Truck and unmanned aerial vehicle collaborative distribution method based on hybrid eagle-variable neighborhood search

Abstract

The invention provides a truck and unmanned aerial vehicle cooperative distribution method based on hybrid eagle-variable neighborhood search, and relates to the field of vehicle and unmanned aerial vehicle cooperative scheduling. According to the method, firstly, truck group resources and customer point demands are acquired; secondly, taking minimization of the total operation cost as an optimization target, and constructing a truck and unmanned aerial vehicle collaborative distribution model without limiting the time sequence relation of arrival of the truck and the unmanned aerial vehicle at the convergence point; and finally, solving and constructing the model by adopting a hybrid eagle-variable neighborhood search algorithm to obtain a global optimal solution, and decoding to obtain an optimal truck group service customer point number, a service sequence of each customer point and total operation cost. In the modeling process, the time sequence relation of arrival of the trucks and the unmanned aerial vehicles at the confluence point is not limited, and the method is closer to the characteristic of a multi-truck unmanned aerial vehicle collaborative distribution problem. And reliable decision support can be provided for distribution enterprises in a complex real truck and unmanned aerial vehicle cooperative distribution environment.

Description

Technical Field

[0001] The present invention relates to the field of vehicle-machine collaborative dispatching, and in particular to a truck-unmanned aerial vehicle collaborative delivery method based on hybrid Skyhawk-variable neighborhood search. Background Art

[0002] The truck-drone collaborative delivery problem is a typical combinatorial optimization problem that has received extensive attention and research in recent years.

[0003] The use of trucks and drones for collaborative transportation can provide fast and low-cost logistics solutions in complex terrain and special scenarios, such as logistics delivery, precision agriculture, and emergency medical response. In general truck-drone collaborative delivery problems, multiple truck groups (a truck group consists of a truck and a drone) perform delivery services for a group of customers, and a drone is dispatched to serve one customer point at a time. The drone takes off from the truck and arrives at the rendezvous point after serving the customer point and rendezvousing with the truck. Drones have the characteristics of fast speed and strong flexibility. Compared with traditional truck delivery problems, they can effectively save time and reduce costs. In previous studies, heuristic algorithms have been widely used to solve truck-drone collaborative delivery problems.

[0004] In the traditional truck-drone collaborative delivery model, it is generally assumed that the demand and time window of each customer point are known, and trucks and drones serve all customers together. Drones only serve one customer point at a time, and trucks serve as launch and recovery platforms for drones. In the coordination of trucks and drones at the rendezvous point, many scholars directly specify that drones must arrive at the rendezvous point later than trucks. However, in actual situations, when the demand of customer points is relatively small and the customer points are densely distributed, drones dispatching to serve multiple customer points at a time may bring greater economic benefits and time savings (reducing the number of drone launches and recoveries); trucks and drones may arrive at the rendezvous point first and wait for rendezvous, and drones may not necessarily arrive at the rendezvous point later than trucks. Summary of the invention

[0005] 1. Technical issues to be resolved In view of the shortcomings of the prior art, the present invention provides a truck-UAV collaborative delivery method based on hybrid Skyhawk-variable neighborhood search, which solves the unreasonable technical problem that a designated UAV must arrive at the meeting point later than the truck.

[0006] (II) Technical solution To achieve the above objectives, the present invention is implemented through the following technical solutions: A truck-UAV collaborative delivery method based on hybrid Skyhawk-variable neighborhood search, comprising: Obtain truck group resources and customer point requirements; Based on the truck group resources and customer point requirements, a truck-drone collaborative delivery model is constructed with the minimization of total operating costs as the optimization goal, and without limiting the time sequence of the truck and the drone arriving at the meeting point; The hybrid Sky Eagle-variable neighborhood search algorithm is used to solve the truck-UAV collaborative delivery model to obtain the global optimal solution, and decode the optimal truck group service customer point number, the service order of each customer point, and the total operating cost.

[0007] Preferably, the parameter information of the truck group resources and customer point requirements includes: The drone truck vehicle group set V = {1, 2, 3…m}, where m is the number of vehicles; Customer point set C = {1, 2, 3…n}, n is the number of customer points; The set of all nodes N={0,1,2,3…n+1}, where 0 and n+1 correspond to warehouse nodes; The drone takeoff set H = {1,2,3…H max}, H max =n / 2 is the maximum number of takeoffs; Truck speed v t , UAV speed v d ; The distance d from node i to node j ij ; The demand quantity q of each customer point i ; The time s for a truck or drone to serve customer point i i ; The time window of the customer point [α i ,β i ]; The maximum load of the truck is Q, the maximum load of the drone is Q d ; The maximum flight time E of the drone; Cost per drone takeofff b ; Fuel consumption per kilometer of trucks c , fuel price per liter f p ; Hourly delay penalty cost S w ; Maximum path time T max .

[0008] Preferably, the truck-drone collaborative delivery model includes: Objective function: Among them, min is the minimization function; f1 is the driving cost of the truck, f2 is the battery usage cost of the drone, and f3 is the penalty cost for exceeding the time window; And the constraints: Formula (5) indicates that each customer point is visited once; Formula (6) indicates that the UAV on truck k does not need to take off H max times, and customer point visits only occur during takeoff; Formula (7) indicates that the h+1th takeoff of the UAV on truck k must occur after the hth takeoff; Equations (8) to (9) represent the UAV path flow balance; Equations (10) to (12) represent the launch point of the UAV and the construction of the rendezvous point with the truck; Equations (13) to (15) indicate that the launch point and the meeting point belong to the truck service point, and the intermediate truck cannot visit other points; Equations (16) to (19) represent the truck path flow balance; Formulas (20) to (21) represent load limits; Formula (22) represents the battery life limit; Formula (23) represents the time constraint for the UAV to reach the launch point, where M represents a large number; Formula (24) represents the time constraint for the drone to reach the customer point; Formula (25) represents the time when the truck leaves the warehouse node and arrives at the first customer point; Formula (26) represents the time constraint for the truck to arrive at the next node j from leaving node i; Formula (27) indicates that the customer point of the hth takeoff of drone k is the rendezvous point i, and truck k has to wait for the drone to rendezvous before continuing from the rendezvous point i to the next node j, without restricting the time sequence of the truck and drone arriving at the rendezvous point i; Formula (28) indicates that the time when the truck arrives at the launch point of the h+1th takeoff of the UAV is not less than the time when the truck arrives at the rendezvous point of the hth takeoff; Formula (29) indicates that node i is both a meeting point and a separation point. To reach the next point j of the UAV, it is necessary to wait until the UAVs meet before continuing; Formulas (30) to (31) represent the end time of the truck and drone serving customer point i respectively; Formula (32) represents the path duration constraint of the truck; The explanations of each variable are as follows: Binary variable x ijk , indicating that truck k travels from node i to node j, if yes, then it is 1, otherwise it is 0; Binary variable y ijkh , indicating that the drone on truck k takes off for the hth time and flies from node i to j. If yes, it is 1, otherwise it is 0; Binary variable z kh , indicating whether the drone on truck k takes off for the hth time, if yes, it is 1, otherwise it is 0; Binary variables , indicating whether truck k serves customer point i, if yes, it is 1, otherwise 0; Binary variables , indicating that the drone on truck k serves customer point i in the hth takeoff, if yes, it is 1, otherwise 0; Binary variables , indicating whether customer point i is the separation point of drone k’s h-th takeoff, if yes, it is 1, otherwise it is 0; Binary variables , indicating whether customer point i is the meeting point for the hth takeoff of drone k, if yes, it is 1, otherwise it is 0; The time when the truck arrives at customer point i ; The time when the drone arrives at customer point i ; Completion time of truck service customer point i ; Completion time of drone service customer point i ; The delay time p of customer point i i ; Subloop elimination variables for trucks ; Sub-loop of drone to eliminate variables .

[0009] Preferably, the hybrid Skyhawk-variable neighborhood search algorithm is used to solve the truck-UAV collaborative delivery model to obtain the global optimal solution; including: S31, set the algorithm parameters of the hybrid Skyhawk-variable neighborhood search algorithm, including the number of iterations t, the maximum number of iterations T, the maximum number of iterations k for variable neighborhood search max , the global optimal solution g best ; S32, introduce the Hammersley sequence and initialize the population; assuming there are X eagle individuals, the position of the qth individual is defined as , x q,j represents the position of customer point j in the qth individual, corresponding to the distribution order of customer point j in the total distribution plan; S33, based on the total operating cost of each individual solution, calculate the fitness of each individual in the search space and calculate the global optimal solution g best and the average position X of individuals in the population mean ; S34, let t=1; S35, for the current iteration number t, calculate the random value rand and the nonlinear balance factor ψ(t), and determine whether rand≤ψ(t) holds. If so, proceed to S36, otherwise proceed to S37; S36: Execute the exploration phase, during which: If rand ≤ 0.5, use the vertical curved high-flying search strategy X a Select the search space and the calculation formula is as follows: Among them, X a (t+1) is the search strategy X a The new solution generated in the t+1th iteration, X best (t) is the optimal solution in the population under the current iteration number t; X mean (t) is the average position of individuals in the population at the current iteration number t, and ; If rand>0.5, use the search strategy of equal-altitude flight with short gliding attack X b Exploring in the divergent search space, the calculation formula is as follows: Among them, X b (t+1) is the search strategy X b The new solution generated in the t+1th iteration; D is the search space, Levy(D) is the Levy flight distribution function with respect to D; X R (t) is the position of a hawk randomly selected from the population at the current iteration number t; x and y are both intermediate parameters used to represent the shape of the search area; S37, execution development phase, during this phase: If rand ≤ 0.5, use the low-flying search strategy X with a slow descent attack c Exploring in the convergent search space, the calculation formula is as follows: Among them, X c (t+1) is the search strategy X c The new solution generated in the t+1th iteration; UB and LB are the upper and lower bounds of the population space, corresponding to the maximum and minimum values ​​of all customer point numbers; α and δ are both constants; If rand>0.5, the search strategy of walking and grabbing prey to dive is adopted X d To narrow the exploration range, the calculation formula is as follows: Wherein, QF(t) represents the mass function of the eagle at the current iteration number t; G1 is the motion parameter of the eagle when monitoring its prey during flight; X(t) is the initial flight position of the eagle at the current iteration number t; G2 is the flight slope of the eagle when following its prey during flight; S38, adopt search strategy X a , X b , X c or X d The updated solution X new = or , execute the local neighborhood search strategy until the maximum number of neighborhood searches k is reached max ; S39, calculate the fitness of each individual in the current population and update the global optimal solution g best , determine whether the number of iterations t≤T is true, if true, return to S35, otherwise, end the algorithm and output the global optimal solution g best .

[0010] Preferably, the Hammersley sequence is used in S32 to generate the position of the individual, and the calculation formula is as follows: in, is the first sequence value; The base b j The cardinality inversion function, a j-1 To convert the integer j-1 into base b.

[0011] Preferably, the nonlinear balance factor is expressed as: Among them, ξ is the nonlinear perturbation coefficient, max , min are the maximum and minimum values ​​of ξ respectively; γ is the disturbance factor; cos is the cosine function.

[0012] Preferably, in S38, for the solution X new , perform the following steps in sequence: Step 1: Set the number of local neighborhood searches k=1; Step 2: For the current solution, select the neighborhood structure N1 to perform neighborhood change: Randomly select two customer points served by trucks on the path, exchange their service order, and get a new solution X N1 ; Step 3: If the new solution is X N1 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 4, otherwise end the neighborhood search; Step 4: Select the neighborhood structure N1 to perform neighborhood changes: Randomly select a customer point served by a drone and a customer point served by a truck on the path, exchange their service order and service mode, and get a new solution X N2 ; Step 5: If the new solution is X N2 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 6, otherwise end the neighborhood search; Step 6: Select the neighborhood structure N3 to perform neighborhood changes: Randomly select a customer point served by a truck and change its service method to obtain a new solution X N3 ; Step 7: If the new solution is X N3 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 8, otherwise end the neighborhood search; Step 8: Select the neighborhood structure N4 to perform neighborhood changes: Randomly select a drone task, change its service order, and get a new solution N4 ; Step 9: If the new solution is X N4 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 2, otherwise end the neighborhood search.

[0013] A truck-UAV collaborative delivery system based on hybrid Skyhawk-variable neighborhood search, comprising: The acquisition module is used to obtain truck group resources and customer point requirements; A construction module is used to construct a truck-drone collaborative delivery model based on the truck group resources and customer point requirements, with minimization of total operating costs as the optimization goal, and without limiting the time sequence of the truck and the drone arriving at the meeting point; The solution module is used to solve the truck-UAV collaborative delivery model by adopting a hybrid Sky Eagle-variable neighborhood search algorithm to obtain the global optimal solution, and decode the optimal truck group service customer point number, the service order of each customer point, and the total operating cost.

[0014] A storage medium stores a computer program for truck-drone collaborative delivery based on hybrid Skyhawk-variable neighborhood search, wherein the computer program enables a computer to execute the truck-drone collaborative delivery method based on hybrid Skyhawk-variable neighborhood search as described above.

[0015] An electronic device, comprising: One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, the programs including methods for executing the truck-drone collaborative delivery method based on the hybrid Sky Eagle-variable neighborhood search as described above.

[0016] (III) Beneficial effects The present invention provides a truck-drone collaborative delivery method based on hybrid Skyhawk-variable neighborhood search. Compared with the prior art, it has the following beneficial effects: In the present invention, firstly, the resources of the truck group and the demand of the customer point are obtained; secondly, the truck-drone collaborative distribution model is constructed with the optimization goal of minimizing the total operating cost, and the time sequence of the truck and the drone arriving at the meeting point is not restricted; finally, the hybrid Eagle-variable neighborhood search algorithm is used to solve the construction model, obtain the global optimal solution, and decode the optimal truck group service customer point number, the service order of each customer point, and the total operating cost. In the modeling process, the time sequence of the truck and the drone arriving at the meeting point is not restricted, which is closer to the characteristics of the multi-truck drone collaborative distribution problem. The model is further solved by the hybrid Eagle algorithm and the variable neighborhood search algorithm, which is conducive to providing reliable decision support for distribution companies in the complex real truck drone collaborative distribution environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 A block diagram of a truck-drone collaborative delivery method based on hybrid Skyhawk-variable neighborhood search provided by an embodiment of the present invention; Figure 2 A schematic diagram of a truck-drone collaborative delivery provided by an embodiment of the present invention; Figure 3 A flow chart of a hybrid Skyhawk-variable neighborhood search algorithm provided by an embodiment of the present invention; Figure 4 A two-dimensional initialization population distribution diagram with a scale of 100 generated by a Hammersley sequence and a pseudo-random method respectively provided in an embodiment of the present invention; Figure 5 A function change curve diagram of a nonlinear balance factor provided in an embodiment of the present invention (the value of γ is 3 or 4). DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0020] The embodiment of the present application solves the unreasonable technical problem that a designated drone must arrive at the meeting point later than the truck by providing a truck-drone collaborative delivery method based on a hybrid Skyhawk-variable neighborhood search.

[0021] The technical solution in the embodiment of the present application is to solve the above technical problems, and the overall idea is as follows: On the one hand, through literature survey, the applicant found that no researcher has constructed a complex scheduling model by taking into account the single dispatch service for multiple customer points, the customer point time window, and the time coordination of trucks and drones at the meeting point. However, in the actual collaborative distribution environment, these problems may exist at the same time. Solving this complex problem is the key to solving the "last mile" distribution, but the traditional truck-drone collaborative distribution model cannot effectively solve this problem.

[0022] On the other hand, in terms of method, the applicant thought of using the Eagle algorithm to solve the problem. However, it cannot be ignored that although the Eagle algorithm has a strong global search capability, it still has defects such as weak local search capability. When it is combined with other algorithms, it can show good performance, including the combination with heuristic algorithms in certain specific problems. The traditional Eagle algorithm is difficult to apply to solving the current complex collaborative distribution problem.

[0023] Therefore, the applicant proposed a hybrid Sky Eagle-variable neighborhood search algorithm based on a full understanding of the problem, and solved the problem by combining the two to obtain an ideal distribution plan.

[0024] In summary, the embodiment of the present invention aims to solve the problem of multi-truck UAV collaborative delivery under time window constraints, with the goal of determining the customer points served by trucks and UAVs in each truck group, the delivery order of trucks and UAVs serving customer points in each truck group, and determining the launch point and rendezvous point nodes of the UAVs to minimize the delivery cost. Furthermore, based on the characteristics of the problem, an effective hybrid algorithm is proposed using rational analysis and mathematical derivation to solve the combinatorial optimization problem, providing a new method for the "last mile" problem of trucks and UAVs in complex environments.

[0025] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0026] Embodiment 1: like Figure 1 As shown, A truck-UAV collaborative delivery method based on hybrid Skyhawk-variable neighborhood search, characterized by comprising: S1. Obtain truck group resources and customer point requirements; S2. Based on the resources of the truck group and the needs of the customer points, a truck-drone collaborative delivery model is constructed with the minimization of the total operating cost as the optimization goal, and without restricting the time sequence of the truck and the drone arriving at the meeting point; S3. Use the hybrid Sky Eagle-variable neighborhood search algorithm to solve the truck-UAV collaborative delivery model, obtain the global optimal solution, and decode the optimal truck group service customer point number, the service order of each customer point, and the total operating cost.

[0027] The embodiment of the present invention does not limit the time sequence of the trucks and drones arriving at the meeting point during the modeling process, which is closer to the characteristics of the multi-truck drone collaborative delivery problem. The model is further solved by hybrid Sky Eagle algorithm and variable neighborhood search algorithm, which is conducive to providing reliable decision support for distribution companies in a complex real-world truck drone collaborative delivery environment.

[0028] It should be noted that the embodiments of the present invention mainly study the collaborative delivery tasks of multiple trucks and multiple drones (such as package delivery tasks). The relevant problem description is as follows: A truck group consists of a truck and a drone, which are loaded on the truck. For each truck group, the truck is equipped with a drone and travels on the road network. When the truck arrives at a customer demand point, the nearby stations can be handed over to the drone for delivery. Due to the particularity of the roads in the city, if the truck stays in place for a long time waiting for the drone to return, it may cause traffic congestion and other undesirable problems. Therefore, when the drone takes off from the truck at the launch point, the truck will continue to drive to the next station. The truck and the drone will meet at the next station, and the one that arrives first needs to wait for the other to arrive. For each drone, the drone can visit multiple customer points in each flight mission, and the truck can only travel between nodes in the road network. When performing tasks, the customer's time window constraints must be met. Each customer has a service earliest and latest time window [α i ,β i ], α i and β i They correspond to the earliest and latest service times of client node i∈C respectively. If the client arrives outside the time window, it has to wait, and if it exceeds the latest time window, it will be punished.

[0029] like Figure 2 As shown in Figure 1, the problem under study can be described by an undirected graph G=(N,A). The set of all nodes on the plane N=C∪O, where C={1,2,3…n} represents the set of all n customer nodes that need to be served. 0 represents the warehouse node, which is the node where the vehicle departs and returns. Given a vehicle with the same load Q k homogeneous trucks. A fleet of V = {1,⋯,m}, each truck is equipped with a load capacity of Q d drone. Perform delivery tasks for all n customers and meet the customer needs of all customer points q i Each customer point can only be served once by a truck or drone during the entire mission execution process, and each customer point i will have a service time s i , the service customer point must be within a predefined hard time window [α i ,β i ] is executed within, α i and β i They correspond to the earliest and latest service times of customer node i∈C respectively.

[0030] In addition, referring to the concept of "chaotic time window" in the prior art, the embodiment of the present invention stipulates that if a vehicle arrives at node i too early, it must wait until the arrival start time before being served.

[0031] After clarifying the above content, the following will introduce the various steps of the above technical solution in detail: In step S1, truck group resources and customer point requirements are obtained.

[0032] To facilitate subsequent modeling, the parameter information of truck group resources and customer point requirements obtained in this step includes the following information: The drone truck vehicle group set V = {1, 2, 3…m}, where m is the number of vehicles; Customer point set C = {1, 2, 3…n}, n is the number of customer points; The set of all nodes N={0,1,2,3…n+1}, where 0 and n+1 correspond to warehouse nodes; The drone takeoff set H = {1,2,3…H max}, H max =n / 2 is the maximum number of takeoffs; Truck speed v t , UAV speed v d ; The distance d from node i to node j ij ; The demand quantity q of each customer point i ; The time s for a truck or drone to serve customer point i i ; The time window of the customer point [α i ,β i ]; The maximum load of the truck is Q, the maximum load of the drone is Q d ; The maximum flight time E of the drone; Cost per drone takeofff b ; Fuel consumption per kilometer of trucks c , fuel price per liter f p ; Hourly delay penalty cost S w ; Maximum path time T max .

[0033] Among them, for H max=n / 2, it is necessary to point out that for drone missions, in the prior art, drone missions generally consist of three parts: launch point-service point-convergence point. Therefore, in this case, assuming that the drone can only serve one customer point at a time, the maximum number of drone missions is n / 3 (because three customer points constitute one drone mission). However, in the problem setting of the embodiment of the present invention, there is such a special possibility: the convergence point of a drone mission can be used as the launch point of the next mission. Therefore, in this case, the maximum number of drone missions is greater than n / 3. Therefore, here, the drone mission Hmax is designed with an upper limit of n / 2 (in the actual solution process, there is a situation where a mission serves multiple customer points. In fact, the maximum mission volume of the drone, that is, the maximum number of take-offs, is always less than or equal to n / 2).

[0034] Further, it is necessary to introduce the following variables, the relevant explanations are as follows: Binary variable x ijk , indicating that truck k travels from node i to node j, if yes, then it is 1, otherwise it is 0; Binary variable y ijkh , indicating that the drone on truck k takes off for the hth time and flies from node i to j. If yes, it is 1, otherwise it is 0; Binary variable z kh , indicating whether the drone on truck k takes off for the hth time, if yes, it is 1, otherwise it is 0; Binary variables , indicating whether truck k serves customer point i, if yes, it is 1, otherwise 0; Binary variables , indicating that the drone on truck k serves customer point i in the hth takeoff, if yes, it is 1, otherwise 0; Binary variables , indicating whether customer point i is the separation point of drone k’s h-th takeoff, if yes, it is 1, otherwise it is 0; Binary variables , indicating whether customer point i is the meeting point for the hth takeoff of drone k, if yes, it is 1, otherwise it is 0; The time when the truck arrives at customer point i ; The time when the drone arrives at customer point i ; Completion time of truck service customer point i ; Completion time of drone service customer point i ; The delay time p of customer point i i ; Subloop elimination variables for trucks ; Sub-loop of drone to eliminate variables .

[0035] In step S2, based on the truck group resources and customer point requirements, a truck-drone collaborative delivery model is constructed with minimizing the total operating cost as the optimization goal, and without restricting the time sequence of the truck and the drone arriving at the meeting point.

[0036] First, it should be understood that the mathematical modeling of the embodiment of the present invention is performed based on the following problem assumptions: Assumption 1: The number of batteries loaded on the truck is sufficient for the drone to complete all delivery tasks, regardless of the situation where the drone battery is insufficient.

[0037] Assumption 2: The truck also acts as a warehouse during the distribution process. The drone and the cargo are stored on the truck, and the truck can also perform delivery tasks.

[0038] Assumption 3: It is assumed that the time for drones to load and unload packages is constant, and the tasks completed by all drones will not exceed the maximum load constraint of the drones.

[0039] Assumption 4: The impact of wind speed, slope and unexpected situations is not considered during the delivery process.

[0040] Assumption 5: Under the premise of meeting the UAV's load capacity and maximum flight time restrictions, multiple customer point delivery tasks can be performed in one mission.

[0041] Assumption 6: The drone must take off from the truck and must also end the flight mission on the truck, which means that the warehouse node cannot be used as the launch point and rendezvous point for the drone mission.

[0042] Specifically, the truck-drone collaborative delivery model includes: Objective function: Among them, min is the minimization function; f1 is the driving cost of the truck, which is calculated by multiplying the fuel consumption of the truck per kilometer by the driving distance; f2 is the battery usage cost of the drone, which is calculated by multiplying the number of drone missions by the unit battery usage cost. Although there are studies in the prior art that calculate the cost according to the mileage of the drone, in real life, the cost of the drone is mainly composed of the battery usage cost; f3 is the penalty cost for exceeding the time window, which is calculated by multiplying the difference between the time when the truck or drone arrives at the customer point and the latest service time of the customer point by the unit penalty cost.

[0043] And the constraints: Formula (5) indicates that each customer point is visited once; Formula (6) indicates that the UAV on truck k does not need to take off H max times, and customer point visits only occur during takeoff; Formula (7) indicates that the h+1th takeoff of the UAV on truck k must occur after the hth takeoff; Equations (8) to (9) represent the UAV path flow balance; Equations (10) to (12) represent the launch point of the UAV and the construction of the rendezvous point with the truck; Equations (13) to (15) indicate that the launch point and the meeting point belong to the truck service point, and the intermediate truck cannot visit other points; Equations (16) to (19) represent the truck path flow balance; Formulas (20) to (21) represent load limits; Formula (22) represents the battery life limit; Formula (23) represents the time constraint for the UAV to reach the launch point, where M represents a large number; Formula (24) represents the time constraint for the drone to reach the customer point; Formula (25) represents the time when the truck leaves the warehouse node and arrives at the first customer point; Formula (26) represents the time constraint for the truck to arrive at the next node j from leaving node i; Formula (27) indicates that the customer point of the hth takeoff of drone k is the rendezvous point i, and truck k has to wait for the drone to rendezvous before continuing from the rendezvous point i to the next node j, without restricting the time sequence of the truck and drone arriving at the rendezvous point i; Formula (28) indicates that the time when the truck arrives at the launch point of the h+1th takeoff of the UAV is not less than the time when the truck arrives at the rendezvous point of the hth takeoff; Formula (29) indicates that node i is both a meeting point and a separation point. To reach the next point j of the UAV, it is necessary to wait until the UAVs meet before continuing; Formulas (30) to (31) represent the end time of the truck and drone serving customer point i respectively; Formula (32) represents the path duration constraint of the truck.

[0044] It should be emphasized that the above formula (27) indicates that the customer point of the h-th takeoff of drone k is the rendezvous point i, and truck k has to wait for the drone to rendezvous before continuing from the rendezvous point i to the next node j, without restricting the time sequence of the truck and drone arriving at the rendezvous point i; it can be interpreted as follows: The customer point of the h-th takeoff of drone k is the rendezvous point i, and truck k goes from rendezvous point i to the next node j, then formula (27) is meaningful. Otherwise, or For a very large number, the inequality never holds.

[0045] After the above two conditions are met, the following two situations can be discussed: (1) The truck arrives at the meeting point i later than the drone, that is, > , at this time, the departure time of truck k from the meeting point i to the next node j is the time it arrives at the meeting point i , the corresponding arrival time at node j Always greater than , the inequality holds and the less-than sign is taken; (2) The truck arrives at the meeting point i no later than the drone, that is, ≤ , at this time, the departure time of truck k from the meeting point i to the next node j is the time when the drone arrives at the meeting point i , the corresponding arrival time at node j = + , the inequality holds and this is the special case of taking the equality sign.

[0046] Therefore, the embodiment of the present invention does not limit the time sequence of the truck and the drone arriving at the meeting point i, and expresses it as the inequality of formula (27). This setting is different from the prior art that specifies that the drone must arrive at the meeting point later than the truck, and is closer to the characteristics of the multi-truck drone collaborative delivery problem.

[0047] In step S3, the hybrid Sky Eagle-variable neighborhood search algorithm is used to solve the truck-UAV collaborative delivery model to obtain the global optimal solution, and decode the optimal truck group service customer point number, the service order of each customer point, and the total operating cost.

[0048] Additional note: The Eagle Algorithm (AO) is a swarm intelligence algorithm proposed by Laith Abualigah et al. in 2021, inspired by the behavior of eagles in the hunting process. The algorithm has two hunting (exploration) and two hunting (exploitation) modes. The two exploration modes are high-altitude gliding and vertical dive (X a ) and silhouette flight and short slide attack (X b ), two development methods are low-altitude flight and slow descent attack (X c ) and walking and grabbing prey (X d ).

[0049] The main features of the traditional Skyhawk algorithm are as follows: The algorithm randomly generates a set of initial solutions and continuously updates the optimal solution in each iteration. The algorithm continuously switches between the exploration and development phases. When the number of iterations t≤2 / 3T, the exploration phase is executed, otherwise it enters the development phase. In the exploration phase, a random number rand between 0 and 1 is generated before each iteration. If rand≤0.5, high-altitude gliding and vertical dive (X a ) search strategy, otherwise perform contour flight and short slide attack (X b ). In the development phase, the same as the exploration phase. When rand ≤ 0.5, perform low-altitude flight and slow descent attack (X c ), otherwise execute walking and grabbing prey (X d ). After each iteration, all solutions in the population are updated, and the fitness of all new solutions in the population is calculated, and then the current optimal solution is updated. When the termination condition is reached, that is, the maximum number of iterations T is reached, the algorithm ends and the global optimal solution is output.

[0050] As mentioned above, the traditional Skyhawk algorithm has defects such as weak local search capability, so the embodiment of the present invention proposes a method such as Figure 3 The hybrid Eagle-variable neighborhood search algorithm shown solves the problem by combining the Eagle algorithm with the variable neighborhood search algorithm, thereby obtaining an ideal distribution plan.

[0051] Accordingly, combined Figure 3 This step includes: S31, set the algorithm parameters of the hybrid Skyhawk-variable neighborhood search algorithm, including the number of iterations t, the maximum number of iterations T, the maximum number of iterations k for variable neighborhood search max , the global optimal solution gbest .

[0052] S32, introduce the Hammersley sequence and initialize the population; assuming there are X eagle individuals, the position of the qth individual is defined as , x q,j It represents the position of customer point j in the qth individual, corresponding to the distribution order of customer point j in the total distribution plan.

[0053] Due to the complexity of the problem, the traditional single chromosome encoding method is not applicable to the problem here. Therefore, the embodiment of the present invention adopts double-layer chromosome encoding to encode and decode the solution through two chromosomes of equal length.

[0054] Exemplary: As shown in Table 1, if truck group 1 visits customer nodes 1, 2, 3, 4, 5, the default warehouse node is 0, and if no drone is involved in the work, then the chromosome can be encoded as 0-1-2-3-4-5-0.

[0055] Table 1 As shown in Table 2, if the drone joins at this time and serves customer points 2 and 4, then the updated solution is: the truck path is 0-1-3-5-0, and the drone solution is 1-2-3, 3-4-5. To explain in detail, when the truck starts from the warehouse and drives to customer point 1, the drone takes off from customer point 1 and goes to serve customer point 2, and will meet the truck at customer point 3. In this scenario, customer point 1 is the launch point of the drone mission, and customer point 3 is the meeting point of the drone mission.

[0056] Table 2 When multiple truck groups are involved, the chromosome length will change. Assuming that truck group 2 serves customer points 6, 7, and 8, where 7 is the drone service point, the total encoding chromosome is shown in Table 3: Table 3 It should be noted that in the problem, multiple truck groups depart from the warehouse at the same time, and all depart from the warehouse and return to the warehouse after completing their tasks. Therefore, the first and last chromosomes of each truck group should be warehouse nodes.

[0057] Accordingly, during the decoding process: First, the chromosome is segmented, that is, the entire chromosome is divided into different truck groups, and then the customer points with "1" in the lower half of the chromosome of each truck group are marked as drone service points, and the two customer points before and after the customer point are used as the launch point and the convergence point of the task respectively. If the drone serves multiple customer points, then the customer points at the two positions before and after the customer group are used as the launch point and convergence point of the drone, as shown in Table 4. In this task, the values ​​on the second column of chromosomes corresponding to 2 and 3 are both "1", that is, in this task, the drone serves customer points 2 and 3 in turn, and the decoded solution is, truck path: 0-1-4-5-0, drone path: 1-2-3-4, 1 and 4 are the launch point and convergence point respectively.

[0058] Table 4 Furthermore, the following rounding strategy is given: Since the search strategy of the Sky Eagle algorithm is updated through formula calculation, and the lower half is a binary chromosome of 0-1, decimals are inevitable. In our problem, a sorting and rounding method is used, that is, the values ​​of each chromosome after the update are rounded in descending order. If the chromosome of an individual after the update is shown in Table 5: Table 5 There are decimals in both the upper and lower parts of the table. Therefore, according to the sorting and rounding strategy, 1.4<2.1<3.4<5.3, so we round them in order of size. The rounded chromosomes in the upper part are shown in Table 6: Table 6 Since the values ​​of the chromosomes in the lower half are small and between 0 and 1, we use binary rounding. When the value x in the chromosome is ≥ 0.5, it is recorded as 1, otherwise it is recorded as 0. After rounding, the chromosomes in the lower half are shown in Table 7: Table 7 As shown in Table 8, the encoding result after integration is: Table 8 Decoding it gives the solution: truck path 0-3-2-1-0, drone path: 2-4-1.

[0059] In addition, when the Eagle algorithm iterates to find the optimal solution, the Eagle population position is generate: Among them, UB and LB are the upper and lower bounds of the population space (here refers to the maximum and minimum values ​​of all customer point numbers), n is the dimension of the solution space (here refers to the number of nodes), and rand is a random number between 0 and 1. The structure of the initial population has an important influence on the convergence speed and accuracy. The randomly distributed initial population is not evenly distributed in the search space and cannot guarantee the population diversity. Therefore, a low-discrepancy sequence Hammersley sequence is introduced, and the position generation of individuals is based on the following formula: in, is the first sequence value; The base b j The cardinality inversion function, a j-1 To convert the integer j-1 into base b.

[0060] See also Figure 4 , Figure 4 The two-dimensional initialization population distribution diagram of size 100 is generated by Hammersley sequence and pseudo-random method respectively. It can be seen that the population of Skyhawks generated by Hammersley sequence is more evenly distributed, covers a wider range of solution space, maintains good population diversity, and thus improves the optimization speed and convergence accuracy of the algorithm.

[0061] After updating, the population initialization formula is: .in is the Hammersley population, x q It is the Hammersley sequence.

[0062] It is particularly important to point out that in the initialization scheme, the above method only generates the chromosomes for the upper half, and the chromosomes for the lower half are generated by randomly selecting drone service customer points.

[0063] S33, based on the total operating cost of each individual solution, calculate the fitness of each individual in the search space and calculate the global optimal solution g best and the average position X of individuals in the population mean .

[0064] S34. Let t=1.

[0065] S35. Calculate the random value rand and the nonlinear balance factor ψ(t) for the current iteration number t, and determine whether rand≤ψ(t) holds. If so, proceed to S36; otherwise, proceed to S37.

[0066] In the traditional Tianying algorithm, the switch between the exploration phase and the development phase is performed under the condition t≤2T / 3. This method of dividing the phases based on the fixed number of iterations results in a lack of information exchange in each iteration, making it difficult to effectively balance the global search and local development capabilities, and making it easier to fall into the local optimum. Therefore, a nonlinear balance factor ψ(t) is introduced here to switch between the exploration and development phases, and t≤2T / 3 Modify to rand≤ψ(t) to improve the global coordination of the algorithm. The expression of the nonlinear balance factor is as follows: Among them, ξ is the nonlinear perturbation coefficient, max , min are the maximum and minimum values ​​of ξ respectively; γ is the disturbance factor; cos is the cosine function.

[0067] For example, max The value is 0.8, ξ min The value of is 0.2; γ is the disturbance factor, and the value of ψ is disturbed by combining the rand function. The value of γ is 3 or 4, and the function change curve is as follows: Figure 5 shown.

[0068] Combination Figure 5 To analyze, change the condition to rand≤ψ(t). The nonlinear decreasing ψ value can improve the balance between the global search and local development of the algorithm in the optimization algorithm. In the early stage of iteration, a larger ψ value makes the algorithm tend to conduct global search in the extensive exploration phase, and at the same time, there is a certain probability of entering the development phase to improve search efficiency. As the number of iterations increases, the ψ value decreases, and the algorithm conducts more local deep development phases to improve the optimization accuracy, while retaining the probability of executing the exploration phase to prevent falling into the local optimum. The nonlinear decreasing ψ value effectively balances the exploration phase and the development phase at different iteration stages, which can improve the optimization speed and accuracy of the algorithm.

[0069] S36: Execute the exploration phase, during which: If rand ≤ 0.5, use the vertical curved high-flying search strategy X a Select the search space and the calculation formula is as follows: Among them, X a (t+1) is the search strategy X a The new solution generated in the t+1th iteration, X best (t) is the optimal solution in the population under the current iteration number t; X mean (t) is the average position of individuals in the population at the current iteration number t, and ; If rand>0.5, use the search strategy of equal-altitude flight with short gliding attack X b Exploring in the divergent search space, the calculation formula is as follows: Among them, X b (t+1) is the search strategy X b The new solution generated in the t+1th iteration; D is the search space, Levy(D) is the Levy flight distribution function with respect to D; X R (t) is the position of a hawk randomly selected from the population at the current iteration number t; x and y are both intermediate parameters used to represent the shape of the search area.

[0070] S37, execution development phase, during this phase: If rand ≤ 0.5, use the low-flying search strategy X with a slow descent attack c Exploring in the convergent search space, the calculation formula is as follows: Among them, X c (t+1) is the search strategy X c The new solution generated in the t+1th iteration; UB and LB are the upper and lower bounds of the population space, corresponding to the maximum and minimum values ​​of all customer point numbers; α and δ are both constants; If rand>0.5, the search strategy of walking and grabbing prey to dive is adopted X d To narrow the exploration range, the calculation formula is as follows: Among them, QF(t) represents the mass function of the eagle at the current iteration number t; G1 is the motion parameter of the eagle when monitoring its prey during flight; X(t) is the initial flight position of the eagle at the current iteration number t; G2 is the flight slope of the eagle when following its prey during flight.

[0071] S38, adopt search strategy X a , X b , X c or X d The updated solution X new = or , execute the local neighborhood search strategy until the maximum number of neighborhood searches k is reached max .

[0072] Regarding the local neighborhood search strategy, here for the solution X new , perform the following steps in sequence: Step 1: Set the number of local neighborhood searches k=1; Step 2: For the current solution, select the neighborhood structure N1 to perform neighborhood change: Randomly select two customer points served by trucks on the path, exchange their service order, and get a new solution X N1 ; Step 3: If the new solution is X N1 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 4, otherwise end the neighborhood search; Step 4: Select the neighborhood structure N1 to perform neighborhood changes: Randomly select a customer point served by a drone and a customer point served by a truck on the path, exchange their service order and service mode, and get a new solution X N2 ; Step 5: If the new solution is X N2 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 6, otherwise end the neighborhood search; Step 6: Select the neighborhood structure N3 to perform neighborhood changes: Randomly select a customer point served by a truck and change its service method to obtain a new solution X N3 ; Step 7: If the new solution is X N3 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 8, otherwise end the neighborhood search; Step 8: Select the neighborhood structure N4 to perform neighborhood changes: Randomly select a drone task, change its service order, and get a new solution N4 ; Step 9: If the new solution is X N4 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 2, otherwise end the neighborhood search.

[0073] S39, calculate the fitness of each individual in the current population and update the global optimal solution g best , determine whether the number of iterations t≤T is true, if true, return to S35, otherwise, end the algorithm and output the global optimal solution g best .

[0074] Finally, the global optimal solution g is decoded by the above decoding rules. best Decoding is performed to obtain the optimal truck group service customer point number, the service order of each customer point, and the total operating cost.

[0075] So far, the embodiment of the present invention has completed the entire process of the truck-UAV collaborative delivery method based on hybrid Skyhawk-variable neighborhood search.

[0076] Embodiment 2: The embodiment of the present invention provides a truck-UAV collaborative delivery system based on hybrid Skyhawk-variable neighborhood search, comprising: The acquisition module is used to obtain truck group resources and customer point requirements; A construction module is used to construct a truck-drone collaborative delivery model based on the truck group resources and customer point requirements, with minimization of total operating costs as the optimization goal, and without limiting the time sequence of the truck and the drone arriving at the meeting point; The solution module is used to solve the truck-UAV collaborative delivery model by adopting a hybrid Sky Eagle-variable neighborhood search algorithm to obtain the global optimal solution, and decode the optimal truck group service customer point number, the service order of each customer point, and the total operating cost.

[0077] Embodiment 3: An embodiment of the present invention provides a storage medium storing a computer program for truck-UAV collaborative delivery based on hybrid Skyhawk-variable neighborhood search, wherein the computer program enables a computer to execute the truck-UAV collaborative delivery method based on hybrid Skyhawk-variable neighborhood search as described in Example 1.

[0078] Embodiment 4: An embodiment of the present invention provides an electronic device, including: One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and the programs include a method for executing the truck-drone collaborative delivery method based on hybrid Sky Eagle-variable neighborhood search as described in Example 1.

[0079] It can be understood that the truck-UAV collaborative delivery system based on hybrid Skyhawk-variable neighborhood search, storage medium and electronic device provided in the embodiments of the present invention correspond to the truck-UAV collaborative delivery method based on hybrid Skyhawk-variable neighborhood search provided in the embodiments of the present invention. The explanations, examples and beneficial effects of the relevant contents can refer to the corresponding parts in the truck-UAV collaborative delivery method, and will not be repeated here.

[0080] In summary, compared with the prior art, the present invention has the following beneficial effects: 1. The embodiment of the present invention aims at the problem of truck-drone collaborative delivery under time window constraints. Through the hybrid Eagle-variable neighborhood search algorithm, the customer points are first allocated to each truck group in the form of coding, and then the customer points in each truck group are allocated according to the nature of the problem. The trucks and drones in the truck group jointly perform the delivery task of the customer points, and the allocation scheme of all customer points to the truck group and the best truck-drone collaborative delivery scheme in each truck group are obtained in polynomial time; the exploration and development phases are performed for each Eagle individual; based on the fitness of each Eagle individual in the population after the development and exploration phases, the local neighborhood search strategy is performed to further develop the Eagle individuals in the population; through repeated iterations, the Eagle individuals in the population are continuously updated, and the optimal solution is finally obtained. The improved hybrid Eagle-variable neighborhood search algorithm is a very efficient algorithm in terms of convergence speed and convergence results; through this algorithm, the problem of truck-drone collaborative delivery under time window constraints can be solved, the delivery efficiency of the "last mile of express delivery" in the actual environment can be improved, and effective decision support can be provided for distribution companies, which is conducive to accelerating the intelligent process of enterprises.

[0081] 2. The embodiment of the present invention proposes that under the time window constraint, a single dispatch of a drone in the collaborative delivery of trucks and drones can serve multiple customer points. This ensures that after the customer point task is assigned to each drone, the drone can serve more customers in a shorter time, reducing the time and power consumption of multiple takeoffs and landings, so that each drone battery can be fully utilized, that is, achieving effective utilization of battery resources.

[0082] 3. The traditional Eagle algorithm has the problem of being easily trapped in local optimality during search. However, the Eagle algorithm can show good performance when combined with other algorithms in applications. The embodiment of the present invention aims at the shortcomings and advantages of the Eagle algorithm and combines it with its specific application in this problem. First, the Hammersley sequence is introduced to enhance the diversity of the population; then an adaptive balance factor is set to balance the development and exploration stages, and the local search capability of the algorithm is enhanced through local neighborhood search to ensure efficient updating of the Eagle population. This not only effectively improves the convergence speed of the algorithm and the diversity of solutions, but also can enhance the local convergence capability of the algorithm to a certain extent.

[0083] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0084] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A truck-UAV collaborative delivery method based on hybrid Skyhawk-variable neighborhood search, characterized in that: include: Obtain truck group resources and customer point requirements; Based on the truck group resources and customer point requirements, a truck-drone collaborative delivery model is constructed with the minimization of total operating costs as the optimization goal, and without limiting the time sequence of the truck and the drone arriving at the meeting point; The hybrid Sky Eagle-variable neighborhood search algorithm is used to solve the truck-UAV collaborative delivery model to obtain the global optimal solution, and decode the optimal truck group service customer point number, the service order of each customer point, and the total operating cost.

2. The truck-drone collaborative delivery method according to claim 1, characterized in that: The parameter information of the truck group resources and customer point requirements includes: The drone truck vehicle group set V = {1, 2, 3…m}, where m is the number of vehicles; Customer point set C = {1, 2, 3…n}, n is the number of customer points; The set of all nodes N={0,1,2,3…n+1}, where 0 and n+1 correspond to warehouse nodes; The drone takeoff set H = {1,2,3…H max }, H max =n / 2 is the maximum number of takeoffs; Truck speed v t , UAV speed v d ; The distance d from node i to node j ij ; The demand quantity q of each customer point i ; The time s for a truck or drone to serve customer point i i ; The time window of the customer point [α i ,β i ]; The maximum load of the truck is Q, the maximum load of the drone is Q d ; The maximum flight time of the drone, E; Cost per drone takeofff b ; Fuel consumption per kilometer of trucks c , fuel price per liter f p ; Hourly delay penalty cost S w ; Maximum path time T max .

3. The truck-drone collaborative delivery method according to claim 2, characterized in that: The truck-drone collaborative delivery model includes: Objective function: Among them, min is the minimization function; f1 is the driving cost of the truck, f2 is the battery usage cost of the drone, and f3 is the penalty cost for exceeding the time window; And the constraints: Formula (5) indicates that each customer point is visited once; Formula (6) indicates that the UAV on truck k does not need to take off H max times, and customer point visits only occur during takeoff; Formula (7) indicates that the h+1th takeoff of the UAV on truck k must occur after the hth takeoff; Equations (8) to (9) represent the UAV path flow balance; Equations (10) to (12) represent the launch point of the UAV and the construction of the rendezvous point with the truck; Equations (13) to (15) indicate that the launch point and the meeting point belong to the truck service point, and the intermediate truck cannot visit other points; Equations (16) to (19) represent the truck path flow balance; Formulas (20)~(21) represent load limits; Formula (22) represents the battery life limit; Formula (23) represents the time constraint for the UAV to reach the launch point, where M represents a large number; Formula (24) represents the time constraint for the drone to reach the customer point; Formula (25) represents the time when the truck leaves the warehouse node and arrives at the first customer point; Formula (26) represents the time constraint for the truck to arrive at the next node j from leaving node i; Formula (27) indicates that the customer point of the hth takeoff of drone k is the rendezvous point i, and truck k has to wait for the drone to rendezvous before continuing from the rendezvous point i to the next node j, without restricting the time sequence of the truck and drone arriving at the rendezvous point i; Formula (28) indicates that the time when the truck arrives at the launch point of the h+1th takeoff of the UAV is not less than the time when the truck arrives at the rendezvous point of the hth takeoff; Formula (29) indicates that node i is both a meeting point and a separation point. To reach the next point j of the UAV, it is necessary to wait until the UAVs meet before continuing; Formulas (30) to (31) represent the end time of the truck and drone serving customer point i respectively; Formula (32) represents the path duration constraint of the truck; The explanations of each variable are as follows: Binary variable x ijk , indicating that truck k travels from node i to node j, if yes, then it is 1, otherwise it is 0; Binary variable y ijkh , indicating that the drone on truck k takes off for the hth time and flies from node i to j. If yes, it is 1, otherwise it is 0; Binary variable z kh , indicating whether the drone on truck k takes off for the hth time, if yes, it is 1, otherwise it is 0; Binary variables , indicating whether truck k serves customer point i, if yes, it is 1, otherwise 0; Binary variables , indicating that the drone on truck k serves customer point i in the hth takeoff, if yes, it is 1, otherwise 0; Binary variables , indicating whether customer point i is the separation point of drone k’s h-th takeoff, if yes, it is 1, otherwise it is 0; Binary variables , indicating whether customer point i is the meeting point for the hth takeoff of drone k, if yes, it is 1, otherwise it is 0; The time when the truck arrives at customer point i ; The time when the drone arrives at customer point i ; Completion time of truck service customer point i ; Completion time of drone service customer point i ; The delay time p of customer point i i ; Subloop for trucks eliminates variables ; Sub-loop of drone to eliminate variables .

4. The truck-drone collaborative delivery method according to claim 1, characterized in that: The hybrid Skyhawk-variable neighborhood search algorithm is used to solve the truck-UAV collaborative delivery model to obtain the global optimal solution; including: S31, set the algorithm parameters of the hybrid Skyhawk-variable neighborhood search algorithm, including the number of iterations t, the maximum number of iterations T, the maximum number of iterations k for variable neighborhood search max , the global optimal solution g best ; S32, introduce the Hammersley sequence and initialize the population; assuming there are X eagle individuals, the position of the qth individual is defined as , x q,j represents the position of customer point j in the qth individual, corresponding to the distribution order of customer point j in the total distribution plan; S33, based on the total operating cost of each individual solution, calculate the fitness of each individual in the search space and calculate the global optimal solution g best and the average position X of individuals in the population mean ; S34, let t=1; S35, for the current iteration number t, calculate the random value rand and the nonlinear balance factor ψ(t), and determine whether rand≤ψ(t) holds. If so, proceed to S36, otherwise proceed to S37; S36: Execute the exploration phase, during which: If rand ≤ 0.5, use the vertical curved high-flying search strategy X a Select the search space and the calculation formula is as follows: Among them, X a (t+1) is the search strategy X a The new solution generated in the t+1th iteration, X best (t) is the optimal solution in the population under the current iteration number t; X mean (t) is the average position of individuals in the population at the current iteration number t, and ； If rand>0.5, use the search strategy of equal-altitude flight with short gliding attack X b Exploring in the divergent search space, the calculation formula is as follows: Among them, X b (t+1) is the search strategy X b The new solution generated in the t+1th iteration; D is the search space, Levy(D) is the Levy flight distribution function with respect to D; X R (t) is the position of a hawk randomly selected from the population at the current iteration number t; x and y are both intermediate parameters used to represent the shape of the search area; S37, execution development phase, during this phase: If rand ≤ 0.5, use the low-flying search strategy X with a slow descent attack c Exploring in the convergent search space, the calculation formula is as follows: Among them, X c (t+1) is the search strategy X c The new solution generated in the t+1th iteration; UB and LB are the upper and lower bounds of the population space, corresponding to the maximum and minimum values ​​of all customer point numbers; α and δ are both constants; If rand>0.5, the search strategy of walking and grabbing prey to dive is adopted X d To narrow the exploration range, the calculation formula is as follows: Wherein, QF(t) represents the mass function of the eagle at the current iteration number t; G1 is the motion parameter of the eagle when monitoring its prey during flight; X(t) is the initial flight position of the eagle at the current iteration number t; G2 is the flight slope of the eagle when following its prey during flight; S38, adopt search strategy X a , X b , X c or X d The updated solution X new = or , execute the local neighborhood search strategy until the maximum number of neighborhood searches k is reached max ; S39, calculate the fitness of each individual in the current population and update the global optimal solution g best , determine whether the number of iterations t≤T is true, if true, return to S35, otherwise, end the algorithm and output the global optimal solution g best .

5. The truck-drone collaborative delivery method according to claim 4, characterized in that: In S32, the Hammersley sequence is used to generate the position of the individual, and the calculation formula is as follows: in, is the first sequence value; The base b j The cardinality inversion function, a j-1 The integer j-1 is converted into a number in base b.

6. The truck-drone collaborative delivery method according to claim 4, characterized in that: The nonlinear balance factor is expressed as: Among them, ξ is the nonlinear perturbation coefficient, max , min are the maximum and minimum values ​​of ξ respectively; γ is the disturbance factor; cos is the cosine function.

7. The truck-drone collaborative delivery method according to claim 4, characterized in that: In S38, for the solution X new , perform the following steps in sequence: Step 1: Set the number of local neighborhood searches k=1; Step 2: For the current solution, select the neighborhood structure N1 to perform neighborhood change: Randomly select two customer points served by trucks on the path, exchange their service order, and get a new solution X N1 ; Step 3: If the new solution is X N1 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 4, otherwise end the neighborhood search; Step 4: Select the neighborhood structure N1 to perform neighborhood changes: Randomly select a customer point served by a drone and a customer point served by a truck on the path, exchange their service order and service mode, and get a new solution X N2 ; Step 5: If the new solution is X N2 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 6, otherwise end the neighborhood search; Step 6: Select the neighborhood structure N3 to perform neighborhood changes: Randomly select a customer point served by a truck and change its service method to obtain a new solution X N3 ; Step 7: If the new solution is X N3 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 8, otherwise end the neighborhood search; Step 8: Select the neighborhood structure N4 to perform neighborhood changes: Randomly select a drone task, change its service order, and get a new solution N4 ; Step 9: If the new solution is X N4 The fitness of the new solution is better, then the original solution is replaced by the new solution, and k=k+1. If k≤k max , then go to step 2, otherwise end the neighborhood search.

8. A truck-drone collaborative delivery system based on hybrid Skyhawk-variable neighborhood search, characterized in that: include: The acquisition module is used to obtain truck group resources and customer point requirements; A construction module is used to construct a truck-drone collaborative delivery model based on the truck group resources and customer point requirements, with minimization of total operating costs as the optimization goal, and without limiting the time sequence of the truck and the drone arriving at the meeting point; The solution module is used to solve the truck-UAV collaborative delivery model by adopting a hybrid Sky Eagle-variable neighborhood search algorithm to obtain the global optimal solution, and decode the optimal truck group service customer point number, the service order of each customer point, and the total operating cost.

9. A storage medium, characterized in that: It stores a computer program for truck-UAV collaborative delivery based on hybrid Skyhawk-variable neighborhood search, wherein the computer program enables the computer to execute the truck-UAV collaborative delivery method based on hybrid Skyhawk-variable neighborhood search as described in any one of claims 1 to 7.

10. An electronic device, characterized in that: include: one or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and the programs include programs for executing the truck-drone collaborative delivery method based on hybrid Sky Eagle-variable neighborhood search as described in any one of claims 1 to 7.

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