A dispatch optimization method and system based on vehicle unmanned aerial vehicle cooperative distribution

Abstract

The application discloses a scheduling optimization method and system based on vehicle-unmanned aerial vehicle (UAV) cooperative distribution, constructs a mixed integer programming model first, and then divides a complex vehicle-UAV cooperative problem into two problems, i.e., a vehicle path planning problem and a UAV take-off and landing point selection problem, by using a logic-based Benders decomposition method, alternately solves the vehicle path planning problem and the UAV take-off and landing point selection problem, dynamically generates Benders cuts to reduce an algorithm search space, iteratively solves a target value of the vehicle-UAV cooperative problem, and obtains accurate path planning, thereby improving the efficiency of cooperative distribution.

Description

Technical Field

[0001] This invention relates to the field of logistics distribution and scheduling technology, and in particular to a scheduling optimization method and system based on vehicle-drone collaborative delivery. Background Technology

[0002] With the continuous maturation of drone technology, drones have been widely used in various scenarios (such as communication delay, surveillance, and urban logistics). However, drones have relatively low range and carrying capacity. During logistics delivery, drones need to coordinate with different transportation vehicles, such as drones and trucks, to achieve last-mile delivery.

[0003] While conventional path planning algorithms can plan the paths for drones and vehicles to deliver goods separately, they do not take into account the limitations and constraints of collaborative delivery, resulting in inaccurate path planning and low efficiency in collaborative delivery. Summary of the Invention

[0004] The main objective of this invention is to provide a scheduling optimization method, system, intelligent terminal, and computer-readable storage medium based on vehicle-drone collaborative delivery, aiming to solve the problems of inaccurate route planning and low efficiency in collaborative delivery in the prior art.

[0005] To achieve the above objectives, the first aspect of the present invention provides a scheduling optimization method for vehicle-drone collaborative delivery, comprising:

[0006] Based on the constraints of vehicle-drone collaborative delivery, a mixed integer programming model is constructed;

[0007] The mixed integer programming model is decomposed into a vehicle path planning problem and an UAV take-off and landing point selection problem using the logic-based Benders decomposition method.

[0008] Solve the vehicle routing problem to obtain the optimal solution to the vehicle routing problem;

[0009] Based on the optimal solution to the vehicle path planning problem, the UAV take-off and landing point selection problem is solved, and Benders cut is generated.

[0010] The Benders cut is added to the vehicle routing problem, and the vehicle routing problem is solved iteratively until the preset conditions are met to obtain the scheduling optimization result.

[0011] Optionally, the vehicle delivery route is set as a coupling variable between the vehicle routing problem and the UAV take-off and landing point selection problem to update the vehicle routing problem and the UAV take-off and landing point selection problem. The vehicle routing problem is modeled as a column generation model and solved using a column generation algorithm. The optimal solution to the vehicle routing problem is a set of routes.

[0012] Optionally, the mixed-integer programming model is further decomposed into the original vehicle routing problem and the original UAV take-off and landing point selection problem, where the coupling variables are not the vehicle delivery route. The generation of Benders cut includes:

[0013] When the UAV take-off and landing point selection problem has no feasible solution, the Benders solver is used to verify the feasibility of the original UAV take-off and landing point selection problem and obtain the verification result.

[0014] The Benders cut is generated based on the verification result.

[0015] Optional, also includes:

[0016] When the number of iterations increases by a preset threshold and the UAV take-off and landing point selection problem has an optimal solution, the original UAV take-off and landing point selection problem is solved to generate the Benders cut.

[0017] Optionally, the step of using a column generation algorithm to solve the vehicle routing problem includes:

[0018] An initial feasible solution is generated based on a genetic algorithm;

[0019] Using the initial feasible solution as the initial column, a restricted linear principal problem is constructed.

[0020] Solving the restricted linear principal problem yields the dual vector;

[0021] Based on the dual vector, an elementary shortest path problem with resource constraints is constructed according to the pricing problem.

[0022] Solve the elementary shortest path problem with resource constraints to generate a new column;

[0023] Add the new column to the restricted linear principal problem, return to the solution of the restricted linear principal problem to obtain the dual vector for iterative solution, until the new column can no longer be obtained and the solution of the restricted linear principal problem is output.

[0024] Optionally, solving the elementary shortest path problem with resource constraints includes:

[0025] When the heuristic algorithm can find columns with negative test numbers, the same heuristic algorithm used to generate the initial feasible solution is used to filter columns with negative test numbers to solve the restricted linear principal problem; otherwise, the labeling algorithm is used to solve the restricted linear principal problem.

[0026] Optionally, the dual vector is a smooth dual vector, which is obtained by weighting the dual vector of the previous iteration and the dual vector of the current iteration to obtain a weighted dual vector and updating the dual vector of the current iteration.

[0027] A second aspect of the present invention provides a scheduling optimization system for vehicle-drone collaborative delivery, wherein the system comprises:

[0028] A mixed-integer programming model building module is used to construct mixed-integer programming models based on the constraints of vehicle-drone collaborative delivery.

[0029] The decomposition module is used to decompose the mixed integer programming model into a vehicle path planning problem and an UAV take-off and landing point selection problem according to the logic-based Benders decomposition method.

[0030] The solution module is used to solve the vehicle routing problem and obtain the optimal solution to the vehicle routing problem.

[0031] The Benders cut module is used to solve the UAV take-off and landing point selection problem based on the optimal solution of the vehicle path planning problem, and generate Benders cuts.

[0032] The iteration module is used to add the Benders cut to the vehicle routing problem, return the solution to the vehicle routing problem for iterative solution, until the preset conditions are met and the scheduling optimization result is obtained.

[0033] A third aspect of the present invention provides a smart terminal, the smart terminal including a memory, a processor, and a scheduling optimization program for vehicle-drone collaborative delivery stored in the memory and executable on the processor, wherein the scheduling optimization program for vehicle-drone collaborative delivery, when executed by the processor, implements any one of the steps of the scheduling optimization method for vehicle-drone collaborative delivery.

[0034] A fourth aspect of the present invention provides a computer-readable storage medium storing a scheduling optimization program for vehicle-drone collaborative delivery, wherein the scheduling optimization program for vehicle-drone collaborative delivery, when executed by a processor, implements any of the steps of the scheduling optimization method for vehicle-drone collaborative delivery.

[0035] As can be seen from the above, this invention first constructs a mixed integer programming model, and then uses a logic-based Benders decomposition method to divide the complex vehicle-drone collaboration problem into two problems: the vehicle path planning problem and the drone take-off and landing point selection problem. The vehicle path planning problem and the drone take-off and landing point selection problem are solved alternately, and Benders cuts are dynamically generated to reduce the algorithm search space. The objective value of the vehicle-drone collaboration problem is solved iteratively to obtain accurate path planning and improve the efficiency of collaborative delivery. Attached Figure Description

[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a schematic diagram of the scheduling optimization method based on vehicle-drone collaborative delivery provided in an embodiment of the present invention;

[0038] Figure 2 for Figure 1 A schematic diagram of a collaborative delivery scenario in the embodiment;

[0039] Figure 3 A flowchart illustrating the process of generating Benders cuts;

[0040] Figure 4 This is a flowchart illustrating the process of solving the vehicle routing problem using a column generation algorithm.

[0041] Figure 5 for Figure 1 The example demonstrates the results data applied to small-scale collaborative delivery problems;

[0042] Figure 6 for Figure 1 The example demonstrates the application of results data to medium-scale collaborative delivery problems;

[0043] Figure 7 for Figure 1 The example data is applied to the problem of large-scale collaborative delivery.

[0044] Figure 8 This is a schematic diagram of the scheduling optimization system based on vehicle-drone collaborative delivery provided in an embodiment of the present invention;

[0045] Figure 9 This is a block diagram illustrating the internal structure of a smart terminal provided in an embodiment of the present invention. Detailed Implementation

[0046] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of the invention. However, those skilled in the art will understand that the invention can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of the invention with unnecessary detail.

[0047] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0048] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0049] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0050] As used in this specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrases "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0053] Drones have gained widespread attention due to their advantages such as low energy consumption, low cost, and high accessibility, and have been widely used in various scenarios (such as communication delays, surveillance, and urban logistics). However, drones have relatively low range and carrying capacity, therefore, they need to be used in conjunction with different transportation vehicles for delivery, such as drones and trucks, or drones and unmanned vehicles.

[0054] When planning routes for the Dynamic Vehicle-Unmanned Aerial Vehicle Cooperative Scheduling Problem (DTDCSP), it is necessary to consider not only the classic vehicle routing problem but also the routing and combination of drones. Furthermore, the coupling condition between truck and drone routes must be considered, i.e., the truck needs to receive the drone after completing its service at a certain delivery point.

[0055] Current path planning algorithms can only plan the paths of drones and vehicles for individual delivery, respectively. When applied to the scheduling optimization of collaborative delivery, the path planning is inaccurate and inefficient.

[0056] Although there is some research on drone collaboration, it mainly focuses on broader application environments and computational efficiency, ignoring the limitations of collaboration strategies, such as long waiting times for trucks and fixed trucks for drone take-off and landing, which cannot achieve efficient scheduling of vehicle-drone collaboration.

[0057] This invention proposes a scheduling optimization method for vehicle-drone collaborative delivery. The vehicle-drone collaborative delivery problem is decomposed into a vehicle path planning problem and a drone take-off and landing point selection problem based on the logic-based Benders decomposition method. The vehicle path planning problem and the drone take-off and landing point selection problem are solved alternately. After optimizing the vehicle path planning problem based on the generated Benders cut, the solution process is carried out again. Through multiple iterations, the scheduling optimization result of collaborative delivery is obtained.

[0058] Exemplary method

[0059] This invention provides a scheduling optimization method for vehicle-drone collaborative delivery, deployed on electronic devices such as computers and servers. The application scenario is urban emergency response, specifically targeting the collaborative delivery of trucks and drones. The type of vehicle is not limited; it can be any type of vehicle, including unmanned vehicles, trucks, and other similar vehicles. Specifically, as shown... Figure 1 As shown, the above method includes the following steps:

[0060] Step S100: Based on the constraints of vehicle-drone collaborative delivery, construct a mixed integer programming model.

[0061] Specifically, the implementation scenarios of collaborative delivery are as follows: Figure 2As shown, there is a set of rescue delivery points C (hereinafter referred to as demand points for convenience), a set of trucks K, a set of drones U, and a comprehensive warehouse for trucks and drones. The emergency response scenario can be represented as graph G = (N, A), where N is the set of nodes including all demand points, and A is the set of arcs connecting each node, A = {(i, j) | i ≠ j}. The time taken for a truck and a drone to traverse an edge (i, j) of A is denoted as d. ij and For each truck in k∈K, it carries n when it leaves the warehouse. k A drone.

[0062] To facilitate modeling without loss of generality, the following constraints are set: 1. Only one type of truck and one type of drone are considered; 2. Drones can complete charging and replenishment of supplies during the truck's journey without additional time consumption; the service time of the truck and drone at the demand point is known; 3. Drones fly along straight-line distances, calculated using Euclidean distance; trucks need to travel along the road network, with travel distances calculated using Manhattan distance; 4. Each demand point is visited only once by either the truck or the drone; 5. Drone takeoff and landing may occur at any demand point visited by the truck (excluding the origin and destination), but the same demand point can only be taken off or landed by a drone at most once; 6. The truck's cargo capacity is sufficient to meet the total demand of any delivery point on any route, and the drone can only visit one demand point per flight; 7. The number of drones that can be parked on the truck is limited, and the number of drones on the truck at any given time cannot exceed this limit.

[0063] Under the premise of satisfying the above constraints, with the optimization objective of minimizing response time delay, and considering realistic constraints such as truck route, number of drones and range, a mixed integer programming model is constructed for the original problem of truck-drone collaboration (referred to as OP).

[0064] For ease of explanation and understanding, the variables used in this model will be explained uniformly below:

[0065] K is the set of all trucks; U is the set of all drones; C is the set of all delivery points; d i,j Let $\frac{i}{j}$ be the travel time of the truck from delivery point $i$ to delivery point $j$. T represents the flight time of the drone from delivery point i to j. i The latest service time for the i-th delivery point; The service time for the i-th delivery point; q i Let be the number of drones at the i-th delivery point; M be an arbitrarily large positive number; L be the drone's range; N3 be the maximum number of drones allowed to be carried on the truck; α be an adjustable coefficient in the objective function; and c be the number of delivery points. This is a Boolean variable indicating whether the i-th delivery point is served by truck k; This is a Boolean variable indicating whether the i-th delivery point is served by drone u; This is a Boolean variable indicating whether truck k has moved from delivery point i to delivery point j; Let t be a Boolean variable, indicating whether drone u flies from delivery point i to j; i The time it takes for the truck or drone to arrive at the i-th delivery point; l i Let i be the time when the truck or drone leaves the i-th delivery point.

[0066] The specific expression for the mixed-integer programming model is:

[0067]

[0068] The constraints are:

[0069]

[0070]

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[0072]

[0073]

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[0075]

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[0080]

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[0082]

[0083]

[0084]

[0085] The constraints (2)-(3) above ensure the balance of truck traffic, and constraints (4)-(5) ensure the normal operation of drone traffic. Specifically, constraint (2) states that the number of trucks leaving the depot should not exceed the total number of available trucks. Constraint (3) states that for each node, the number of trucks leaving must equal the number of vehicles arriving at that node. Constraints (4)-(6) ensure that each rescue request node is accessed by only one drone. Constraints (7)-(8) ensure that each request is accessed by only one truck or drone. In addition, constraints (9)-(10) establish the relationship between travel and arrival times, and constraint (11) ensures that each truck / drone can only leave after serving the delivery point. Constraint (12) stipulates that the departure time of a drone cannot be earlier than its arrival time. Constraints (13)-(16) impose restrictions on the number of drones carried by each truck. Specifically, constraint (13) stipulates that the number of drones carried by each truck at each point is greater than zero only when the truck serves that point. Constraint (14) ensures that the number of drones carried by each truck does not exceed its drone capacity. Constraints (15)-(16) provide formulas for calculating the number of drones carried by each truck. Finally, constraint (17) limits the range of each drone.

[0086] Step S200: Decompose the mixed integer programming model into a vehicle path planning problem and an UAV take-off and landing point selection problem according to the logic-based Benders decomposition method.

[0087] Specifically, Benders decomposition is used to handle problems with complex variables. Benders decomposition breaks down the primal problem into a master problem and a series of subproblems. The master problem is a relaxation of the primal problem, typically introducing new variables to approximate the original objective function. After finding a solution to the master problem, the subproblems are solved based on this solution, generating Benders cuts which are then added to the master problem. This process is iterated multiple times until a stopping condition is met and the optimal solution is obtained. However, classic Benders decomposition methods usually require the subproblems to be linear programming problems, deriving the Benders cut formula through the duality of linear programming. While this method can conveniently and efficiently generate Benders cuts, the linear programming requirement of the subproblems limits the application scope of the Benders decomposition framework and is not suitable for the application scenario of this embodiment.

[0088] The logic-based Benders decomposition method used in this embodiment is a variant of the classic Benders decomposition method. In principle, the logic-based Benders decomposition method allows subproblems to be any optimization problem, rather than specific linear or nonlinear programming problems. When certain decision variables are fixed, it can handle a wide variety of large-scale decoupling or simplification problems. In summary, the logic-based Benders decomposition method extends the underlying Benders decomposition strategy to the case where the subproblems are arbitrary optimization problems. The Benders cut is obtained by solving the inferential dual of the subproblems; when the subproblems are linear, they can be simplified to the dual of linear programming.

[0089] When performing a logic-based Benders decomposition, the demand points in the truck-drone collaborative scheduling problem are first divided into two categories: truck access points and drone access points. Once the categories of demand points are determined, the truck route planning is similar to the classic vehicle route planning problem, while the drone route planning can be simplified to the selection of take-off and landing points. Based on this insight, the truck-drone collaborative problem can be decomposed into a vehicle route planning problem (i.e., the main problem) that accesses a subset of customers and a drone take-off and landing point selection problem (i.e., the subproblem).

[0090] According to the fifth constraint set in step S100: the take-off and landing of the drone may occur at any demand point visited by the truck (excluding the origin and destination), but the same demand point can only have a maximum of one take-off or landing of the drone. The truck-drone collaborative system with c demand points can have at most... Each demand point can be accessed by a drone. When solving the vehicle routing problem, only the truck route needs to be considered; at least one demand point is selected from all demand points. The decision variables for the vehicle routing problem are: [List of demand points to be served to minimize response time latency]. and The vehicle routing problem can be represented as:

[0091]

[0092] The constraints are:

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[0097]

[0098]

[0099] The constraints (19)-(20) above are flow balance constraints; constraints (21)-(22) are time constraints, used to ensure timely delivery; constraint (23) is used to force trucks to serve the minimum number of times. One requirement point; constraint (24) is used to ensure that the variable values ​​are consistent.

[0100] Then, based on determining which demand points the trucks visited, the demand points not visited by the trucks are assigned to the drones when solving the drone take-off and landing point selection problem. The take-off and landing locations for the drones are then selected, and the truck routes are re-optimized.

[0101] Step S300: Solve the vehicle routing problem to obtain the optimal solution.

[0102] Step S400: Based on the optimal solution of the vehicle path planning problem, solve the UAV take-off and landing point selection problem and generate Benders cut.

[0103] Specifically, if the vehicle routing problem and the drone landing point selection problem are solved separately, the vehicle routing problem does not consider the constraints related to the collaboration between the truck and the drone, as well as the drone's endurance. This may lead to inappropriate delivery point selection results, causing excessive waiting times for both the truck and the drone, resulting in poor solutions, or even situations where some delivery points are inaccessible. Therefore, this invention uses a mixed-integer programming solver in the logic-based Benders decomposition method to first solve the optimal solution of the vehicle routing problem. The optimal solution is then substituted into the mixed-integer programming model to reduce the variables in the mixed-integer programming model. Next, the drone landing point selection problem is solved to obtain its solution. A dual vector is constructed based on the optimal solution of the vehicle routing problem and the solution of the drone landing point selection problem, and a Benders cut is generated based on the dual vector.

[0104] The cuts generated by the mixed-integer programming solver include feasibility cuts and optimality cuts.

[0105] Because the variables x and y in the mixed-integer programming model are connected by constraints, the UAV take-off and landing point selection problem may be infeasible, i.e., unsolvable, given a certain x. In this case, even The vehicle routing problem is feasible, and the optimal solution for the vehicle-drone collaborative delivery problem is ( ). * ,*) must satisfy In other words, the feasible region of the vehicle routing problem is now too large and should be further restricted. To correct this, a feasibility cut needs to be added to the vehicle routing problem. Regarding... The feasibility of cutting is Inequalities of the form, where It is a function with the following properties:

[0106]

[0107] After adding a feasible cut, the vehicle routing problem can be solved again, and the above steps can be repeated until a feasible solution is obtained. In the worst case, a no-good cut can be used, i.e. This eliminates currently useless solutions, but only the single, definitive solution is eliminated. Ideally, as many infeasible solutions as possible should be eliminated at once.

[0108] In this embodiment, the infeasibility of the UAV take-off and landing point selection problem means that, given the truck route y, due to limitations in UAV flight endurance and quantity, not all demand points not visited by trucks can be visited by UAVs. Assume C... k (Y k Let C represent the set of demand points accessed by trucks in the current solution. Then, the set of demand points not accessed by trucks (i.e., the set of demand points that must be accessed by drones) is C. u (Y k ) = CC k (Y k Therefore, the discard cut in this embodiment can be expressed as:

[0109] Based on the formula for discarding cuts, we can derive the proposition: If set The discard cuts of the two are related as follows: C u The resulting cut-occupying advantage C u The resulting cut.

[0110] That is: when There will always be a time when...

[0111]

[0112] when When the vehicle routing problem is the optimal solution and the UAV take-off and landing point selection problem has a feasible solution, according to the physical meaning of the integer programming model, the UAV take-off and landing point selection problem cannot be without a solution; therefore, an optimal solution must exist. At this time, it may occur In the case of, and The optimal objective values ​​for the vehicle routing problem and the drone take-off and landing point selection problem are respectively (the same as the optimal objective value for the vehicle-drone collaborative delivery problem), which means that the constraints in the current vehicle routing problem are not tight enough. Therefore, an optimal cut needs to be added to the vehicle routing problem. Regarding... The optimal cut is An inequality of the form, where B y :y→R satisfies If and only if The equality holds when the inequality is in effect. The optimal cut can be expressed as:

[0113]

[0114] That is: if the demand point is based on the current C k C u If the solutions are classified, the optimal objective value z of the vehicle-drone collaborative delivery problem must be greater than or equal to the optimal objective value of the current drone take-off and landing point selection problem.

[0115] Step S500: Add Benders cut to the vehicle routing problem, return to solve the vehicle routing problem iteratively until the preset conditions are met, and obtain the scheduling optimization result.

[0116] Specifically, the strength of the optimal cut is determined by how close it is to other feasible solutions. The optimality condition of the logic-based Benders algorithm is: Let... and This is the optimal solution to the vehicle path planning problem after adding some Benders cuts, and the optimal solution to the UAV take-off and landing point selection problem is denoted as... At this time, if but It is also the optimal solution to the problem of vehicle-drone collaborative delivery.

[0117] After adding the optimal cut to the vehicle routing problem, the vehicle routing problem is solved again. If the solution is still optimal for the vehicle routing problem, it means that z has correctly estimated the objective value of the vehicle-drone collaborative delivery problem, thus obtaining the scheduling optimization result. Otherwise, the drone take-off and landing point selection problem is solved again to generate a new Benders cut. By alternately solving the vehicle routing problem and the drone take-off and landing point selection problem, and adding the generated Benders cut to the vehicle routing problem to avoid generating the same or worse solutions in subsequent solutions, the objective value of the vehicle-drone collaborative delivery problem can be obtained after a sufficient number of iterations, i.e., the scheduling optimization result can be obtained.

[0118] In summary, by using a logic-based Benders decomposition method, the complex vehicle-drone collaboration problem is divided into two problems: vehicle path planning and drone take-off and landing point selection. At the same time, based on delivery logic, a dynamic generation mechanism for Benders cut and dominance rules are designed to reduce the algorithm's search space, solve the objective value of the vehicle-drone collaboration problem, obtain accurate path planning, and improve the efficiency of collaborative delivery.

[0119] like When the set is finite and the vehicle-drone cooperative scheduling problem has feasible solutions, the method in the above embodiment will definitely terminate because it enumerates a finite number of subproblems. However, in other cases, it is not guaranteed that the iteration will terminate, and the convergence speed of the algorithm largely depends on the strength of the Benders cut. The complexity of the dynamic truck-drone cooperative scheduling problem makes the model fuzzy and complex, which poses a significant challenge for the optimizer to solve even small-scale problems within a reasonable time. Due to the huge solution space, finding the optimal solution in a reasonable time is also challenging for heuristic algorithms.

[0120] On the other hand, the solution speed for vehicle routing problems and UAV take-off and landing point selection problems directly affects the solution efficiency of the logic-based Benders method. In this embodiment, the vehicle routing problem is a vehicle routing problem that involves visiting a subset of customers, and its solution complexity is equivalent to that of a general vehicle routing problem. The value is multiplied by , where n represents the total number of demand points and m represents the number of demand points that trucks need to access. Furthermore, since the vehicle routing problem needs to be solved again after each Benders cut, and vehicle routing problems are generally solved using branching and cutting methods, most of the time is spent on the same tree. Even though the added Benders cut can reduce the size of the vehicle routing problem to some extent, evaluating some duplicate nodes in the search tree still wastes a significant amount of time.

[0121] Therefore, to improve the efficiency of the solution, in another embodiment of the present invention, the vehicle routing problem is modeled as a column generation model. After each Benders cut is added, only the columns in the column generation model need to be checked, deleted, or added. This not only avoids repeatedly searching and evaluating truck sub-paths, but also avoids obtaining poor-quality integer solutions to the vehicle routing problem, which is beneficial for generating high-quality Benders cuts for subproblems. This method is called the Logic Benders Decomposition Approach Driven by Column Generation (LBBDCG).

[0122] The specific process is as follows: By setting the coupling variable as the truck delivery route, the mixed-integer programming model is decomposed into a vehicle routing problem and a drone take-off and landing point selection problem. The vehicle routing problem is modeled as a column generation model. Then, a column generation algorithm is used to solve the vehicle routing problem to find the optimal solution and obtain the route set. Correspondingly, the calculation expressions for feasible cuts and optimal cuts also need to be related to the route set. Let R = {r k} represents the set of routes obtained from solving the vehicle path planning problem. If the UAV take-off and landing point selection problem has no solution when solving the vehicle path planning problem, the feasibility cut can be represented as: This indicates that routes in R cannot be selected simultaneously. If there exists an optimal solution f for solving the vehicle routing problem and the UAV take-off and landing point selection problem, the optimal cut can be expressed as: This indicates that when all routes in R are selected, the target value z is f.

[0123] The main objective of the vehicle routing problem is to search for routes for trucks. Since the vehicle type in this invention is singular and the routes are symmetrical, it is naturally suitable for a column generation algorithm. The column generation algorithm not only avoids repeated searching and evaluation of vehicle routes during the iterative process of the vehicle routing problem, but also utilizes many efficient algorithms such as labeling algorithms and genetic algorithms to gradually generate sub-paths.

[0124] As described above, by changing the vehicle routing problem to a column generation model, the repeated solution of truck routes can be avoided, greatly simplifying the UAV take-off and landing point selection problem, and making it easy to transfer existing efficient vehicle routing algorithms to solve the vehicle routing problem.

[0125] Although the Benders cuts obtained by the feasibility cut calculation formula (3) and the optimal cut calculation formula (4) satisfy the requirements of the column generation algorithm, they are not tight enough, and the potential number is much larger than the Benders cuts generated by the feasibility cut calculation formula (1) and the optimal cut calculation formula (2), resulting in an increase in the number of iterations. Considering that solving the optimal solution of the UAV take-off and landing point selection problem may be difficult, but checking its feasibility using a solver is relatively easy, optimization was performed when generating the Benders cut in another embodiment. Other variables that are not vehicle delivery paths are also selected as coupling variables, decomposing the mixed integer programming model into the original vehicle routing problem and the original UAV take-off and landing point selection problem. That is, the vehicle routing problem and the UAV take-off and landing point selection problem with vehicle delivery paths as coupling variables are solved simultaneously, as well as the original vehicle routing problem and the original UAV take-off and landing point selection problem with non-vehicle delivery paths as coupling variables. Figure 3 As shown, the steps for generating Benders cuts include:

[0126] Step S410: When there is no feasible solution to the UAV take-off and landing point selection problem, the feasibility of the original UAV take-off and landing point selection problem is verified using the Benders solver, and the verification result is obtained.

[0127] Step S420: Generate Benders cut based on the verification results.

[0128] Specifically, when there is no feasible solution to the UAV take-off and landing point selection problem, the feasibility of the original UAV take-off and landing point selection problem is checked. When the check result is feasible, the Benders cut of the feasibility cut formula (1) is added to the vehicle path planning problem.

[0129] Optionally, when the number of iterations increases by a preset threshold and the UAV take-off and landing point selection problem has an optimal solution, a Benders cut can be generated by solving the UAV take-off and landing point selection problem. That is, after a certain number of iterations, when the UAV take-off and landing point selection problem has an optimal solution, the original human-machine take-off and landing point selection problem is solved, and the Benders cut of the optimal cut formula (2) is added to the vehicle path planning problem.

[0130] By optimizing the generated Benders cut as described above, the shortcomings of the Benders cut generated by the feasible cut formula (3) and the optimal cut formula (4) being not tight enough can be overcome.

[0131] Column generation algorithms are powerful optimization algorithms for solving large-scale integer programming problems. Their basic principle is essentially the same as the principle of selecting the basis variables in the simplex method iteration. In the process of solving column generation algorithms, the integer programming problem is linearly relaxed to become a linear master problem (LMP). Given the large number of variables, only a small subset is considered initially, constructing a restricted linear master problem (RLMP). By solving the optimal solution of the restricted linear master problem, the dual variables of the linear programming problem are obtained. Then, a pricing problem (PP) is constructed to find new variables that can optimize the objective function, and these are added to the restricted linear master problem for further solving. This process is iterated until no variables that can optimize the objective function can be found, at which point the optimal solution to the restricted linear master problem is obtained. If the solution is an integer, it is the optimal solution to the master problem; if the solution contains fractions, other methods are needed to obtain the optimal integer solution.

[0132] In this embodiment, as Figure 4 As shown, a column generation algorithm is used to solve the vehicle routing problem, including:

[0133] Step S310: Generate an initial feasible solution using a genetic algorithm;

[0134] Step S320: Using the initial feasible solution as the initial column, construct the restricted linear master problem;

[0135] Specifically, initial feasible solutions are a necessary prerequisite for constructing a set partition model of the restricted linear master problem (RLMP), and a good set of initial columns can reduce the number of iterations of the column generation algorithm. This embodiment uses a genetic algorithm (GA) to generate a batch of feasible solutions to the vehicle routing problem, constructs the vehicle routing problem model using Dantzig-Wolfe (DW), constructs a set partition model for all truck tasks as the restricted linear master problem, and uses the initial feasible solutions as the initial columns for the restricted linear master problem.

[0136] The expression for the restricted linear principal problem is: (MP2)∑ r∈Ω p r z r This indicates that the selected truck route minimizes delivery delays and travel distances.

[0137] The constraints are:

[0138]

[0139]

[0140]

[0141]

[0142] Among them, constraint (25) is used to ensure that N1 delivery routes are selected; constraint (26) is used to ensure that each demand point belongs to at most one delivery route, where a ir Indicates whether demand point i belongs to delivery route r; constraint (27) is used to ensure that the total number of demand points accessed by the truck is at least 1. Constraint (28) is used to apply to the decision variable z r , Apply binary restrictions.

[0143] Genetic algorithms use a simplified genetic process to perform heuristic searches of complex search spaces, ultimately finding suboptimal solutions with a relatively high probability. This embodiment constructs chromosomes for the vehicle routing problem using permutation encoding and employs a reinforced elite-preserving genetic algorithm (SEGA) for individual selection, recombination, and mutation, completing the population's evolutionary iterations and yielding a batch of good initial feasible solutions.

[0144] Step S330: Solve the restricted linear master problem to obtain the dual vector;

[0145] Specifically, the model of the restricted linear principal problem is obtained by linearly relaxing the set partitioning model and using it as a column generation algorithm. The restricted linear principal problem can be solved using the simplex method to obtain the optimal objective value (which is also the numerical lower bound of the linear principal problem) and the dual variable.

[0146] Step S340: Based on the dual vector, construct an elementary shortest path problem with resource constraints according to the pricing problem;

[0147] Step S350: Solve the elementary shortest path problem with resource constraints and generate a new column;

[0148] Step S360: Add the new column to the restricted linear principal problem, return to the solution of the restricted linear principal problem to obtain the dual vector for iterative solution, until no new column can be obtained, and output the solution of the restricted linear principal problem.

[0149] Specifically, the pricing problem aims to find variables with negative test numbers, thereby optimizing the objective function of the constrained linear master problem by adding new variables. In this embodiment, the variable represents a feasible truck route, which is a single trip by a truck. During operation, the truck needs to minimize the delay at the access point. Therefore, the pricing problem is constructed as an elementary shortest path problem with resource constraints (ESPPRC).

[0150] The expression for the pricing problem is:

[0151] (PP)min cost(r)=∑ i∈C (w i -a i λ i )-σ, (29), are used to reduce route costs, where σ and λ i The dual constraint variables represented by constraints (25) and (26) are shown. w represents the intermediate variable representing the delay of the access demand point.

[0152] The constraints are:

[0153]

[0154]

[0155]

[0156]

[0157] t i ,w i ≥0, (34)

[0158]

[0159] Constraint (30) is used to ensure the feasibility of the route; constraint (31) is used to ensure that the number of visits to each demand point does not exceed once; constraints (32)-(34) are used to calculate the time delay w of the demand point. i Constraint (35) is used to apply to decision variable a i , Apply binary restrictions.

[0160] Then, the labeling algorithm is used to solve the ESPPRC model, generating new columns. These new columns are then added to the restricted linear main problem, and the process returns to step S330 for iterative solving. When no new columns can be obtained, the solution process ends, and the solution to the restricted linear main problem is output.

[0161] The superiority criterion in the labeling algorithm is a crucial tool for improving performance. If the superiority criterion is highly effective, the number of elements in the sets U and P during the iteration process will be significantly reduced, thereby significantly accelerating the solution speed. Generally, the superiority criterion identifies useless paths by comparing the objective values ​​of two paths P and Q with the same tail node with the feasible expansion sets E and F. The basic superiority criterion for the pricing problem in this embodiment can be described as follows:

[0162] If some paths Q1 and Q2 satisfy the following formulas (36)-(39), then Q1 is dominant over Q2, and some paths Q2 can be removed from U without changing the optimal solution. cost(Q1)≤cost(Q2),(37); L(Q1)≤L(Q2),(39). Where, v Q Let ξ(Q) represent the tail node of the partial path Q, cost(Q) be the current reduction cost of Q, ξ(Q) be the expandable set of Q, and L(Q) be the tail node v in the partial path Q. Q Departure time.

[0163] This proposition asserts that any partial path that can be connected with Q2 to form a complete path can also be connected with Q1 to form a complete path. Furthermore, Q1 can always generate at least one minimum-cost complete path, the cost of which is no greater than the cost of any path generated from Q2. Based on this observation, we strengthen the dominance rule.

[0164] If the condition is satisfied: (Q1)≤cost(Q2),(40); Then, path Q1 is dominant over path Q2.

[0165] in Indicates from node The travel time to v2. Equations (36) and (39) require that the tail nodes of the two partial paths be the same. However, we replace them with Equation (42), which only requires that the partial paths extend to the same nodes and satisfy the previous dominance rule.

[0166] Due to the degenerate nature of the restricted master problem and the instability of the dual variables from one iteration to the next, the column generation algorithm suffers from convergence problems in later iterations. In one implementation scenario, a smoothing technique is used to accelerate convergence. The pricing problem is constructed using the smoothed dual vector π = απ0 + (1-)π1, where π1 is the dual solution of the restricted master problem in the current iteration, π0 is the dual solution of the restricted master problem in the previous iteration, π is the smoothed dual solution, and α∈(0,1) is the smoothing factor. When using the above smoothing technique, the generated columns may have the following three cases: a) The test numbers of the column based on the dual vectors π0 and π1 are both negative. In this case, the column with negative test numbers is directly added to the current restricted master problem; b) The test number of the column based on the dual vector π1 is negative, but the test number based on the dual vector π0 is non-negative. In this case, the value of α is gradually decreased; c) There is no column with negative test numbers based on the dual vector π1. In this case, the value of α is gradually decreased, and the updated π1 is solved simultaneously. Therefore, convergence is accelerated by weighting the dual vectors of the previous iteration and the current iteration to obtain a weighted dual vector and then updating the dual vector of the current iteration.

[0167] While the labeling method based on dynamic programming can solve the ESPPERC model precisely, it is relatively time-consuming. In fact, in the column generation algorithm, except for the final iteration which requires precise solving to verify the optimality of the current solution, subsequent iterations do not need to find the column with the most negative test result; they only need to find columns with relatively negative test results. Therefore, in the early iterations, fast and efficient heuristic algorithms (such as greedy algorithms, tabu search, genetic algorithms, etc.) can be used to find columns with negative test results. Only when the heuristic algorithm cannot find columns with negative test results is the labeling algorithm executed for precise solving. Therefore, in the early stages of column generation iterations, the same heuristic algorithm used for generating the initial solution is used to search for columns with negative test results, thereby reducing the number of calls to the labeling algorithm. In other words, when the heuristic algorithm can find columns with negative test results, the same heuristic algorithm used to generate the initial feasible solution is used to filter for columns with negative test results to solve the restricted linear main problem; otherwise, the labeling algorithm is used to solve the restricted linear main problem.

[0168] By iteratively solving the restricted linear master problem and the pricing problem, and gradually adding columns of route cost reductions that are negative to the restricted linear master problem until the route cost reductions for all routes are integers, it indicates that the restricted linear master problem has reached its optimum. At this point, if the optimal solution to the restricted linear master problem is an integer, it is the optimal solution to the master problem; if the solution is a decimal, it is a lower bound (LB) for the master problem. If the integer solution obtained from solving the integer programming version of the restricted linear master problem is an upper bound (UB) for the master problem, then a branch and price algorithm can be used to branch on variables with decimal values. Based on this branching operation at each leaf node of the binary tree, the column generation algorithm is continued, updating the upper and lower bounds until the algorithm terminates to find the optimal solution to the master problem.

[0169] This invention, within the framework of logic-based Benders decomposition, may require further iterative solving of the master problem. Therefore, it employs a bounding method (also known as the route-enumeration method in VRP) that allows adding more columns to the constrained master problem in advance to find the optimal integer solution, rather than a branch-and-price algorithm. The bounding algorithm, after generating all columns where the cost reduction of a route is negative, continues to add columns that meet the bounding requirements but have not yet been added to the constrained linear master problem, thus ensuring that the optimal solution to the constrained linear master problem is always an integer.

[0170] In summary, this embodiment organically integrates the Benders decomposition algorithm and the column generation algorithm, utilizing logic-based Benders cut, route enumeration, and dual variable smoothing techniques to improve solution efficiency. First, the Benders decomposition method divides the complex vehicle-drone collaborative delivery problem into two problems: one focusing on vehicle paths and global lower bounds, and the other on drone routes and the objective function, thus avoiding complex mathematical calculations and improving solution efficiency. Simultaneously, a dynamic generation mechanism for Benders cut and dominance rules based on logic are designed to reduce the algorithm's search space. Second, the column generation algorithm's characteristic of gradually increasing model size effectively avoids the algorithm getting trapped in local optima, and an efficient genetic algorithm is designed for the pricing problem, further improving the algorithm's efficiency. Route enumeration and labeling algorithms are used to ensure the algorithm's global search capability. This approach combines the efficiency of the Benders decomposition algorithm with the flexibility of the column generation algorithm, offering significant advantages in solving collaborative delivery problems.

[0171] The algorithm of this invention also features strong applicability. It can be applied to different scales and UAV configurations, and can be adjusted and optimized according to the specific characteristics of the problem to adapt to different needs. For example, the route enumeration and labeling algorithms in the algorithm framework are the main culprits for time consumption. Numerous experiments show that approximately 90% of the time of the column generation algorithm is consumed in the precise solution of the pricing problem. Although a genetic algorithm is introduced to reduce the number of calls to the labeling algorithm, route enumeration using the labeling algorithm is still necessary to ensure the optimality of the final solution. In real-world applications, the problem scale is often large, and the decision-making time is limited, requiring a quick acquisition of a feasible and optimal solution without focusing on proving the optimality of the solution. This is also the original intention of many heuristic algorithm designs. Thanks to the flexibility of the column generation algorithm, a highly efficient mathematical heuristic algorithm for this problem can be obtained by simply modifying the algorithm framework, removing the path enumeration step, limiting the number of calls to the labeling algorithm and the search depth, and terminating the algorithm using the total number of iterations, the number of iterations without improvement, and the running time.

[0172] The scheduling optimization method based on vehicle-drone collaborative delivery in this embodiment was applied to small-scale, medium-scale, and large-scale collaborative delivery scenarios to comprehensively verify the stability, reliability, and applicability of the algorithm, and to obtain the following results: Figures 5-7 The results data shown.

[0173] Exemplary system

[0174] like Figure 8 As shown, corresponding to the above-mentioned scheduling optimization method based on vehicle-drone collaborative delivery, this embodiment of the invention also provides a scheduling optimization system based on vehicle-drone collaborative delivery, the above-mentioned scheduling optimization system based on vehicle-drone collaborative delivery includes:

[0175] The mixed-integer programming model construction module 600 is used to construct a mixed-integer programming model based on the constraints of vehicle-drone collaborative delivery.

[0176] The decomposition module 610 is used to decompose the mixed integer programming model into a vehicle path planning problem and an unmanned aerial vehicle take-off and landing point selection problem according to the logic-based Benders decomposition method.

[0177] Solver module 620 is used to solve the vehicle routing problem and obtain the optimal solution to the vehicle routing problem;

[0178] Benders cut module 630 is used to solve the UAV take-off and landing point selection problem based on the optimal solution of the vehicle path planning problem and generate Benders cut;

[0179] The iteration module 640 is used to add the Benders cut to the vehicle routing problem, return to solve the vehicle routing problem for iterative solution, until the preset conditions are met and the scheduling optimization result is obtained.

[0180] Specifically, in this embodiment, the specific functions of the above-mentioned vehicle-drone collaborative delivery scheduling optimization system can also be referred to the corresponding description in the above-mentioned vehicle-drone collaborative delivery scheduling optimization method, which will not be repeated here.

[0181] Based on the above embodiments, the present invention also provides a smart terminal, the principle block diagram of which can be as follows: Figure 9 As shown. The aforementioned intelligent terminal includes a processor, memory, network interface, and display screen connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and a scheduling optimization program for vehicle-drone collaborative delivery. The internal memory provides an environment for the operation of the operating system and the scheduling optimization program for vehicle-drone collaborative delivery stored in the non-volatile storage medium. The network interface of the intelligent terminal is used for communication with external terminals via a network connection. When the scheduling optimization program for vehicle-drone collaborative delivery is executed by the processor, it implements the steps of any of the aforementioned scheduling optimization methods for vehicle-drone collaborative delivery. The display screen of the intelligent terminal can be a liquid crystal display (LCD) or an e-ink display.

[0182] Those skilled in the art will understand that Figure 9 The block diagram shown is merely a partial structural diagram related to the present invention and does not constitute a limitation on the smart terminal to which the present invention is applied. A specific smart terminal may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0183] In one embodiment, a smart terminal is provided, the smart terminal including a memory, a processor, and a scheduling optimization program for vehicle-drone collaborative delivery stored in the memory and executable on the processor. When the scheduling optimization program for vehicle-drone collaborative delivery is executed by the processor, it implements the steps of any of the scheduling optimization methods for vehicle-drone collaborative delivery provided in the embodiments of the present invention.

[0184] This invention also provides a computer-readable storage medium storing a scheduling optimization program for vehicle-drone collaborative delivery. When executed by a processor, the scheduling optimization program implements the steps of any of the scheduling optimization methods for vehicle-drone collaborative delivery provided in this invention.

[0185] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0186] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the above device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this invention. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0187] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0188] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0189] In the embodiments provided by this invention, it should be understood that the disclosed apparatus / terminal devices and methods can be implemented in other ways. For example, the apparatus / terminal device embodiments described above are merely illustrative. For instance, the division of the above modules or units is merely a logical functional division, and in actual implementation, it can be divided in other ways. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0190] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not mean that the essence of the corresponding technical solutions deviates from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A scheduling optimization method based on vehicle-drone collaborative delivery, characterized in that, The method includes: Based on the constraints of vehicle-drone collaborative delivery, a mixed integer programming model is constructed; The mixed-integer programming model is decomposed into a vehicle routing problem and a drone take-off and landing point selection problem using the logic-based Benders decomposition method. The coupling variable between the vehicle routing problem and the drone take-off and landing point selection problem is the vehicle delivery route. The vehicle routing problem is modeled as a column generation model, and a column generation algorithm is used to solve the vehicle routing problem. The optimal solution to the vehicle routing problem is a set of routes. The process of solving the vehicle routing problem using the column generation algorithm includes: generating an initial feasible solution using a genetic algorithm; using the initial feasible solution as an initial column to construct a restricted linear master problem; solving the restricted linear master problem to obtain a dual vector; and based on the dual vector, constructing an elementary shortest path problem with resource constraints according to the pricing problem. The problem involves solving the resource-constrained elementary shortest path problem to generate a new column; adding the new column to the restricted linear master problem; returning to the solution of the restricted linear master problem to obtain the dual vector for iterative solution until the new column cannot be obtained and outputting the solution of the restricted linear master problem; the solution of the resource-constrained elementary shortest path problem includes: when the heuristic algorithm can find a column with a negative test number, using the same heuristic algorithm as that used to generate the initial feasible solution to filter the column with a negative test number to solve the restricted linear master problem; otherwise, using a labeling algorithm to solve the restricted linear master problem; the dual vector is a smoothed dual vector, obtained by weighting the dual vector of the previous iteration and the dual vector of the current iteration, and updating the dual vector of the current iteration; Solve the vehicle routing problem to obtain the optimal solution to the vehicle routing problem; Based on the optimal solution to the vehicle path planning problem, the UAV take-off and landing point selection problem is solved, and Benders cut is generated. The Benders cut is added to the vehicle routing problem, and the vehicle routing problem is solved iteratively until the preset conditions are met to obtain the scheduling optimization result.

2. The scheduling optimization method for vehicle-drone collaborative delivery as described in claim 1, characterized in that, The mixed-integer programming model is further decomposed into the original vehicle routing problem and the original UAV take-off and landing point selection problem, where the coupling variables are not the vehicle delivery route. The generation of Benders cut includes: When the UAV take-off and landing point selection problem has no feasible solution, the Benders solver is used to verify the feasibility of the original UAV take-off and landing point selection problem and obtain the verification result. The Benders cut is generated based on the verification result.

3. The scheduling optimization method for vehicle-drone collaborative delivery as described in claim 2, characterized in that, Also includes: When the number of iterations increases by a preset threshold and the UAV take-off and landing point selection problem has an optimal solution, the original UAV take-off and landing point selection problem is solved to generate the Benders cut.

4. A scheduling optimization system based on vehicle-drone collaborative delivery, characterized in that, The system includes: A mixed-integer programming model building module is used to construct mixed-integer programming models based on the constraints of vehicle-drone collaborative delivery. The decomposition module is used to decompose the mixed-integer programming model into a vehicle routing problem and a drone take-off and landing point selection problem according to the logic-based Benders decomposition method. The coupling variable between the vehicle routing problem and the drone take-off and landing point selection problem is the vehicle delivery route. The vehicle routing problem is modeled as a column generation model, and the vehicle routing problem is solved using a column generation algorithm. The optimal solution to the vehicle routing problem is a set of routes. The process of solving the vehicle routing problem using the column generation algorithm includes: generating an initial feasible solution using a genetic algorithm; constructing a restricted linear master problem using the initial feasible solution as an initial column; solving the restricted linear master problem to obtain a dual vector; and constructing an elementary optimal solution with resource constraints based on the dual vector and the pricing problem. The problem involves solving the elementary shortest path problem with resource constraints to generate a new column; adding the new column to the restricted linear master problem; returning to the solution of the restricted linear master problem to obtain the dual vector for iterative solution until the new column cannot be obtained and the solution of the restricted linear master problem is output; solving the elementary shortest path problem with resource constraints includes: when the heuristic algorithm can find a column with a negative test number, using the same heuristic algorithm as that used to generate the initial feasible solution to filter the column with a negative test number to solve the restricted linear master problem; otherwise, using a labeling algorithm to solve the restricted linear master problem; the dual vector is a smoothed dual vector, which is obtained by weighting the dual vector of the previous iteration and the dual vector of the current iteration to obtain a weighted dual vector and updating the dual vector of the current iteration; The solution module is used to solve the vehicle routing problem and obtain the optimal solution to the vehicle routing problem. The Benders cut module is used to solve the UAV take-off and landing point selection problem based on the optimal solution of the vehicle path planning problem, and generate Benders cuts. The iteration module is used to add the Benders cut to the vehicle routing problem, return the solution to the vehicle routing problem for iterative solution, until the preset conditions are met and the scheduling optimization result is obtained.

5. A smart terminal, characterized in that, The smart terminal includes a memory, a processor, and a scheduling optimization program for vehicle-drone collaborative delivery stored in the memory and executable on the processor. When the scheduling optimization program for vehicle-drone collaborative delivery is executed by the processor, it implements the steps of the scheduling optimization method for vehicle-drone collaborative delivery as described in any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a scheduling optimization program for vehicle-drone collaborative delivery, which, when executed by a processor, implements the steps of the scheduling optimization method for vehicle-drone collaborative delivery as described in any one of claims 1-3.

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