time is: in: The time when the vehicle arrives at the distribution center. Let k be the time when the drone arrives at the distribution center after its kth launch. To take the larger function, n is the number of nodes.

[0058] In this embodiment, the optimization algorithm is the simulated annealing algorithm.

[0059] To verify the validity of this application, the path optimization model designed in this application was run on a computer. Since there are currently no specific examples to solve this type of problem, one set of data from different categories in the Solomon instance dataset was used to generate three different scales of 100, 50, and 25 nodes, for a total of 9 different sets of data.

[0060] To verify the effectiveness of the design algorithm, Chinese patent application CN113139678A was used as a comparative example. The method of this application and the comparative example were used for verification, and the results are shown in Table 1.

[0061] Table 1 The results show that the optimization rate of this application has been significantly improved, and the optimized results are as follows: Figures 3 to 4 As shown.

[0062] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A method for optimizing delivery routes using both drones and vehicles, comprising: Step S1: Obtain the location of all delivery points and the delivery needs; Its characteristic is that it further includes: Step S2: Construct one or more combinations of constraints; Step S3: Treat the distribution center and all delivery points as nodes, and randomly generate a node sequence, wherein the first and last nodes in the node sequence are both distribution centers, and the remaining delivery points are randomly ordered between the first and last nodes; Step S4: Based on the current node sequence and all constraints, define the delivery attributes of each node as vehicle delivery node, drone delivery node, or docking point, and generate vehicle routes and one or more drone routes based on the delivery attributes of each node and the order of the nodes. Step S5: Generate the total delivery time based on the obtained vehicle routes and all drone routes; Step S6: After updating the node sequence using the optimization algorithm, repeat steps S3 to S5 multiple times, and generate a delivery plan by combining the vehicle route with the shortest total delivery time and all drone routes.

2. The method for optimizing a joint delivery route using drones and vehicles according to claim 1, characterized in that, The combination of constraints includes at least the maximum payload constraint of the UAV, the maximum range constraint of the UAV, and the cooperative constraint of the UAV. Step S4 includes: Step S4-1: Define the delivery attributes of the first and last nodes in the node sequence as docking points, and select the first node in the node sequence as the first node; Step S4-2: Traverse from the current first node to the next node, and select the second node based on the maximum payload constraint and the maximum range constraint of the UAV; Step S4-3: Define the delivery attribute of the current second node as a docking point, and define the delivery attribute of all nodes between the first and second nodes that have not defined delivery attributes as drone delivery nodes; Step S4-4: Traverse from the current second node onwards, and select the third node based on the UAV cooperative constraints; Step S4-5: Define the nodes with undefined delivery attributes between the second and third nodes, as well as the third node, as vehicle delivery nodes; Step S4-6: Determine if there are still nodes with undefined delivery attributes. If yes, then make the third node the new first node and return to step S4-2; otherwise, execute step S4-7. Steps S4-8: Based on the delivery attributes of each node and the order of the nodes, generate vehicle routes and one or more drone routes.

3. The method for optimizing a joint delivery route using drones and vehicles according to claim 2, characterized in that, Step S4-2 includes: Step S4-2-1: Select the next node with undefined delivery attributes after the current first node as the target node; Step S4-2-2: Determine whether all of the following conditions are true: The total distance from the first node through each node with undefined delivery attributes to the target node is less than the drone's maximum range. The total weight of goods delivered from the first node through each node with undefined delivery attributes to the target node is less than the maximum payload of the drone. If yes, then proceed to step S4-2-3; otherwise, proceed to step S4-2-4. Step S4-2-3: Take the next node of the current target node as the target node, and return to step S4-2-2; Step S4-2-4: Determine whether the current target node is the next node with undefined delivery attributes after the first node. If yes, then the current target node is taken as the second node; otherwise, the node preceding the current target node is taken as the second node.

4. The method for optimizing a joint delivery route using drones and vehicles according to claim 3, characterized in that, Specifically, step S4-2-3 is as follows: determine whether the current target node is the second to last node in the node sequence. If it is, then take the current target node as the second node and execute step S4-3. Otherwise, take the next node of the current target node as the target node and return to step S4-2-2.

5. The method for optimizing a joint delivery route using drones and vehicles according to claim 2, characterized in that, Step S4-4 includes: Step S4-4-1: Initialize the candidate node set to an empty set, and select the next node of the current second node as the target node; Step S4-4-2: Calculate the first time of the drone flight from the first node through each node with the delivery attribute of drone delivery node to the second node, and calculate the second time of the vehicle travel from the first node through each node with the undefined delivery attribute after the second node to the target node and then to the current target node. Step S4-4-3: Calculate whether the ratio of the second duration to the first duration falls within the first ratio range; Step S4-4-5: Determine whether the ratio of the second duration to the first duration is less than the left boundary of the first ratio interval. If yes, select the next node of the current target node as the target node and return to step S4-4-2. Otherwise, execute step S4-4-6. Step S4-4-6: Determine whether the ratio of the second duration to the first duration is within the first ratio range. If yes, add the current target node to the candidate node set, select the next node of the current target node as the target node, and return to step S4-4-2. Otherwise, execute step S4-4-7. Step S4-4-7: Determine whether the candidate node set is empty. If it is, proceed to step S4-6. Otherwise, select the node in the candidate node set that is closest to the midpoint of the first proportional interval as the third node.

6. The method for optimizing a joint delivery route using drones and vehicles according to claim 5, characterized in that, Step S4-4-6 specifically includes: Step S4-4-6-1: Determine whether the ratio of the second duration to the first duration is within the first ratio range. If yes, proceed to step S4-4-6-2; otherwise, proceed to step S4-4-7. Step S4-4-6-2: Add the current target node to the candidate node set and determine whether the current target node is the second to last node in the node sequence. If yes, proceed to step S4-4-7; otherwise, the next node of the current target node is taken as the target node, and return to step S4-4-2.

7. The method for optimizing a joint delivery route using drones and vehicles according to claim 1, characterized in that, The total delivery time is: ； in: The time when the vehicle arrives at the distribution center. Let k be the time when the drone arrives at the distribution center after its kth launch. To take the larger function, n is the number of nodes.

8. The method for optimizing a joint delivery route using drones and vehicles according to claim 1, characterized in that, The optimization algorithm is the simulated annealing algorithm.

9. A device for optimizing delivery routes using both drones and vehicles, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1-8.

10. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements the method as described in any one of claims 1-8.

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