Vehicle and unmanned aerial vehicle cooperative distribution path planning method based on temporary waiting mode

Abstract

The invention discloses a vehicle and unmanned aerial vehicle cooperative distribution path planning method based on a temporary waiting mode, and the method comprises the steps: carrying out the preprocessing of a customer set, carrying out the clustering of the customer set served by a vehicle-mounted unmanned aerial vehicle based on the capacity of a truck, obtaining a clustering center and affiliated to-be-served customers, and obtaining an initial network; modifying the initial network, constructing a spatial expansion network, splitting each clustering center into an unmanned aerial vehicle virtual outflow node and a virtual inflow node, and introducing a corresponding virtual arc; establishing a mixed integer nonlinear programming model; performing objective function and soft time window constraint linearization processing on the mixed integer nonlinear programming model, and establishing an arc-based mixed integer linear programming model; and solving to obtain an optimal distribution scheme. According to the invention, complex constraints of multi-vehicle multi-unmanned aerial vehicle cooperative distribution can be systematically considered, distribution cost minimization and time window constraint satisfaction are realized, and a scientific and efficient scheduling planning scheme is provided for urban logistics and intelligent distribution.

Description

Technical Field

[0001] This invention belongs to the field of logistics distribution and intelligent scheduling technology, and relates to delivery route planning technology, specifically to a method for collaborative delivery route planning of vehicles and drones based on a temporary waiting mode. Background Technology

[0002] With the rapid growth of e-commerce and on-demand delivery demands, traditional pure vehicle delivery models are increasingly showing their shortcomings in terms of efficiency, cost, and flexibility, making it difficult to meet the timeliness and diversity requirements of last-mile delivery in cities. Drones, as an emerging delivery tool, offer advantages such as mobility, high transportation efficiency, and immunity to ground traffic congestion, and have received widespread attention and are being explored for application in last-mile logistics. However, drones are limited by their range and payload capacity, making it difficult for them to handle complex delivery tasks for large-scale, multi-type customers when used alone. Therefore, a truck-drone collaborative delivery model is gradually emerging, leveraging the long-distance transport capabilities of trucks and the flexible coverage advantages of drones to achieve synergistic optimization of cost and efficiency.

[0003] Existing research primarily focuses on single-truck-single-drone collaborative models, often based on idealized and simplified assumptions. These assumptions include ignoring vehicle and drone capacity limitations, mileage constraints, and customer service time windows, or considering only a single customer visit. While these models have theoretical value, they are ill-suited for large-scale urban logistics scenarios. Furthermore, some studies fail to consider practical operational factors such as heterogeneous fleets (e.g., the coexistence of drones operating independently and those relying on trucks), truck waiting synchronization mechanisms, and the need for multiple customer visits, thus limiting the models' applicability and generalizability.

[0004] Therefore, a new technological solution is needed to address these issues. Summary of the Invention

[0005] Purpose of the invention: To address the problems of constraint simplification, neglect of heterogeneity, and poor algorithm adaptability in existing truck-drone collaborative delivery models, this invention provides a vehicle-drone collaborative delivery path planning method based on a temporary waiting mode. This method can systematically consider the complex constraints of multi-vehicle and multi-drone collaborative delivery, minimize delivery costs and satisfy time window constraints, and provide a scientific and efficient scheduling and planning solution for urban logistics and intelligent delivery.

[0006] Technical Solution: To achieve the above objectives, this invention provides a method for collaborative delivery route planning between vehicles and drones based on a temporary waiting mode, comprising the following steps:

[0007] S1: Preprocess the customer set by dividing the customers into the customer set served by independent drones and the customer set served by vehicle-mounted drones according to the given drone service radius. Then, cluster the customer set served by vehicle-mounted drones based on the truck capacity to obtain the cluster center and its associated customers to be served, thus obtaining the initial network.

[0008] S2: Modify the initial network to construct a spatially extended network, split each cluster center into virtual outflow nodes and virtual inflow nodes for drones, and introduce corresponding virtual arcs to eliminate sub-loops in multi-drone path planning and allow trucks to wait temporarily.

[0009] S3: Define the truck arc, the vehicle-mounted drone arc, the independent drone arc, and their corresponding time, access order, and waiting variables; establish a mixed-integer nonlinear programming model based on arcs, considering time windows, capacity constraints, distance constraints, and multiple access modes of drones.

[0010] S4: Linearize the objective function and soft time window constraints of the mixed integer nonlinear programming model to establish an arc-based mixed integer linear programming model;

[0011] S5: Solve the mixed-integer linear programming model precisely to obtain the optimal delivery plan;

[0012] S6: Based on the solution results, the preprocessing results or local scheduling of the solution in step S1 can be further adjusted to adapt to actual operational needs.

[0013] Furthermore, the preprocessing in step S1 includes:

[0014] A1: Based on the spatial distribution of the parking lot and customers, customers are assigned according to the given service radius γL of the drone. d The customers are divided into two groups: S0, which is served by independent drones, and S1, which is served by vehicle-mounted drones.

[0015] A2: Based on the classification results, and considering the truck capacity Q t Clustering the customer set S1 served by the vehicle-mounted drone yields several cluster centers c∈C and their associated unserved customers N. c .

[0016] Further, step A1 specifically includes:

[0017] Centered on the starting point parking lot O, construct a system with a given unmanned aerial vehicle (UAV) service radius γL. d A circle with radius L, where L dγ is the maximum flight distance of the drone, and γ is the safety factor. To ensure that the drone can return smoothly, its value ranges from 0 to γ ​​to 0.5. Customers within this circle are classified into a customer set S0 served by independent drones, while customers outside the circle are classified into a customer set S1 served by vehicle-mounted drones.

[0018] Further, step A2 specifically includes:

[0019] For a customer set S1 served by vehicle-mounted drones, a K-means clustering method that considers both truck capacity and drone service radius is used to obtain several cluster centers c∈C and their corresponding customer subsets. For each customer subset N c The following constraints must be met:

[0020] It contains customers s∈N c Total demand It must not exceed the vehicle capacity Q t Furthermore, the spatial distribution radius of customers within the subset must not exceed γL. d (0<γ<0.5) to ensure that the delivery task can be completed smoothly.

[0021] Furthermore, in step S2, the initial network is modified to construct a spatially extended network. The specific steps are as follows:

[0022] B1: Construct virtual nodes, introducing a virtual destination parking lot D corresponding to the starting parking lot O. The two are spatially identical but distinguished by different spatial indices. For all cluster center nodes c∈C, split them at the same spatial location to generate two types of virtual nodes: drone outflow nodes c-∈C. - and the drone flowing into node c+∈C + The two nodes have the same spatial location but different indices to distinguish the departure and return flows of UAVs in the modeling process. Thus, all nodes in the network can be represented as N = {O, D} ∪ S0 ∪ S1 ∪ C - ∪C + ;

[0023] B2: Construct virtual arcs. In addition to the existing connection arcs between parking lots and customer nodes, and between customer nodes, for each cluster center node c∈C, establish a virtual arc from the drone outgoing node c-∈C on its corresponding virtual node. + The drone flows into node c+∈C +A directed connection arc (c-, c+) is introduced, which represents the behavior of a drone staying on the vehicle without performing a delivery task, and also represents the behavior of a truck staying in place after launching a drone at the cluster center and waiting to retrieve it; similarly, a directed connection arc (O, D) is introduced from the virtual starting point vehicle yard O to the virtual ending point vehicle yard D to ensure the integrity of the path of the extra drones and extra vehicles carried during the transportation process.

[0024] Furthermore, step S3 specifically includes:

[0025] C1: Define decision variables, including: truck arc route 0-1 variables. Indicates whether the truck k∈K transports along the arc (i,j); the arc route of the vehicle-mounted drone is a 0-1 variable. Indicates whether the vehicle-mounted drone l∈L1 performs delivery along the arc (i,j) with the truck k∈K; independent drone arc variable, arc route 0-1 variable. Let l∈L0 represent whether an independent drone performs delivery along arc (i,j). For the above 0-1 decision variables, 1 means choosing to travel along that arc, and 0 means not choosing it.

[0026] C2: Define auxiliary decision variables, including: non-negative continuous-time variables. and These are used to track the routing and time relationships of three types of vehicles: trucks, vehicle-mounted drones, and stand-alone drones; non-negative sequential access order variables. and Let $i$ represent the order in which trucks, vehicle-mounted drones, and stand-alone drones access node $i$, respectively, to break sub-loops; non-negative consecutive truck waiting variables. This represents the temporary dwell time of the truck at cluster node i;

[0027] C3: Based on the defined variables, establish the objective function of the model;

[0028] C4: Constraints for establishing the model.

[0029] Furthermore, in step C3, F1, F2, and F3 represent the fixed outbound cost of the truck and the drone, the route cost, and the penalty for violating the time window, respectively, to establish the objective function:

[0030] min F1+F2+F3 (1)

[0031]

[0032] Here, F1 represents the total fixed usage cost of trucks and drones, F2 represents the total route cost, and F3 represents the penalty for violating the time window rule.

[0033] Furthermore, the constraints of the model in step C4 include customer service constraints for trucks and drones, network flow constraints, node access synchronization and logic constraints, mileage limit constraints, capacity constraints, sub-loop breaking constraints, and time resource expansion constraints, specifically expressed as follows:

[0034]

[0035]

[0036] The meanings of the constraints are explained as follows: Constraints (5)-(7) specify the service requirements, ensuring that each cluster center must be accessed by trucks and that each customer can receive delivery services from drones; Constraints (8)-(11) define the network flow balance of trucks, requiring each truck to start from the starting warehouse O and reach the destination warehouse D, maintaining flow conservation at intermediate cluster nodes. Since each cluster is split into two types of virtual nodes, c- and c+, the corresponding flow conservation conditions are described separately; Constraints (12)-(14) control the flow balance of vehicle-mounted drones, which are similar in form to the flow constraints of trucks, but with the additional condition that vehicle-mounted drones are only allowed to start from c- and return to c+ when the corresponding truck accesses cluster center c; Constraints (15)-(17) define the network flow constraints of independent drones, ensuring the feasibility of their origin, destination and access paths; Constraint (18) further strengthens the consistency between vehicles and drones, that is, drones can only depart from a cluster center to perform tasks when a truck visits a cluster center, indicating that drone launch and recovery can only be carried out in the cluster center; Constraints (19)-(21) limit the maximum driving distance of trucks and drones to ensure that they operate within their range; Constraints (22)-(24) impose capacity constraints on the cumulative delivery load of trucks and drones; Constraints (25)-(27) use MTZ-type constraints to eliminate sub-loops in the paths of trucks and drones; Constraints (28)-(34) characterize the temporal dynamics of truck and drone access nodes through resource expansion mechanisms, tending to allow services to be completed within a specified time window; Finally, Constraints (35)-(37) give the range of values ​​for decision variables, thus fully defining the feasible solution space of the model.

[0037] Furthermore, in step S4, the time window penalty term in the model objective function is linearized to establish an arc-based mixed-integer linear programming model. The specific steps are as follows:

[0038] D1: Introduce auxiliary variables for the non-linear operators involving the positive and negative parts in the time window penalty term. Let $\mathbf$ and $\mathbf$ represent the lead time and delay when a vehicle-mounted drone (l\mathbf$) serves customer $i\mathbf$ on a vehicle (k\mathbf$). These values ​​are zero if no violation occurs. Additionally, an auxiliary variable is introduced to represent the case where an independent drone (l\mathbf$) directly serves customer $i\mathbf$ from the warehouse. The corresponding time window deviation is represented and reconstructed in the objective function in a linear form, as shown in constraints (38)-(39), thereby realizing the piecewise penalty for advance and delay;

[0039]

[0040] D2: To ensure that the auxiliary variables can accurately reflect the deviation between customer service time and its time window, corresponding disjunctive constraints are constructed: constraints (40)-(41) specify the relationship between the advance and delay of vehicle-mounted drones, and constraints (42)-(43) specify the relationship between the advance and delay of independent drones. The activation state of the constraints is controlled by a sufficiently large constant M. Combined with the minimization effect of the objective function, the auxiliary variables are kept at zero when there is no default, and the corresponding advance or lag deviation is accurately recorded when there is a default. After this linearization process, the original model (1)-(37) is reconstructed into a mixed integer linear programming (MILP) model containing (1)-(3), (5)-(37) and (38)-(43).

[0041]

[0042] Furthermore, in step S5, the objective function and the constraint system are solved jointly by calling a commercial solver. Based on the values ​​of the decision variables, all arcs with variable values ​​equal to 1 are plotted to obtain the optimal decision scheme, which includes truck path, UAV task allocation and launch and recovery node selection, waiting time of each vehicle and time window penalty.

[0043] If an infeasible solution is encountered during the solution process, the node sets contained in the customer's classification results S0 and S1 can be further adjusted reasonably.

[0044] This invention addresses the delivery scheduling problem under a temporary truck waiting synchronous mode, taking into account the path planning, time window constraints, capacity and mileage limitations of both trucks and heterogeneous drones, aiming to minimize the total delivery cost, including fixed dispatch cost, driving cost and time window penalty cost.

[0045] This invention can systematically consider the complex constraints of multi-vehicle and multi-drone collaborative delivery, minimize delivery costs and satisfy time window constraints, and provide a scientific and efficient scheduling and planning scheme for urban logistics and intelligent delivery.

[0046] Beneficial effects: Compared with the prior art, the present invention has the following advantages:

[0047] 1. Propose a new collaborative mode: This invention introduces a multi-vehicle and multi-drone collaborative delivery framework under the temporary waiting mode in the path planning for the first time, which takes into account the synchronous and asynchronous collaboration between trucks and drones, and improves the flexibility and coordination of the system.

[0048] 2. Comprehensive utilization of heterogeneous drones: By introducing a heterogeneous combination of independent drones and vehicle-mounted drones, the scheduling flexibility and resource utilization efficiency of drones are enhanced, and the adaptability in complex environments is improved.

[0049] 3. Refined modeling capability: Constructs an arc-based mixed integer programming model that integrates key real-world factors such as capacity constraints, mileage limits, soft time windows, and multiple accesses, enabling it to accurately depict the operational mechanisms in actual delivery networks.

[0050] 4. Preprocessing and network modification mechanisms: The project proposes methods such as customer set partitioning, capacity-based clustering, virtualization of cluster center nodes, and introduction of directed virtual arc design between two points, which effectively reduce model complexity, eliminate sub-loop and redundant scheduling problems, and improve solution efficiency.

[0051] 5. Linear processing of soft time windows: The soft time window linearization method is introduced into the modeling process to transform the model from a non-linear model to a linear model. This can balance service quality and scheduling cost, and realize flexible scheduling under time window constraints. It has higher practicality and promotion value than the existing single-vehicle single-machine or simplified model. Attached Figure Description

[0052] Figure 1 This is a flowchart of the method of the present invention;

[0053] Figure 2 This is a schematic diagram illustrating how customers are divided into two groups served by different types of drones in this invention;

[0054] Figure 3 This is a schematic diagram illustrating how vehicle-mounted drone customers are divided into several subsets according to clustering in this invention;

[0055] Figure 4 This is a schematic diagram of the extended network in which virtual nodes and virtual arcs are introduced in this invention;

[0056] Figure 5 This is a schematic diagram of the optimal path results for trucks and drones in this invention;

[0057] Figure 6 The network used for calculation in Example 2;

[0058] Figure 7 This is a diagram showing the customer segmentation and clustering results in Example 2;

[0059] Figure 8This is the modified spatial extension network diagram in Example 2;

[0060] Figure 9 This is the optimal path solution for the truck drone in Example 2. Detailed Implementation

[0061] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0062] Example 1:

[0063] like Figure 1 As shown, this embodiment provides a method for collaborative delivery route planning between vehicles and drones based on a temporary waiting mode, including the following steps:

[0064] S1: Preprocess the customer set by dividing the customers into the customer set served by independent drones and the customer set served by vehicle-mounted drones according to the given drone service radius. Then, cluster the customer set served by vehicle-mounted drones based on the truck capacity to obtain the cluster center and its associated customers to be served, thus obtaining the initial network.

[0065] S2: Modify the initial network to construct a spatially extended network, split each cluster center into virtual outflow nodes and virtual inflow nodes for drones, and introduce corresponding virtual arcs to eliminate sub-loops in multi-drone path planning and allow trucks to wait temporarily.

[0066] S3: Define the truck arc, the vehicle-mounted drone arc, the independent drone arc, and their corresponding time, access order, and waiting variables; establish a mixed-integer nonlinear programming model based on arcs, considering time windows, capacity constraints, distance constraints, and multiple access modes of drones.

[0067] S4: Linearize the objective function and soft time window constraints of the mixed integer nonlinear programming model to establish an arc-based mixed integer linear programming model;

[0068] S5: Solve the mixed-integer linear programming model precisely to obtain the optimal delivery plan;

[0069] S6: Based on the solution results, the preprocessing results or local scheduling of the solution in step S1 can be further adjusted to adapt to actual operational needs.

[0070] The preprocessing in step S1 includes:

[0071] A1: Based on the spatial distribution of the parking lot and customers, customers are assigned according to the given service radius γL of the drone.d The customers are divided into two groups: S0, which is served by independent drones, and S1, which is served by vehicle-mounted drones.

[0072] Centered on the starting point parking lot O, construct a system with a given unmanned aerial vehicle (UAV) service radius γL. d A circle with radius L, where L d Let γ be the maximum flight distance of the drone, and γ be a safety factor, which takes a value of 0 < γ < 0.5 to ensure the drone can return smoothly. Customers falling within this circle are classified into a customer set S0 served by independent drones, while customers outside the circle are classified into a customer set S1 served by vehicle-mounted drones. The classification results are as follows: Figure 2 As shown.

[0073] A2: Based on the classification results, and considering the truck capacity Q t Clustering the customer set S1 served by the vehicle-mounted drone yields several cluster centers c∈C and their associated unserved customers N. c ;

[0074] For a customer set S1 served by vehicle-mounted drones, a K-means clustering method that considers both truck capacity and drone service radius is used to obtain several cluster centers c∈C and their corresponding customer subsets. For each customer subset N c The following constraints must be met:

[0075] It contains customers s∈N c Total demand It must not exceed the vehicle capacity Q t Furthermore, the spatial distribution radius of customers within the subset must not exceed γL. d (0<γ<0.5) to ensure the delivery task can be completed smoothly. The clustering results are as follows: Figure 3 As shown.

[0076] In step S2, the initial network is modified to construct a spatially extended network. The specific steps are as follows:

[0077] B1: Construct virtual nodes, introducing a virtual destination parking lot D corresponding to the starting parking lot O. The two are spatially identical but distinguished by different spatial indices. For all cluster center nodes c∈C, split them at the same spatial location to generate two types of virtual nodes: drone outflow nodes c-∈C. - and the drone flowing into node c+∈C + The two nodes have the same spatial location but different indices to distinguish the departure and return flows of UAVs in the modeling process. Thus, all nodes in the network can be represented as N = {O, D} ∪ S0 ∪ S1 ∪ C - ∪C + The introduction of virtual nodes, such as Figure 4 As shown;

[0078] B2: Construct virtual arcs. In addition to the existing connection arcs between parking lots and customer nodes, and between customer nodes, for each cluster center node c∈C, establish a virtual arc from the drone outgoing node c-∈C on its corresponding virtual node. + The drone flows into node c+∈C + A directed connection arc (c-, c+) is introduced, which represents the behavior of a drone staying on the vehicle without performing a delivery task, and also represents the behavior of a truck staying in place after launching a drone at the cluster center and waiting to retrieve it; similarly, a directed connection arc (O, D) is introduced from the virtual starting point vehicle yard O to the virtual ending point vehicle yard D to ensure the integrity of the path of the extra drones and extra vehicles carried during the transportation process.

[0079] Step S3 specifically includes:

[0080] C1: Define decision variables, including: truck arc route 0-1 variables. Indicates whether the truck k∈K transports along the arc (i,j); the arc route of the vehicle-mounted drone is a 0-1 variable. Indicates whether the vehicle-mounted drone l∈L1 performs delivery along the arc (i,j) with the truck k∈K; independent drone arc variable, arc route 0-1 variable. Let l∈L0 represent whether an independent drone performs delivery along arc (i,j). For the above 0-1 decision variables, 1 means choosing to travel along that arc, and 0 means not choosing it.

[0081] C2: Define auxiliary decision variables, including: non-negative continuous-time variables. and These are used to track the routing and time relationships of three types of vehicles: trucks, vehicle-mounted drones, and stand-alone drones; non-negative sequential access order variables. and Let $i$ represent the order in which trucks, vehicle-mounted drones, and stand-alone drones access node $i$, respectively, to break sub-loops; non-negative consecutive truck waiting variables. This represents the temporary dwell time of the truck at cluster node i;

[0082] C3: Based on the defined variables, establish the objective function of the model;

[0083] Let F1, F2, and F3 represent the fixed outbound cost of trucks and drones, the route cost, and the penalty for violating the time window, respectively. Establish the objective function as follows:

[0084] min F1+F2+F3 (1)

[0085]

[0086] Here, F1 represents the total fixed usage cost of trucks and drones, F2 represents the total route cost, and F3 represents the penalty for violating the time window rule.

[0087] C4: Establish the constraints for the model, including customer service constraints for trucks and drones, network flow constraints, node access synchronization and logic constraints, mileage limit constraints, capacity constraints, sub-loop breaking constraints, and time resource expansion constraints, specifically expressed as follows:

[0088]

[0089]

[0090]

[0091] The meanings of the constraints are explained as follows: Constraints (5)-(7) specify the service requirements, ensuring that each cluster center must be accessed by trucks and that each customer can receive delivery services from drones; Constraints (8)-(11) define the network flow balance of trucks, requiring each truck to start from the starting warehouse O and reach the destination warehouse D, maintaining flow conservation at intermediate cluster nodes. Since each cluster is split into two types of virtual nodes, c- and c+, the corresponding flow conservation conditions are described separately; Constraints (12)-(14) control the flow balance of vehicle-mounted drones, which are similar in form to the flow constraints of trucks, but with the additional condition that vehicle-mounted drones are only allowed to start from c- and return to c+ when the corresponding truck accesses cluster center c; Constraints (15)-(17) define the network flow constraints of independent drones, ensuring the feasibility of their origin, destination and access paths; Constraint (18) further strengthens the consistency between vehicles and drones, that is, drones can only depart from a cluster center to perform tasks when a truck visits a cluster center, indicating that drone launch and recovery can only be carried out in the cluster center; Constraints (19)-(21) limit the maximum driving distance of trucks and drones to ensure that they operate within their range; Constraints (22)-(24) impose capacity constraints on the cumulative delivery load of trucks and drones; Constraints (25)-(27) use MTZ-type constraints to eliminate sub-loops in the paths of trucks and drones; Constraints (28)-(34) characterize the temporal dynamics of truck and drone access nodes through resource expansion mechanisms, tending to allow services to be completed within a specified time window; Finally, Constraints (35)-(37) give the range of values ​​for decision variables, thus fully defining the feasible solution space of the model.

[0092] In step S4, the time window penalty term in the model objective function is linearized to establish an arc-based mixed-integer linear programming model. The specific steps are as follows:

[0093] D1: Introduce auxiliary variables for the non-linear operators involving the positive and negative parts in the time window penalty term. Let $\mathbf$ and $\mathbf$ represent the lead time and delay when a vehicle-mounted drone (l\mathbf$) serves customer $i\mathbf$ on a vehicle (k\mathbf$). These values ​​are zero if no violation occurs. Additionally, an auxiliary variable is introduced to represent the case where an independent drone (l\mathbf$) directly serves customer $i\mathbf$ from the warehouse. The corresponding time window deviation is represented and reconstructed in the objective function in a linear form, as shown in constraints (38)-(39), thereby realizing the piecewise penalty for advance and delay;

[0094]

[0095] D2: To ensure that the auxiliary variables can accurately reflect the deviation between customer service time and its time window, corresponding disjunctive constraints are constructed: constraints (40)-(41) specify the relationship between the advance and delay of vehicle-mounted drones, and constraints (42)-(43) specify the relationship between the advance and delay of independent drones. The activation state of the constraints is controlled by a sufficiently large constant M. Combined with the minimization effect of the objective function, the auxiliary variables are kept at zero when there is no default, and the corresponding advance or lag deviation is accurately recorded when there is a default. After this linearization process, the original model (1)-(37) is reconstructed into a mixed integer linear programming (MILP) model containing (1)-(3), (5)-(37) and (38)-(43).

[0096]

[0097] In step S5, a commercial solver is used to jointly solve the objective function and the constraint system. Based on the values ​​of the decision variables, all arcs with a variable value of 1 are plotted, yielding the optimal decision scheme, which includes the truck path, UAV task allocation and launch / recovery node selection, vehicle waiting time, and time window penalties. The optimal solution describes the path results for the truck and UAV as follows: Figure 5 As shown;

[0098] If an infeasible solution is encountered during the solution process, the node sets contained in the customer's classification results S0 and S1 can be further adjusted reasonably.

[0099] Example 2:

[0100] To verify the effectiveness and results of the method of the present invention, this embodiment applies the method to an example, and the following is a detailed explanation in conjunction with solving a 15-node network:

[0101] Solution results and analysis of the 15-node network:

[0102] First, the network used for calculation in this embodiment is as follows: Figure 6As shown, a square area of ​​7000m x 7000m is covered. The coordinates of parking lot 0 are (2000, 4000). The customer indexes are 1 to 14, with coordinates of (1000, 5000), (2000, 5000), (3000, 4000), (2000, 3000), (1000, 4000), (4000, 5000), (5000, 6000), (6000, 5000), (6000, 3000), (5000, 2000), (7000, 1000), (0, 2000), (1000, 0), (2000, 1000). The coordinate unit is meters. Customer requirements are represented in parentheses in the diagram as follows: 4, 2, 2, 3, 1, 2, 3, 1, 1, 3, 1, 2, 2, 4.

[0103] Next, the customers are divided into two sets: S0, which is served by individual drones, and S1, which is served by vehicle-mounted drones. Customer set S1 is then clustered to obtain corresponding cluster centers, which serve as nodes for launching, waiting for, and retrieving drones from the vehicle. The coordinates are (5000, 5000), (6000, 2000), and (2000, 1000), respectively, with indices 15, 16, and 17. Figure 7 As shown in the figure, the partitioning results show that the customer set for individual drone services is S0 = {1,2,3,4,5}, while the customer set for vehicle-mounted drone services is S1 = {6,7,8,9,10,11,12,13,14}. For each cluster center, the customer set radiating from it can be described as: N 15 ={6,7,8}, N 16 ={9,10,11}, N 17 ={12,13,14}, which respectively satisfy the maximum flight range constraint of the UAV and the capacity constraint of the truck.

[0104] Then, to facilitate modeling, corresponding virtual nodes for the parking lot and cluster centers, as well as virtual arcs, are introduced to modify the network, resulting in the corresponding spatially extended network, such as... Figure 8 As shown. The origin and destination parking lots O and D are represented by indices 0 and 21 respectively; the set of clustered nodes from which the drones flow is C. - ={15,16,17}, while the human and machine flow into the cluster node set C. + ={18,19,20}. The spatial extension network used for modeling is now complete, containing a total of 22 nodes.

[0105] Based on this, the relevant parameter values ​​in the problem are set as shown in Table 1. For the customer set S0 = {1, 2, 3, 4, 5} of a single drone service, the time window is uniformly set to 0 seconds to 100 seconds (a s=0, b s =100), while the time window for the customer set S1 = {6,7,8,9,10,11,12,13,14} of the vehicle-mounted drone service is uniformly set to 0 seconds to 150 seconds (a s =0, b s =150), in the whole system, a total of two trucks are set up to serve customers, each truck carries two drones to provide delivery services for customer group S0. In addition, a total of three independent drones are set up to take off directly from the parking lot to provide delivery services for customer group S1.

[0106] Table 1. Parameter settings for the model in the embodiment.

[0107]

[0108] The model was solved using the Gurobi solver in 0.56 seconds, with an optimal value of 1684.56 yuan. The arcs with values ​​of 1 in the decision variables were plotted online, allowing visualization of the optimal solution. Figure 9 As shown.

Claims

1. A temporary waiting mode based vehicle and UAV cooperative delivery path planning method, characterized in that, The method comprises the following steps: S1: preprocessing the customer set, dividing the customers into a customer set served by independent drones and a customer set served by truck-mounted drones according to a given drone service radius, clustering the customer set served by the truck-mounted drones based on truck capacity to obtain a clustering center and its affiliated customers to be served, and obtaining an initial network; S2: modifying the initial network to construct a spatial expansion network, splitting each clustering center into a virtual outflow node and a virtual inflow node of a drone, and introducing corresponding virtual arcs to eliminate sub-loops in multi-drone path planning and allow the truck to temporarily wait; S3: defining truck arcs, truck-mounted drone arcs, independent drone arcs, and their corresponding time, access order, and waiting variables, and establishing a mixed integer nonlinear programming model based on arcs, considering time windows, capacity constraints, distance constraints, and multi-access modes of drones; S4: linearizing the objective function and soft time window constraints of the mixed integer nonlinear programming model to establish a mixed integer linear programming model based on arcs; S5: precisely solving the mixed integer linear programming model to obtain an optimal distribution scheme; S6: based on the solution, the preprocessing results of step S1 or the local scheduling of the solution can be further adjusted to adapt to actual operation requirements. 2.The temporary waiting mode based vehicle and UAV cooperative delivery path planning method of claim 1, wherein, The preprocessing in step S1 comprises: A1: According to the spatial distribution of parking lots and customers, customers are divided into a customer set S0 served by independent drones and a customer set S1 served by drones on vehicles according to the service radius γL of a given drone d A1: According to the spatial distribution of parking lots and customers, customers are divided into a customer set S0 served by independent drones and a customer set S1 served by drones on vehicles according to the service radius γL of a given drone A2: Based on the classification result, the truck capacity Q t Cluster the customer set S1 served by the UAV to obtain a number of clustering centers c e C and their affiliated customers to be served N c . 3.The temporary waiting mode based path planning method for vehicle and UAV cooperative delivery according to claim 2, wherein, The step A1 specifically comprises: With the starting point of the garage O as the center, a circle with a given UAV service radius γL d is constructed, where L d is the maximum flight distance of the UAV, and γ is the safety factor; the customers falling within the range of the circle are divided into a customer set S0 served by independent UAVs, and the customers outside the circle are divided into a customer set S1 served by the vehicle-mounted UAVs. 4.The temporary waiting mode based vehicle and UAV cooperative delivery path planning method of claim 3, wherein, The step A2 specifically comprises: For the customer set S1 served by the UAV on the truck, the K-means clustering method considering both the truck capacity and the UAV service radius is adopted to obtain a number of clustering centers c∈C and their corresponding customer subsets For each customer subset N c , the following constraint conditions need to be met: It contains the sum of demands of customers s ∈ N c The sum of demands of customers s ∈ N The sum of demands of customers s ∈ N t The sum of demands of customers s ∈ N d The sum of demands of customers s ∈ N 5.The temporary waiting mode based vehicle and UAV cooperative delivery path planning method of claim 4, wherein, The step S2 of modifying the initial network to construct a spatial expansion network comprises the following specific steps: B1: Construct virtual nodes, introduce a virtual end station D corresponding to the starting station O, which are the same in space but distinguished by different space indexes; for all cluster center nodes c∈C, split at the same spatial position to generate two types of virtual nodes: UAV outflow nodes c-∈C - and UAV inflow nodes c+∈C + , which are the same in space but different in index to distinguish the departure and return flow of UAV in modeling, so that all nodes in the network are represented as N={O,D}∪S0∪S1∪C - ∪C + ; B2: Construct virtual arcs. In addition to the existing connection arcs between parking lots and customer nodes, and between customer nodes, for each cluster center node c∈C, establish a virtual arc from the drone outgoing node c-∈C on its corresponding virtual node. + The drone flows into node c+∈C + A directed connection arc (c-, c+) is introduced, which represents the behavior of the drone staying on the vehicle without performing the delivery task, and also represents the behavior of the truck staying in place after launching the drone at the cluster center point and waiting to retrieve it; a directed connection arc (O, D) is introduced from the virtual starting point vehicle yard O to the virtual ending point vehicle yard D to ensure the integrity of the path of the extra drones and extra vehicles carried during the transportation process. 6.The temporary waiting mode based vehicle and UAV cooperative delivery path planning method of claim 5, wherein, The step S3 specifically comprises: C1: Define decision variables, introduce including: truck arc route 0-1 variable denotes whether truck k e K transports along arc (i,j); drone on truck arc route 0-1 variable denotes whether drone on truck l e L1 performs delivery along arc (i,j) with truck k e K; independent drone arc variable arc route 0-1 variable denotes whether independent drone l e L0 performs delivery along arc (i,j), for the above 0-1 decision variable, 1 means to choose this arc to drive, 0 is not selected; C2: define auxiliary decision variables, introduce: non-negative continuous time variables and are used to track the relationship between the route and time of the three types of vehicles: trucks, drones on trucks, and independent drones; non-negative continuous access order variables and represent the order of the three types of vehicles accessing node i: trucks, drones on trucks, and independent drones, which are used to break sub-loops; non-negative continuous truck waiting variables represent the temporary stay time of the truck at the cluster node i; C3: based on the defined variables, establish the objective function of the model; C4: establish the constraint conditions of the model.

7. The temporary waiting mode based vehicle and UAV cooperative delivery path planning method of claim 6, wherein, In the step C3, F1, F2, and F3 represent the fixed warehouse-out cost of the truck and the drone, the driving route cost, and the penalty for violating the time window, respectively, and the objective function is established as: min F1+F2+F3 (1) Wherein, F1 represents the total fixed use cost of the truck and the drone, F2 represents the total path cost, and F3 represents the penalty for violating the time window rule. 8.The temporary waiting mode based vehicle and UAV cooperative delivery path planning method of claim 7, wherein, In the step C4, the constraint conditions of the model include customer service constraints of the truck and the drone, network flow constraints, node access synchronization and logic constraints, driving distance limit constraints, capacity constraints, sub-loop constraints, and time resource expansion constraints, which are specifically expressed as follows: The meanings of the constraints are explained as follows: the constraints (5)-(7) specify service requirements, ensuring that each cluster center must be accessed by a truck, while each customer can obtain the delivery service of the UAV; the constraints (8)-(11) define the network flow balance of the truck, requiring each truck to start from the starting warehouse O and arrive at the terminal warehouse D, and to maintain flow conservation at the intermediate cluster nodes, since each cluster is split into two types of virtual nodes, c-and c+, the corresponding flow conservation conditions are described respectively; the constraints (12)-(14) control the flow balance of the vehicle-mounted UAV, with the additional condition that the vehicle-mounted UAV is allowed to start from c-and return to c+ only when the corresponding truck accesses the cluster center c; the constraints (15)-(17) define the network flow constraints of the independent UAV, ensuring the feasibility of the start and end points and the access path; the constraint (18) further strengthens the consistency between the vehicle and the UAV, i.e., the UAV can only start to perform a task at a cluster center when the truck accesses the cluster center, indicating that the launch and recovery of the UAV can only be performed at the cluster center; the constraints (19)-(21) limit the maximum driving distance of the truck and the UAV, ensuring that they operate within the range of the endurance; the constraints (22)-(24) impose capacity constraints on the cumulative delivery load of the truck and the UAV; the constraints (25)-(27) eliminate the sub-rings in the paths of the truck and the UAV by using the MTZ type of constraint; the constraints (28)-(34) depict the time dynamics of the access nodes of the truck and the UAV through a resource expansion mechanism, tending to allow the service to be completed within the specified time window; finally, the constraints (35)-(37) give the value range of the decision variables. 9.The temporary waiting mode based vehicle and UAV cooperative delivery path planning method of claim 8, wherein, In the step S4, the time window penalty term in the model objective function is linearized, and an arc-based mixed integer linear programming model is established, and the specific steps are as follows: D1: Introduce auxiliary variables for the positive and negative nonlinear operators involved in the time window penalty terms respectively represent the earliness and lateness of the UAVs on vehicle k∈K serving customer i∈S1 by UAV l∈L1, which take value zero if no violation occurs; meanwhile, auxiliary variables are introduced for the case of independent UAV l∈L0 serving customer i∈S0 directly from the warehouse denote the corresponding time window deviations, and are reconstructed in a linear form in the objective function as shown in constraints (38)-(39), so as to achieve the piecewise penalty for earliness and lateness; D2: In order to ensure that the auxiliary variable can accurately reflect the deviation of the customer service time from the time window, corresponding disjunctive constraints are constructed: the constraints (40)-(41) specify the relationship between the advance and delay of the vehicle-mounted UAV, and the constraints (42)-(43) specify the relationship between the advance and delay of the independent UAV, wherein the activation state of the constraint is controlled by the constant M; in combination with the minimization of the objective function, the auxiliary variable remains zero when there is no violation, and accurately records the advance or lag deviation when there is a violation; after the linearization, the original model (1)-(37) is reconstructed into a mixed integer linear programming model containing (1)-(3), (5)-(37) and (38)-(43); 10.The temporary waiting mode based vehicle and UAV cooperative delivery path planning method of claim 9, wherein, In the step S5, the objective function and the constraint system are jointly solved by calling a commercial solver, and according to the value of the decision variable, all arcs with a variable value equal to 1 are drawn, and an optimal decision scheme is obtained.

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