Truck-UAV multi-target collaborative delivery and pickup route planning method

Abstract

The present invention discloses a truck-drone multi-objective collaborative express delivery and retrieval route planning method, which includes obtaining relevant parameters and constraint condition sets of the vehicle-machine collaborative logistics service; constructing an objective function set based on the relevant parameters to minimize the path cost of all customer points of the vehicle-machine collaborative logistics service; jointly solving the objective function set and the constraint condition set in combination with a heuristic algorithm to obtain the optimal delivery and retrieval route plan for the vehicle-machine collaborative logistics service; and controlling drones and trucks based on the optimal delivery and retrieval route plan to achieve delivery and retrieval of express parcels to customer points. In this method, the truck performs the retrieval task of the express parcel, and the drone only performs the delivery task of the express parcel under the premise that the load and range constraints are met, thereby increasing the feasibility; through sub-area division and the loading of multiple drones by the truck, each drone only takes off once in each sub-area and can provide delivery services to multiple customer points, greatly improving the service efficiency of the customer points. Through reasonable route planning, the total driving cost of the truck and drone is optimized.

Description

Technical Field

[0001] The present invention relates to the field of drone technology, and in particular to a truck-drone multi-target collaborative express delivery path planning method. Background Art

[0002] At present, drone logistics distribution is mainly used in express delivery, e-commerce, medical and other fields. However, drone transportation has disadvantages such as short range and small load capacity. Therefore, a two-level collaborative distribution system constructed by trucks and drones has become the mainstream of research, that is, trucks transport express and drones to the corresponding locations, and then drones complete the express delivery to minimize delivery costs. In this process, trucks serve as mobile warehouses and mobile charging stations for drones. Its essence is an extension of the two-echelon routing problem (2E-RP), which is an NP-hard problem. Compared with traditional transportation, by carrying drones on trucks, the advantages of trucks' long range and large load capacity can be combined with the advantages of drone transportation such as high efficiency, low cost, strong adaptability, environmental protection and energy saving. At present, the relevant vehicle-machine collaborative logistics technologies have the following problems:

[0003] First: Some related technologies consider the cooperation of vehicle-mounted drones for express delivery, only consider one drone, or the truck only acts as a mobile warehouse and charging station. The above situations will lead to low efficiency of truck-drone collaborative logistics, which will extend the overall logistics time.

[0004] Secondly, most current research on collaborative logistics focuses solely on express delivery services. Drone delivery offers the advantage of being able to serve a wider range of customer locations, while maintaining a limited range. This makes it particularly advantageous for delivery within a large service area. However, when customer locations are concentrated, frequent takeoffs and landings lead to high total route costs. Furthermore, this approach fails to meet the potential demand for retrieval of packages from customer locations, making it less practical.

[0005] Third, while some technologies consider courier retrieval, these tasks are typically performed by drones. However, drone retrieval is significantly constrained by practical constraints, such as the impact of the surrounding environment due to descent altitude and the need for personnel coordination at the customer site. Therefore, the retrieval conditions are relatively stringent, making it difficult to implement in real life. Summary of the Invention

[0006] The present invention provides a truck-UAV multi-objective collaborative express delivery and retrieval path planning method to overcome the technical problems in existing UAV-truck collaborative logistics distribution services, such as low efficiency and high time cost of UAVs in the process of retrieving express deliveries due to practical constraints, and inability to meet customer needs in a realistic situation.

[0007] In order to achieve the above object, the technical solution of the present invention is:

[0008] A truck-UAV multi-target collaborative express delivery and pickup path planning method, comprising:

[0009] S1: Obtain relevant parameters and constraint conditions for the vehicle-machine collaborative logistics service, including drone parameters, customer point parameters, and deployment point parameters; the constraint condition set is used to constrain the delivery method of trucks and drones within the total service area;

[0010] S2: constructing an objective function set for the vehicle-machine collaborative logistics service based on the relevant parameters, wherein the objective function set is an objective function for minimizing the path cost of all customer points of the vehicle-machine collaborative logistics service;

[0011] S3: Using a heuristic algorithm to jointly solve the objective function set and the constraint condition set, an optimal delivery and pickup route solution for the vehicle-machine collaborative logistics service is obtained, wherein the optimal delivery and pickup route solution satisfies the requirement of minimizing the route cost for all customer points of the vehicle-machine collaborative logistics service;

[0012] S4: Based on the optimal delivery and pickup route plan, control drones and trucks to deliver and retrieve express packages to customer points.

[0013] Furthermore, the set of constraints in S1 includes:

[0014] Restrictions on drones include but are not limited to:

[0015] Constraint 1: The total energy consumption of the a-th UAV in performing its mission cannot exceed the ideal maximum energy consumption budget of the UAV, as shown in formula (1).

[0016]

[0017] in, represents the total energy consumption of the a-th UAV in performing its mission, J max represents the ideal maximum energy consumption of the UAV; p l represents the coordinates of the truck-drone rendezvous point, i.e., the coordinates of the landing point of the drone swarm;

[0018] Constraint 2: The total range of the a-th UAV's mission cannot exceed the UAV's ideal maximum range, that is, the UAV's maximum range constraint, as shown in formula (2).

[0019]

[0020] in, represents the total distance flown by the a-th UAV in the sub-area k to be divided, represents the ideal maximum flight range of the a-th UAV; all sub-areas k in the following constraints refer to the sub-areas to be divided;

[0021] Constraint 3: The actual load of the a-th UAV at the take-off point cannot exceed the maximum load capacity of the UAV, that is, the maximum load constraint of the UAV, as shown in formula (3),

[0022]

[0023] in, Indicates that the a-th UAV is at the take-off point p f Actual load at takeoff, Q max Indicates the ideal maximum payload of the drone;

[0024] Constraint 4: The total weight of the delivered express within the sub-area cannot exceed the maximum load capacity of all drones, that is, the maximum weight constraint of the express delivery required by the customer point, as shown in formula (4).

[0025]

[0026] in, represents the weight of the express delivered by the drone to the i-th delivery point in sub-area k; p s represents the set of delivery points, P s ={p1,p2,...,p N1}, N1 is the number of delivery points; Constraint 5: Obtain the energy consumption model of the a-th UAV and obtain the actual energy consumption of the a-th UAV so that it is less than the maximum ideal energy consumption of the UAV. The energy consumption model is shown in formula (5).

[0027]

[0028] Among them, Q a (n) represents the load of the a-th UAV after traversing the n-th customer point, W represents the weight of the UAV, g represents the acceleration of gravity, ρ represents the density of the fluid (air), ζ represents the area of ​​the rotating blade disk, and r represents the number of rotors of the UAV. It represents the total flight time of the a-th UAV traversing each delivery point in the area, n a(max) represents the maximum number of delivery points traversed by the a-th drone, Q a (n) represents the load of the a-th UAV after traversing the n-th point. Its value is negatively correlated with the number of traversed points n. Q a (n a(max) )=0;

[0029] Constraint 6: All customer points that need to deliver express can only be served by drones once at most, as shown in formula (6).

[0030]

[0031] in, is a binary decision variable. If the a-th UAV in sub-area k starts from point p i Fly to point p j ,but The value of is 1, otherwise it is 0;

[0032] Constraint 7: All customer points that need delivery services must be served by drones, as shown in formula (7),

[0033]

[0034] in, Represents the number of all delivery points in sub-area k;

[0035] The constraints imposed on trucks within the sub-area include but are not limited to:

[0036] Constraint 8: All customer points that need to pick up express delivery can only be served by a truck once at most, as shown in formula (8).

[0037]

[0038] in, is a binary decision variable. If the truck starts from the pickup point p i Drive to the pickup point p j ,but The value of is 1, otherwise it is 0;

[0039] Constraint 9: All customer points that need to be picked up must be served by trucks, as shown in formula (9),

[0040]

[0041] in, represents the number of all customer points that need to retrieve services in sub-area k;

[0042] The constraints on trucks between sub-regions include but are not limited to:

[0043] Constraint 10: All sub-areas need to be traversed by trucks, as shown in formula (10),

[0044]

[0045] in, is a binary decision variable. If the truck comes from sub-area k i Travel to sub-area k j , then the value is 1, otherwise it is 0;

[0046] Constraint 11: All sub-areas can be traversed by trucks only once, as shown in formula (11),

[0047]

[0048] Among them, N k Indicates the number of sub-regions.

[0049] Furthermore, S2 constructs an objective function set of the vehicle-machine collaborative logistics service based on the relevant parameters, including:

[0050] Construct the distance cost function for the drone to pick up the express from the customer point, as shown in formula (12):

[0051]

[0052] Among them, K is the total service area where the customer point is located, is the ath UAV in sub-area k from point p i To point p j distance;

[0053] Construct the distance cost function for trucks to deliver express to customers, as shown in formula (13):

[0054]

[0055] in, The truck in sub-area k starts from the pickup point p i To the pickup point j Distance moved;

[0056] Construct the cost function of the truck's travel distance between sub-regions, as shown in formula (14),

[0057]

[0058] in, For trucks in subregion k i To subregion k j the distance travelled between them;

[0059] The three objective functions satisfy the shortest distance of the truck and drone delivery paths under the constraint set, as shown in formula (15).

[0060]

[0061] Where D represents the shortest distance between the truck and drone delivery paths that satisfies the constraint set.

[0062] Furthermore, S3 combines a heuristic algorithm to jointly solve the objective function set and the constraint condition set, including:

[0063] S31. Determine whether the total service area satisfies the constraint condition set. If not, design a constrained k-means clustering method based on the K-means algorithm. Use the constrained k-means clustering method to divide the total service area into several sub-areas that meet the UAV payload and range constraints. Use the cluster center to represent the location of the sub-area and serve as the landing point for the UAV swarm within the sub-area.

[0064] S32: The truck starts from a warehouse outside the total service area and traverses all sub-areas. The ant colony algorithm is used to solve the optimal path for the truck to traverse the sub-areas.

[0065] S33, pre-selecting a take-off point for the drones, and designing a genetic-particle swarm algorithm based on the genetic algorithm and the particle swarm algorithm, and using the genetic-particle swarm algorithm to solve the optimal path for the drone swarm to perform the express delivery task in the sub-area;

[0066] S34. Using the takeoff point of the drone swarm as the starting point for the truck within the sub-area and the landing point of the drone swarm as the truck's destination, an ant colony algorithm is used to solve the optimal path for the truck to perform the courier pickup task within the area.

[0067] S35. Based on the three optimal paths, the optimal delivery and pickup route plan is obtained to minimize the path cost of drones and trucks serving all customer points.

[0068] Furthermore, a constrained k-means clustering method is designed based on the K-means algorithm. The constrained k-means clustering method is used to divide the total service area into several sub-areas that meet the UAV payload and range constraints, including:

[0069] S311: Use the elbow method to obtain the optimal number of clusters, which is used as the number of clusters to start the iteration;

[0070] S312: Obtain the objective function of the k-means algorithm, as shown in formula (16):

[0071]

[0072] μ (j) represents cluster k j The cluster center, that is, sub-region k j The center point, p i represents the i-th customer point, n k Indicates the number of clusters, that is, the number of sub-regions after the sub-regions are divided;

[0073] Determine whether all sub-areas currently divided meet the conditions of the longest flight range constraint of the UAV, the maximum load constraint of the UAV, and the minimum J(K) value. If not, iterate the k-means algorithm. Each iteration adds 1 to the number of sub-areas in the previous iteration and repeatedly calculates J(K) to determine whether the current sub-area meets the conditions of the longest flight range constraint of the UAV, the maximum load constraint of the UAV, and the minimum J(K) value.

[0074] Obtain the longest range constraint of the UAV, as shown in formula (17),

[0075]

[0076] p i Represents the coordinates of the i-th customer point; μ (j) represents the coordinates of the cluster center;

[0077] When the number of sub-regions satisfies the UAV's maximum range constraint, the UAV's maximum load constraint, and the minimum J(K) value, the iteration stops and the current divided sub-regions and the number of sub-regions are saved.

[0078] Furthermore, a take-off point for the drones is pre-selected, and a genetic-particle swarm algorithm is designed based on the genetic algorithm and the particle swarm algorithm. The genetic-particle swarm algorithm is used to solve the optimal path for the drone swarm to perform the express delivery task in the sub-area, including:

[0079] S331: Discretize the truck paths between sub-areas and obtain multiple sampling points as candidates for the pre-selected take-off points of the UAV. The discrete formula is shown in formula (18):

[0080]

[0081] Among them, n p represents the number of pre-selected take-off points between sub-area i and sub-area j, D ij represents the distance between sub-region i and sub-region j, and l represents the distance discrete accuracy;

[0082] S332: Using a sequence encoding method, an initial population is created, where the initial population is a set of delivery paths for the drone swarm. The initial population includes Z individual genes, where each individual gene is a delivery path corresponding to a delivery task performed collaboratively by two or more drones.

[0083] Initialize the individual genes in the initial population:

[0084] Use the routing sequence and interruption sequence to form individual genes, calculate the interval of each interruption point, and obtain the initial interruption sequence according to the interval of the interruption points, as shown in formula (19):

[0085]

[0086] Among them, int represents the interval of the break point, represents the number of delivery and pickup points in the kth sub-area, and M is the number of drones. The initial interrupt sequence divides the routing sequence into multiple initial gene subsequences starting from the starting end. The gene subsequence is the delivery path of a drone.

[0087] S333. Determine whether each subsequence of each individual gene meets the maximum load constraint of the drone, and adjust the individual genes that do not meet the maximum load constraint:

[0088] Determine whether the total demand for the delivery and pickup points of the first part of the gene subsequence of the routing sequence of an individual gene meets the maximum load constraint of the UAV;

[0089] If the maximum load constraint of the drone is satisfied, the first element of the gene subsequence adjacent to the first part of the gene subsequence is selected and added to the first part of the gene subsequence to form a new first part of the gene subsequence, and it is determined whether the new first part of the gene subsequence satisfies the maximum load constraint of the drone. If so, the first element in the aforementioned adjacent gene subsequence is added to the first part of the gene subsequence to continue to form a new first part of the gene subsequence; the above process is repeated until the first element selected does not satisfy the maximum load constraint of the drone, and the element is removed; the element represents a certain delivery point sequence number;

[0090] If the maximum payload constraint of the drone is not met, the last element of the first gene subsequence is added to the gene subsequence adjacent to the first gene subsequence to form a new gene subsequence, and the element is removed from the first gene subsequence. The process of removing elements is repeated until the total demand for the delivery and pickup points of the gene subsequence meets the maximum payload constraint of the drone, thus forming a new gene subsequence.

[0091] Repeat the above process of determining whether the total demand for gene subsequence delivery points meets the maximum load constraint of the drone and forming a new gene subsequence until the total demand for delivery points of all generated gene subsequences meets the maximum load constraint of the drone, completing the adjustment of individual genes.

[0092] S334: Use the PSO algorithm to solve the delivery path of a single individual gene and obtain the optimal path for each gene subsequence of the single individual gene:

[0093] Set the number of particle swarms, the speed and position of the initial particles, and the maximum number of iterations to initialize the particle swarm; the particle swarm represents the path set of a gene subsequence;

[0094] The initial position of the particle swarm is the take-off point p of the sub-region f ;

[0095] The particle velocity and position update formulas are shown in formulas (20) and (21), and the next passing delivery point is obtained;

[0096]

[0097]

[0098] in, represents the current velocity of particle i, represents the velocity of particle i at the next moment, Indicates the current position of particle i, Pbest i represents the historical optimal solution of particle i, Gbest i Represents the historical optimal solution of the group, Pbest i -x i There is a swap sequence X that makes X i After X transformation, Pbest is obtained i Similarly, Gbest i -x i is also a swap sequence, symbol Indicates that two exchange sequences are merged into one exchange sequence. The symbol + indicates that a sequence is exchanged according to the exchange sequence. r1 and r2 are parameters, which represent Pbest respectively. i -x i With Gbest i -x i The acceptance probability of is shown in formulas (22) and (23).

[0099]

[0100] w represents the total number of iterations, t represents the number of current iterations, t∈(1,w);

[0101] When Gbest i When convergence is reached, the calculated particle position is the optimal position, that is, the optimal path of a gene subsequence;

[0102] Repeat the PSO algorithm solution process for the Z individual genes in the initial population to obtain the optimal path for each individual gene, that is, Z individuals;

[0103] S334: Use genetic algorithm to update individual genes in the initial population:

[0104] Select operator:

[0105] Using the elitist model, the best individual among the Z individuals obtained by the PSO algorithm in S334 is retained, and the remaining Z-1 individuals are selected according to the roulette method based on the fitness value. γ-1 individuals are selected from the remaining Z-1 individuals and the best individual to form γ individuals;

[0106] Use γ individuals to generate offspring:

[0107] Randomly select two individuals from the γ individuals as parent individuals, and choose one of the sequential crossover operator and the position-based crossover operator to generate the selection parameter λ of the offspring, as shown in formula (24),

[0108]

[0109] Among them, the symbol ⊙ indicates that if the given random number is greater than λ, the sequential crossover operator A is selected. ox Otherwise, the position-based crossover operator A is used. pbx ,symbol Indicates that the selected crossover operator is used to cross the parent generations P1 and P2 to generate new offspring, and C1 and C2 represent the two offspring generated by the crossover of the parent individuals;

[0110] Traverse all individuals in the γ individuals until the number of offspring generated and the sum of the γ individuals are equal to the initial population size, and stop generating offspring;

[0111] Repeat the iterative steps S332-S334 until the total distance of the UAVs converges, stop updating the individual genes, and obtain the optimal path.

[0112] Furthermore, the customer point parameters include customer point coordinates, services required by each customer point, weight of express delivery required by each customer node requiring delivery services, and access status; wherein the access status is a binary variable, taking values ​​of one or zero.

[0113] Beneficial effects: The present invention provides a truck-UAV multi-objective collaborative express delivery and retrieval path planning method. By setting constraints, the constraints on the truck and UAV performing the express retrieval task are determined. The truck performs the express retrieval task, and the UAV only performs the express delivery task under the premise of meeting the load and range constraints, which increases the executability. At the same time, through the division of sub-service areas and the loading of multiple UAVs by trucks, each UAV only takes off once in each sub-service area. Each UAV can provide delivery services to multiple customer points, greatly improving the service efficiency to customer points; setting an objective function for minimizing the path cost, and jointly solving the objective function set and the constraint condition set by combining a heuristic algorithm, a reasonable path planning is obtained, so that the total driving cost of the truck and the UAV is optimized. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0115] Figure 1 A schematic diagram of a method for truck-UAV multi-target collaborative delivery and pickup express delivery path planning according to the present invention;

[0116] Figure 2 Schematic diagram of the trajectory correction of a truck traveling between sub-areas in the present invention;

[0117] Figure 3 Schematic diagram of encoding initialization adjustment of the improved genetic-particle swarm swarm algorithm of the present invention;

[0118] Figure 4 Schematic diagram of the truck-UAV multi-target collaborative delivery and pickup express delivery path planning method in the present invention. DETAILED DESCRIPTION

[0119] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0120] This embodiment provides a truck-UAV multi-target collaborative delivery and collection express delivery path planning method, such as Figure 1 Shown, including:

[0121] S1: Obtain relevant parameters and constraint conditions for the vehicle-machine collaborative logistics service, including drone parameters, customer point parameters, and deployment point parameters; the constraint condition set is used to constrain the delivery method of trucks and drones within the total service area;

[0122] S2: constructing an objective function set for the vehicle-machine collaborative logistics service based on the relevant parameters, wherein the objective function set is an objective function for minimizing the path cost of all customer points of the vehicle-machine collaborative logistics service;

[0123] S3: Using a heuristic algorithm to jointly solve the objective function set and the constraint condition set, an optimal delivery and pickup route solution for the vehicle-machine collaborative logistics service is obtained, wherein the optimal delivery and pickup route solution satisfies the requirement of minimizing the route cost for all customer points of the vehicle-machine collaborative logistics service;

[0124] S4: Based on the optimal delivery and pickup route plan, control drones and trucks to deliver and retrieve express packages to customer points.

[0125] Specifically, first obtain the relevant parameters and constraint condition sets of the vehicle-machine collaborative logistics service, the relevant parameters include drone parameters, customer point parameters and deployment point parameters; the constraint condition set is used to constrain the way trucks and drones deliver express within the total service area, and multiple constraints are set for trucks and drones, which can discuss the feasibility of retrieval services by trucks and drones from a more practical perspective, so that the results obtained are closer to the actual situation; based on the relevant parameters, construct the objective function set of the vehicle-machine collaborative logistics service, the objective function set is the objective function for minimizing the path cost of all customer points of the vehicle-machine collaborative logistics service. This solution sets the objective function to provide a premise for calculating the minimum path cost; combine the heuristic algorithm to jointly solve the objective function set and the constraint condition set, and obtain the vehicle-machine collaborative logistics service. The optimal delivery and pickup route plan satisfies the requirement of minimizing the path cost of all customer points in the vehicle-machine collaborative logistics service. This plan designs a constrained k-means clustering method based on the K-means algorithm, which can ensure that the divided sub-areas meet all constraints. The ant colony algorithm is used to obtain the optimal path for trucks to traverse between sub-areas and the optimal path for trucks to perform express delivery tasks within the area. The genetic-particle swarm hybrid algorithm is designed based on the genetic algorithm and the particle swarm algorithm, which can obtain the optimal path for drone swarms to perform express delivery tasks within the sub-areas, thereby realizing the optimal delivery and pickup route for trucks equipped with multiple drones to provide express delivery and retrieval services to several customers in a certain area. Finally, based on the optimal delivery and pickup route plan, the drones and trucks are controlled to deliver and retrieve express to customer points.

[0126] In a specific embodiment, relevant parameters and constraint sets of a vehicle-machine collaborative logistics service are obtained, wherein the relevant parameters include drone parameters, customer point parameters, and deployment point parameters. The constraint set is used to constrain the delivery method of trucks and drones within the total service area. The scheme is:

[0127] Model the service environment of customer points and assign corresponding coordinate information to each customer point;

[0128] The customer point parameters include the customer point coordinates, the services required by each customer point, the weight of the express delivery required by each customer node that requires delivery services, and the access status; wherein the access status is a binary variable with a value of one or zero;

[0129] The services required by customer nodes are divided into delivery service, retrieval service, and delivery and retrieval service. Delivery service is provided by drones, and retrieval service is provided by trucks. All customer nodes have a required weight for delivery or retrieval. In this embodiment, the weight is randomly distributed between 1-5kg.

[0130] The drone parameters mainly consider the maximum load, actual load and maximum range of each drone, the number of drones deployed in each sub-service area, the number of drones that constitute a drone set, and the service status of each customer node, where the service status is a binary variable with a value of one or zero;

[0131] Restrictions on drones include but are not limited to:

[0132] Constraint 1: The total energy consumption of the a-th UAV in performing this mission cannot exceed the ideal maximum energy consumption budget of the UAV, as shown in formula (25).

[0133]

[0134] in, represents the total energy consumption of the a-th UAV in performing this mission, J max represents the ideal maximum energy consumption of the UAV; p l represents the coordinates of the truck-drone rendezvous point, i.e., the coordinates of the landing point of the drone swarm;

[0135] Constraint 2: The total range of the a-th UAV performing this mission cannot exceed the ideal maximum range of the UAV, that is, the maximum range constraint of the UAV, as shown in formula (26),

[0136]

[0137] in, represents the total distance flown by the a-th UAV in the sub-area k to be divided, represents the ideal maximum flight range of the a-th UAV; all sub-areas k in the following constraints refer to the sub-areas to be divided;

[0138] Constraint 3: The actual load of the a-th UAV at the take-off point cannot exceed the maximum load capacity of the UAV, that is, the maximum load constraint of the UAV, as shown in formula (27),

[0139]

[0140] in, Indicates that the a-th UAV is at the take-off point p f Actual load at takeoff, Q max Indicates the ideal maximum payload of the drone;

[0141] Constraint 4: The total weight of the express delivery within the sub-area cannot exceed the maximum load capacity of all drones, that is, the maximum weight constraint of the express delivery required by the customer point, as shown in formula (28).

[0142]

[0143] in, represents the weight of the express delivered by the drone to the i-th delivery point in sub-area k; p s represents the set of delivery points, P s ={p1,p2,...,p N1}, N1 is the number of delivery points; Constraint 5: Obtain the energy consumption model of the a-th UAV and obtain the actual energy consumption of the a-th UAV so that it is less than the maximum ideal energy consumption of the UAV. The energy consumption model is shown in formula (29).

[0144]

[0145] Among them, Q a (n) represents the load of the a-th UAV after traversing the n-th customer point, W represents the weight of the UAV, g represents the acceleration of gravity, ρ represents the density of the fluid (air), ζ represents the area of ​​the rotating blade disk, and r represents the number of rotors of the UAV. It represents the total flight time of the a-th UAV traversing each delivery point in the area, n a(max) represents the maximum number of delivery points traversed by the a-th drone, Q a (n) represents the load of the a-th UAV after traversing the n-th point. Its value is negatively correlated with the number of traversed points n. Q a (n a(max) )=0;

[0146] Constraint 6: All customer points that need to deliver express can only be served by drones once at most, as shown in formula (30).

[0147]

[0148] in, is a binary decision variable. If the a-th UAV in sub-area k starts from point p i Fly to point p j ,but The value of is 1, otherwise it is 0;

[0149] Constraint 7: All customer points that need delivery services must be served by drones, as shown in formula (31),

[0150]

[0151] in, Indicates the number of all delivery points in sub-area k;

[0152] The constraints imposed on trucks within the sub-area include but are not limited to:

[0153] Constraint 8: All customer points that need to pick up express delivery can only be served by a truck once at most, as shown in formula (32).

[0154]

[0155] in, is a binary decision variable. If the truck starts from the pickup point p i Drive to the pickup point p j ,but The value of is 1, otherwise it is 0;

[0156] Constraint 9: All customer points that need to be picked up must be served by trucks, as shown in formula (33),

[0157]

[0158] in, represents the number of all customer points that need to retrieve services in sub-area k;

[0159] The constraints on trucks between sub-regions include but are not limited to:

[0160] Constraint 10: All sub-areas need to be traversed by trucks, as shown in formula (34),

[0161]

[0162] in, is a binary decision variable. If the truck comes from sub-area k i Travel to sub-area k j , then the value is 1, otherwise it is 0;

[0163] Constraint 11: All sub-areas can be traversed by trucks only once, as shown in formula (35),

[0164]

[0165] Among them, N k Indicates the number of sub-service areas.

[0166] In this solution, multiple constraints are set for trucks and drones, which can discuss the feasibility of retrieval services by trucks and drones from a more practical perspective, making the results closer to reality.

[0167] In a specific embodiment, an objective function set of the vehicle-machine collaborative logistics service is constructed based on the relevant parameters. The objective function set is a scheme for minimizing the path cost of all customer points of the vehicle-machine collaborative logistics service:

[0168] Construct the distance cost function for the drone to pick up the express from the customer point, as shown in formula (36):

[0169]

[0170] Among them, K is the total service area where the customer point is located, is the ath UAV in sub-area k from point p i To point p j distance;

[0171] Construct the distance cost function for trucks to deliver express to customers, as shown in formula (37),

[0172]

[0173] in, The truck in sub-area k starts from the pickup point p i To the pickup point j Distance moved;

[0174] Construct the cost function of the truck's travel distance between sub-service areas, as shown in formula (38),

[0175]

[0176] in, For trucks in subregion k i To subregion k j the distance travelled between them;

[0177] The three objective functions satisfy the shortest distance of the truck and drone delivery paths under the constraint condition set, as shown in formula (39),

[0178]

[0179] Where D represents the shortest distance between the truck and drone delivery paths that satisfies the constraint set.

[0180] The objective problem of truck-drone collaborative path planning is the objective function. The objective function includes the objective function of drone delivery under payload range constraints, the objective function of truck retrieval of packages within the sub-area, and the objective function of truck driving between sub-areas. This scheme sets the objective function to provide a prerequisite for calculating the minimum path cost.

[0181] In a specific embodiment, the objective function set and the constraint condition set are jointly solved by combining a heuristic algorithm to obtain an optimal delivery and pickup route solution for the vehicle-machine collaborative logistics service. The optimal delivery and pickup route solution satisfies the requirement of minimizing the path cost for all customer points of the vehicle-machine collaborative logistics service:

[0182] S31. Determine whether the total service area meets the constraint condition set. If not, design a constrained k-means clustering method based on the K-means algorithm. Use the constrained k-means clustering method to divide the total service area into several sub-areas that meet the UAV payload and range constraints. Cluster all the delivery and pickup points in the area under the premise of meeting constraints (3) and (4). Obtain the optimal number of clusters m and each sub-task area. Use the cluster center point to represent the location of the sub-area and serve as the landing point P of the UAV group in the sub-area. l :

[0183] S311: Use the elbow method to obtain the optimal number of clusters, which is used as the number of clusters to start the iteration;

[0184] S312: Obtain the objective function of the k-means algorithm, as shown in formula (40):

[0185]

[0186] μ (j) represents cluster k j The cluster center, that is, sub-region k j The center of p i represents the i-th customer point, n k Indicates the number of clusters, that is, the number of sub-regions after the sub-regions are divided;

[0187] Determine whether all sub-areas currently divided meet the conditions of the longest flight range constraint of the UAV, the maximum load constraint of the UAV, and the minimum J(K) value. If not, iterate the k-means algorithm. Each iteration adds 1 to the number of sub-areas in the previous iteration and repeatedly calculates J(K) to determine whether the current sub-area meets the conditions of the longest flight range constraint of the UAV, the maximum load constraint of the UAV, and the minimum J(K) value.

[0188] Obtain the longest range constraint of the UAV, as shown in formula (41),

[0189]

[0190] p i Represents the coordinates of the i-th customer point; μ (j) represents the coordinates of the cluster center;

[0191] When the number of sub-areas satisfies the UAV's maximum range constraint, the UAV's maximum load constraint, and the minimum J(K) value, the iteration stops and the current sub-areas and the number of sub-areas are saved.

[0192] S32, the truck starts from a warehouse outside the total service area and traverses all sub-areas. It is stipulated that between any two sub-areas, the truck takes the previous sub-area K i-1 The cluster center point (i.e., the landing point of the drone) is used as the starting point of the truck. i The direction of the pickup point closest to the starting point is selected as the driving direction of the truck, and the take-off point of the drone in the next sub-area is used as the end point of the truck's travel between sub-areas, so as to shorten the travel distance between the two sub-areas. The ant colony algorithm is used to solve the optimal path for the truck to traverse the sub-areas between sub-areas, and the path planning problem between sub-areas is approximately solved as the optimal traversal order of the truck to the cluster center points of each sub-area, to the optimal path S k ={K1,K2,...,K m}, is the order in which trucks perform tasks between sub-areas; the schematic diagram is as follows Figure 2 As shown;

[0193] S33. Preselect the take-off point of the drones, and design a genetic-particle swarm hybrid algorithm based on the genetic algorithm and the particle swarm algorithm. Use the genetic-particle swarm hybrid algorithm to solve the optimal path for the drone swarm to perform the express delivery task in the sub-area:

[0194] S331: Discretize the truck paths between sub-areas to obtain a series of sampling points as candidates for the pre-selected take-off point of the UAV. The discrete formula is shown in formula (42):

[0195]

[0196] Among them, n p represents the number of pre-selected take-off points between sub-area i and sub-area j, D ij represents the distance between sub-region i and sub-region j, and l represents the distance discrete accuracy;

[0197] S332: Using a sequence encoding method, an initial population is created, wherein the initial population is a set of delivery paths for the drone group; the initial population includes Z individual genes, each of which corresponds to a delivery path corresponding to a delivery task involving two or more drones working together; in this embodiment, the value of Z is 80;

[0198] Initialize the individual genes in the initial population:

[0199] The routing sequence and the interruption sequence are used to form individual genes. Considering the constraints of the UAV, in order to reduce invalid genes, when initializing the interruption sequence, the interval of each interruption point is calculated using prior knowledge, and the initial interruption sequence is obtained according to the interval of the interruption points, as shown in formula (43).

[0200]

[0201] Among them, int represents the interval of the break point, represents the number of delivery and pickup points in the kth sub-area, and M is the number of drones. The interrupt sequence divides the routing sequence from the starting end into multiple initial gene subsequences, i.e., the delivery path of a drone. If int is not an integer, it is rounded up to maintain the margin.

[0202] S333: Determine whether each gene subsequence of each individual gene meets the maximum load constraint of the drone, and adjust the individual genes that do not meet the maximum load constraint:

[0203] Determine whether the total demand for the delivery and pickup points of the first part of the gene subsequence of the routing sequence of an individual gene meets the maximum load constraint of the UAV;

[0204] If the maximum load constraint of the drone is met, the first element of the gene subsequence adjacent to the first gene subsequence is selected and added to the first gene subsequence to form a new first gene subsequence, and then it is determined whether the new first gene subsequence meets the maximum load constraint of the drone;

[0205] Repeat the process of adding elements until the maximum load constraint of the drone is no longer satisfied after adding the first selected element, and then remove the element; the element represents the serial number of a certain delivery point;

[0206] If the maximum payload constraint of the drone is not satisfied, then the last element of the first gene subsequence is added to the gene subsequence adjacent to the first gene subsequence to form a new gene subsequence, and the last element is removed from the first gene subsequence; and it is determined whether the first gene subsequence after removing the last element satisfies the maximum payload constraint of the drone.

[0207] The process of removing elements is repeated until the total demand for the delivery and pickup points of this part of the gene subsequence meets the maximum load constraint of the drone, thus forming a new gene subsequence;

[0208] Repeat the above process of determining whether the total demand for gene subsequence delivery points meets the maximum load constraint of the drone and forming a new gene subsequence until the total demand for delivery points of all generated gene subsequences meets the maximum load constraint of the drone, completing the adjustment of individual genes.

[0209] Schematic diagram as Figure 3 As shown in the figure, the individual gene before adjustment contains three drones, and the interrupt sequence divides the routing sequence into three gene subsequences;

[0210] After determining that the first part of the gene subsequence meets the maximum load constraint of the drone, the first part of the sequence is adjusted, and the first element of the adjacent gene subsequence is added to the first part of the gene subsequence. As shown in the adjusted figure, the fifth element is added to the first part of the gene subsequence to generate a new first part of the gene subsequence. At this time, the first element in the adjacent gene subsequence has a delivery point sequence number of 4. It is re-determined whether the new first part of the gene subsequence meets the maximum load constraint of the drone. If it does, the element with the delivery point sequence number of 4 is added to the new first part of the gene subsequence. This process is repeated until the constraint is no longer met after the first element is added, and the element is removed.

[0211] If the first part of the gene subsequence does not meet the constraint, the last element of the first part of the gene subsequence is added to the adjacent gene subsequence. For example, the element with the input point sequence number 1 is added to the adjacent gene subsequence. At this time, the first part of the gene subsequence has only 3 elements, and the adjacent gene subsequence has 5 elements. After removing the element, it is judged whether the first part of the gene subsequence meets the constraint. If not, the current last element is continued to be added to the adjacent gene subsequence until the constraint is met after removing the element.

[0212] S334: Use the PSO algorithm to solve the delivery path of a single individual gene and obtain the optimal path for each gene subsequence of the single individual gene:

[0213] Set the number of particle swarms, the speed and position of the initial particles, and the maximum number of iterations to initialize the particle swarm; the particle swarm represents the path set of a gene subsequence; in this scheme, the value of the particle swarm is set to 10;

[0214] The initial position of the particle swarm is the take-off point p of the sub-region f ;

[0215] The particle velocity and position update formulas are shown in formulas (44) and (45), and the next passing delivery point is obtained;

[0216]

[0217]

[0218] in, represents the current velocity of particle i, represents the velocity of particle i at the next moment, Indicates the current position of particle i, Pbest i represents the historical optimal solution of particle i, Gbest i Represents the historical optimal solution of the group, Pbest i -x i There is a swap sequence X that makes X i After X transformation, Pbest is obtained i Similarly, Gbest i -x i is also a swap sequence, symbol Indicates that two exchange sequences are merged into one exchange sequence, and the symbol + indicates that a sequence is exchanged according to the exchange sequence.

[0219] In order to prevent the particle swarm algorithm from falling into local optimality and causing stagnation in the later stage, r1 and r2 are designed as parameters, representing Pbest, i -x i With Gbest i -x i The acceptance probability of is shown in formulas (46) and (47),

[0220]

[0221] w represents the total number of iterations, t represents the number of the current iteration, t∈(1,w); as the number of iterations t increases, r1 gradually decreases and r2 gradually increases, so that the algorithm can jump out of the current stagnation and coordinate its local search and global search capabilities to avoid the algorithm falling into the local optimum;

[0222] When Gbest i When convergence is reached, the calculated particle position is the optimal position, that is, the optimal path of a gene subsequence;

[0223] Repeat the PSO algorithm solution process for the Z individual genes in the initial population to obtain the optimal path for each individual gene, that is, Z individuals;

[0224] S335: Use genetic algorithm to update individual genes in the initial population:

[0225] Select operator:

[0226] Using the elitist model, the best individual among the Z individuals obtained by the PSO algorithm in S334 is retained, and the remaining Z-1 individuals are selected according to the roulette method based on the fitness value. γ-1 individuals are selected from the remaining Z-1 individuals and the best individual to form γ individuals;

[0227] Use γ individuals to generate offspring:

[0228] Randomly select two individuals from the γ individuals as parent individuals, and choose one of the sequential crossover operator and the position-based crossover operator to generate the selection parameter λ of the offspring, as shown in formula (48),

[0229]

[0230] Among them, the symbol ⊙ indicates that if the given random number is greater than λ, the sequential crossover operator A is selected. ox Otherwise, the position-based crossover operator A is used. pbx ,symbol Indicates that the selected crossover operator is used to cross the parent generations P1 and P2 to generate new offspring, and C1 and C2 represent the two offspring generated by the crossover of the parent individuals;

[0231] Traverse all individuals in the γ individuals until the number of offspring generated and the sum of the γ individuals are equal to the initial population size, and stop generating offspring;

[0232] Repeat the steps S333-S335 until the total distance of the drones converges, stop updating the individual genes, and get the optimal path

[0233] S34, release point P with drone f As the starting point of the truck in the sub-area, the drone landing point P l The ant colony algorithm is used to solve the optimal path for the truck to perform the express delivery task in the area and obtain the optimal path.

[0234] S35. Based on the three optimal paths, the optimal delivery and pickup path solution S = {S i ,S k}, the schematic diagram is as follows Figure 4 shown.

[0235] This approach uses a genetic and particle swarm optimization (PSO) hybrid algorithm. First, an initial population is created and its genes are initialized. This approach employs a sequence encoding method, where each individual's genes consist of two parts: a routing sequence and a breakpoint sequence. To minimize invalid genes, the breakpoint sequence is initialized using prior knowledge to estimate the interval between each breakpoint, int, to ensure that the delivery point assigned to each drone meets the drone's constraints.

[0236] By incorporating prior knowledge into the population's genetic initialization, we can minimize the presence of individuals that fail to meet constraints (invalid genes), thereby reducing the probability of extreme initial results. Innovations in the population update algorithm effectively increase the diversity of the population's genetics, accelerating the search for optimal solutions. Post-population adjustment involves recoding the genes of individuals that fail to meet constraints, reducing invalid genes and improving the efficiency of each iteration. These operations ensure that the optimal solution is achieved with fewer iterations.

[0237] In summary, this solution designs a constrained k-means clustering method based on the K-means algorithm, which can ensure that the divided sub-areas meet all constraints. The ant colony algorithm is used to obtain the optimal path for trucks to traverse between sub-areas and the optimal path for trucks to perform express delivery tasks within the area. The genetic algorithm and particle swarm algorithm are used to design a genetic particle swarm hybrid algorithm, which can obtain the optimal path for drone swarms to perform express delivery tasks within the sub-areas, thereby realizing the optimal delivery and retrieval path for trucks equipped with multiple drones to provide express delivery and retrieval services to several customers in a certain area.

[0238] In a specific embodiment, the solution for controlling drones and trucks to deliver and retrieve packages to customer locations based on the optimal delivery and pickup route is:

[0239] To optimize the delivery and pickup routing, a truck departs from the warehouse and drives toward the nearest customer location within the first planned area. Upon reaching the takeoff point, the drone is released. From the takeoff point, the drone traverses all delivery points within the area to deliver the package, while the truck sequentially traverses all pickup points within the area to retrieve the package. Upon completing their mission, the drone and truck rendezvous at the landing point. If the drone arrives before the truck, it waits there. If the truck arrives before the drone, the drone lands on the truck. Once all drones have landed, the truck proceeds to the next area.

[0240] From a modeling perspective, unlike most studies on drone delivery and pickup services, this paper explores the feasibility of truck-based pickup services from a more practical perspective. Based on this, the present invention investigates the optimal path planning solution for delivering and picking up services while minimizing the total distance traveled, including both drone delivery and truck pickup. When discussing the path planning problem for drone swarm delivery of express parcels, the optimal takeoff point, flight path, and landing point for each sub-region of the drone swarm were discussed, while satisfying the practical constraints of the drones. This method minimizes the time required to execute a mission while ensuring the shortest total distance possible.

[0241] From an algorithmic design perspective, the different missions of drones and trucks result in a lack of close connectivity between them during mission execution. Therefore, this invention incorporates multiple heuristic algorithms to ensure that customers within each sub-region meet the drone swarm's payload and range constraints. To leverage the drone's speed advantage, it is necessary to release the drones as early as possible. This invention also addresses the selection of takeoff points for the drone swarm. Once the drones' preselected takeoff and landing points are determined, the UAV path planning problem transforms into a constrained MVRP problem. This invention considers the practical constraints of the drone's range and payload, and designs a genetic-particle swarm hybrid algorithm to solve the UAV path planning problem.

[0242] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A truck-UAV multi-target collaborative delivery and pickup express delivery path planning method, characterized in that: include: S1: Obtain relevant parameters and constraint condition sets for vehicle-machine collaborative logistics services, wherein the relevant parameters include drone parameters, customer point parameters, and deployment point parameters; The set of constraints is used to constrain the way in which trucks and drones deliver packages within the total service area; S2: Constructing an objective function set for the vehicle-machine collaborative logistics service based on the relevant parameters. The objective function set is an objective function for minimizing the path cost of all customer points in the vehicle-machine collaborative logistics service. The objective function is specifically as follows: Construct the distance cost function for drones to pick up express delivery from customer points, as shown in formula (1). （1） in, K is the total service area where the customer point is located, For the sub-region k Neidi a Drone from point Arrive distance; Construct the distance cost function for trucks to deliver express to customers, as shown in formula (2). （2） in, For sub-region k Inside the truck from the pickup point To the pickup point Distance moved; Construct the cost function of the truck's driving distance between sub-regions, as shown in formula (3), （3） in, For trucks in sub-areas To sub-area the distance travelled between them; The three objective functions satisfy the shortest distance of the truck and drone delivery paths under the constraint set, as shown in formula (4). （4） in, represents the shortest distance of the truck and drone delivery paths that meet the constraint set; S3: Using a heuristic algorithm to jointly solve the objective function set and the constraint condition set, an optimal delivery and pickup route solution for the vehicle-machine collaborative logistics service is obtained, wherein the optimal delivery and pickup route solution satisfies the requirement of minimizing the route cost for all customer points of the vehicle-machine collaborative logistics service; S4: Based on the optimal delivery and pickup route plan, control drones and trucks to deliver and retrieve express packages to customer points.

2. The truck-UAV multi-target collaborative delivery and pickup express delivery path planning method according to claim 1 is characterized in that: The set of constraints in S1 includes: Constraints on drones include: Constraint 1: a The total energy consumption of a UAV performing a mission cannot exceed the ideal maximum energy consumption budget of the UAV, as shown in formula (5): （5） in, Indicates the a The total energy consumption of a UAV in performing a mission, represents the ideal maximum energy consumption of the UAV; represents the coordinates of the truck-drone rendezvous point, i.e., the coordinates of the landing point of the drone swarm; Constraint 2: a The total range of a UAV performing a mission cannot exceed the ideal maximum range of the UAV, that is, the longest range constraint of the UAV, as shown in formula (6): （6） in, Indicates the a UAVs in the sub-area to be divided The total distance flown, Indicates the a The ideal maximum flight range of a UAV; all sub-areas under the following constraints Both refer to the sub-areas to be divided; Constraint 3: a The actual load of the UAV when taking off from the take-off point cannot exceed the maximum load capacity of the UAV, that is, the maximum load constraint of the UAV, as shown in formula (7), （7） in, Indicates the a Drones at take-off point Actual load at takeoff, Indicates the ideal maximum payload of the drone; Constraint 4: The total weight of the express delivery in the sub-area cannot exceed the maximum load capacity of all drones, that is, the maximum weight constraint of the express delivery required by the customer point, as shown in formula (8). （8） in, Indicates sub-area Internal drone to The weight of the express delivery at each delivery point; Represents the collection of delivery points, , N1 is the number of delivery points; Constraint 5: Get the a The energy consumption model of the UAV is obtained. a The actual energy consumption of a UAV is smaller than the maximum ideal energy consumption of the UAV. The energy consumption model is shown in formula (9): （9） in, Indicates the a The drone traverses n The load after the customer point, Indicates the drone's own weight. represents the acceleration due to gravity, represents the air density, represents the area of ​​the rotating blade disk, Indicates the number of rotors of the drone, Indicates the a The total flight time of the drones traversing each delivery point in the area, Indicates the a The maximum number of delivery points traversed by a drone, Indicates the a The drone traverses n The load after the points, its value is related to the number of traversed points n Negatively correlated, , ; Constraint 6: All customer points that need to deliver express can only be served by drones once at most, as shown in formula (10). （10） in, is a binary decision variable, if the sub-region k Neidi a Drone from point Fly to the point ,but The value of is 1, otherwise it is 0; Constraint 7: All customer points that need delivery services must be served by drones, as shown in formula (11), （11） in, Indicates sub-area The number of all delivery points in the The constraints imposed on trucks within the sub-area include: Constraint 8: All customer points that need to pick up express delivery can only be served by a truck once at most, as shown in formula (12). （12） in, is a binary decision variable. If the truck leaves the pickup point Drive to the pickup point ,but The value of is 1, otherwise it is 0; Constraint 9: All customer points that need to be picked up must be served by trucks, as shown in formula (13), （13） in, Indicates sub-area k The number of all customer points that need to pick up services; The constraints on trucks between sub-regions include: Constraint 10: All sub-areas need to be traversed by trucks, as shown in formula (14), （14） in, is a binary decision variable. If the truck comes from the sub-area Travel to sub-area , then the value is 1, otherwise it is 0; Constraint 11: All sub-areas can be traversed by a truck only once, as shown in formula (15), （11） in, Indicates the number of sub-regions.

3. The truck-UAV multi-target collaborative delivery and pickup route planning method according to claim 1 is characterized in that: S3 combines a heuristic algorithm to jointly solve the objective function set and the constraint condition set, including: S31. Determine whether the total service area satisfies the constraint condition set. If not, design a constrained k-means clustering method based on the K-means algorithm. Use the constrained k-means clustering method to divide the total service area into several sub-areas that meet the UAV payload and range constraints. Use the cluster center to represent the location of the sub-area and serve as the landing point for the UAV swarm within the sub-area. S32: The truck starts from a warehouse outside the total service area and traverses all sub-areas. The ant colony algorithm is used to solve the optimal path for the truck to traverse the sub-areas. S33, pre-selecting a take-off point for the drones, and designing a genetic-particle swarm algorithm based on the genetic algorithm and the particle swarm algorithm, and using the genetic-particle swarm algorithm to solve the optimal path for the drone swarm to perform the express delivery task in the sub-area; S34. Using the takeoff point of the drone swarm as the starting point for the truck within the sub-area and the landing point of the drone swarm as the truck's destination, an ant colony algorithm is used to solve the optimal path for the truck to perform the courier pickup task within the area. S35. Based on the three optimal paths, the optimal delivery and pickup route plan is obtained to minimize the path cost of drones and trucks serving all customer points.

4. The truck-UAV multi-target collaborative delivery and pickup express delivery path planning method according to claim 3 is characterized in that: A constrained k-means clustering method is designed based on the K-means algorithm. The constrained k-means clustering method is used to divide the total service area into several sub-areas that meet the UAV payload and range constraints, including: S311: Use the elbow method to obtain the optimal number of clusters, which is used as the number of clusters to start the iteration; S312: Obtain the objective function of the k-means algorithm, as shown in formula (16): （16） Represents a cluster The cluster center, that is, the sub-region The center point, represents the i-th customer point, Indicates the number of clusters, that is, the number of sub-regions after the sub-regions are divided; Determine whether all sub-areas currently divided meet the maximum range constraint of the UAV, the maximum load constraint of the UAV and If the condition of minimum value is not met, the k-means algorithm is iterated. Each iteration adds 1 to the number of sub-regions in the previous iteration and repeats the calculation. , to determine whether the current sub-area satisfies the maximum range constraint of the UAV, the maximum load constraint of the UAV and The condition for minimum value; Obtain the longest range constraint of the UAV, as shown in formula (17), （17） Indicates the i The coordinates of each customer point; represents the coordinates of the cluster center; When the number of sub-areas satisfies the UAV's maximum range constraint, the UAV's maximum load constraint and When the condition with the smallest value is reached, the iteration stops and the current sub-regions and the number of sub-regions are saved.

5. The truck-UAV multi-target collaborative delivery and pickup route planning method according to claim 3 is characterized in that: Preselect the takeoff point of the drones, design a genetic-particle swarm algorithm based on the genetic algorithm and the particle swarm algorithm, and use the genetic-particle swarm algorithm to solve the optimal path for the drone swarm to perform the express delivery task in the sub-area, including: S331: Discretize the truck paths between sub-areas and obtain multiple sampling points as candidates for the pre-selected take-off points of the UAV. The discrete formula is shown in formula (18). （18） in, Indicates sub-area i With sub-region j The number of pre-selected take-off points, Indicates sub-area i With sub-region j The distance between l Indicates the distance discrete accuracy; S332: Using a sequence encoding method, an initial population is created, where the initial population is a set of delivery paths for the drone swarm. The initial population includes Z individual genes, where each individual gene is a delivery path corresponding to a delivery task performed collaboratively by two or more drones. Initialize the individual genes in the initial population: Use the routing sequence and the interruption sequence to form individual genes, calculate the interval of each interruption point, and obtain the initial interruption sequence according to the interval of the interruption points, as shown in formula (19). （19） in, Indicates the interval of the break points, represents the number of delivery and pickup points in the kth sub-area, and M is the number of drones. The initial interrupt sequence divides the routing sequence into multiple initial gene subsequences starting from the starting end. The gene subsequence is the delivery path of a drone. S333: Determine whether each gene subsequence of each individual gene meets the maximum load constraint of the drone, and adjust the individual genes that do not meet the maximum load constraint: Determine whether the total demand for the delivery and pickup points of the first part of the gene subsequence of the routing sequence of an individual gene meets the maximum load constraint of the UAV; If the maximum load constraint of the drone is satisfied, the first element of the gene subsequence adjacent to the first part of the gene subsequence is selected and added to the first part of the gene subsequence to form a new first part of the gene subsequence, and it is determined whether the new first part of the gene subsequence satisfies the maximum load constraint of the drone. If so, the first element in the aforementioned adjacent gene subsequence is added to the first part of the gene subsequence to continue to form a new first part of the gene subsequence; the above process is repeated until the first element selected does not satisfy the maximum load constraint of the drone, and the element is removed; the element represents a certain delivery point sequence number; If the maximum payload constraint of the drone is not met, the last element of the first gene subsequence is added to the gene subsequence adjacent to the first gene subsequence to form a new gene subsequence, and the element is removed from the first gene subsequence. The process of removing elements is repeated until the total demand for the delivery and pickup points of the gene subsequence meets the maximum payload constraint of the drone, thus forming a new gene subsequence. Repeat the above process of determining whether the total demand for gene subsequence delivery points meets the maximum load constraint of the drone and forming a new gene subsequence until the total demand for delivery points of all generated gene subsequences meets the maximum load constraint of the drone, completing the adjustment of individual genes. The element represents a certain delivery point sequence number S334: Use the PSO algorithm to solve the delivery path of a single individual gene and obtain the optimal path for each gene subsequence of the single individual gene: Set the number of particle swarms, the speed and position of the initial particles, and the maximum number of iterations to initialize the particle swarm; the particle swarm represents the path set of a gene subsequence; The initial position of the particle swarm is the take-off point of the sub-region ; The particle velocity and position update formulas are shown in formulas (20) and (21), and the next passing delivery point is obtained; （20） （21） in, Represents the current particle i speed, Indicates the next moment particle i speed, Represents the current particle i location, Represents particles i The historical optimal solution, represents the historical optimal solution of the group, There is a swap sequence X that makes After X transformation, we get , similarly, is also a swap sequence, symbol Indicates that two exchange sequences are combined into one exchange sequence, symbol Indicates that a sequence is exchanged according to the exchange sequence. and are parameters, representing and The acceptance probability of is shown in formulas (22) and (23), （22） （23） represents the total number of iterations, Indicates the number of current iterations, ; when When convergence is reached, the calculated particle position is the optimal position, that is, the optimal path of a gene subsequence; Repeat the PSO algorithm solution process for the Z individual genes in the initial population to obtain the optimal path for each individual gene, that is, Z individuals; S335: Use genetic algorithm to update individual genes in the initial population: Select operator: Using the elitist model, the best individual among the Z individuals obtained by the PSO algorithm in S334 is retained, and the remaining Z-1 individuals are selected according to the roulette method based on the fitness value. Individuals and optimal individuals together constitute individual; use Individuals generate offspring: exist Randomly select two individuals from the individuals as parent individuals, and choose one of the sequential crossover operator and the position-based crossover operator to generate the selection parameters of the offspring. , as shown in formula (24), （24） Among them, the symbol Indicates that if the given random number is greater than , we use the sequential crossover operator , otherwise the position-based crossover operator is used ,symbol Indicates that the parent is crossovered using the selected crossover operator and Perform crossover to generate new offspring. and Represents two offspring produced by the crossover of parent individuals; Traversal All individuals in individuals, until the number of offspring generated is equal to When the sum of individuals equals the initial population size, generation of offspring stops; Repeat the iterative steps S333-S335 until the total distance of the UAVs converges, stop updating the individual genes, and obtain the optimal path.

6. The truck-UAV multi-target collaborative express delivery path planning method according to claim 1 is characterized in that: The customer point parameters include customer point coordinates, the services required by each customer point, the weight of the express delivery required by each customer node that requires delivery services, and the visited status; wherein the visited status is a binary variable with a value of one or zero.

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