Multi-vehicle path planning method, system, device and medium with binning constraint

Abstract

The application provides a multi-vehicle path planning method, system, device and medium with bin packing constraints, comprising the following steps: S1, constructing a path planning main model; S2, relaxing the main model into a relaxed model; S3, writing a restricted relaxed model based on a set of initial solutions; S4, writing a dual problem of the restricted relaxed model; S5, constructing a sub-model based on the optimal solution of the dual problem; S6, solving the sub-model; S7, judging whether there is an optimal path according to the solution of the sub-model, if there is an optimal path, adding the optimal path to the restricted relaxed model, updating the restricted relaxed model, and starting the cycle from step S4; if there is no optimal path, ending the cycle; S8, solving the main model according to the solution space R ′ obtained in step S7 ′ to obtain the solution of the path planning problem. The application can combine bin packing and path planning, meet the actual needs of the business, and improve the application value of the algorithm.

Description

Technical Field

[0001] This invention relates to the field of algorithm technology for combinatorial optimization problems. Specifically, it designs a multi-vehicle path planning problem with binning constraints based on a column generation algorithm, and particularly relates to a method, system, device, and medium for multi-vehicle path planning with binning constraints. Background Technology

[0002] In today's rapidly developing economy, enterprises and institutions have an ever-increasing demand for logistics transportation and distribution. While ensuring timely and sufficient delivery of goods, it's also crucial to consider the associated logistics costs, including time, number of vehicles, and distance constraints. Therefore, optimizing vehicle routing has become a critical issue in the logistics field. The goal of vehicle routing problems is to design a set of feasible routes that meet customer needs while minimizing costs. Generally, cost is positively correlated with travel distance. Therefore, the modeling objective is usually to minimize the total mileage. Simultaneously, the number and load capacity of vehicles are finite. Considering the carpooling needs at different stations, it's necessary to maximize vehicle loading rates to reduce the number of vehicles and lower costs. Therefore, solving multi-vehicle routing problems with container loading constraints can effectively meet the cost reduction and efficiency improvement needs of enterprises and institutions.

[0003] For real-world problems, both the bin packing problem and the multi-vehicle routing problem are NP-hard problems, becoming increasingly difficult to solve as the problem size increases. Directly searching for the exact optimal solution is impractical for such large-scale problems; therefore, a series of algorithms for finding approximate solutions have been developed to accelerate the search for the optimal solution, resulting in better optimization performance when solving complex large-scale NP problems. In bin packing problem algorithms, the skyline algorithm can quickly find the optimal bin packing scheme. In vehicle routing problem algorithms, the column generation algorithm based on the simplex algorithm is a good method for efficiently solving large-scale linear optimization problems. Although algorithms applied to both bin packing and routing problems have been extensively studied, the application of bin packing constraints in vehicle routing problems has not been well extended or practically implemented.

[0004] In real-world logistics orders, the constraints of packing become more complex with a large number of orders and stations, making vehicle routing planning (VRP) extremely difficult to find the optimal solution. In typical routing problems, to simplify the problem, goods are often treated as fluid components during packing; loading is considered complete as long as the total volume of the goods is less than the vehicle's capacity. This can lead to situations where, even after obtaining the optimal route plan, actual loading may not be achievable, rendering the plan unimplementable. Therefore, existing solutions have room for improvement. This invention addresses the multi-vehicle routing problem with numerous stations and packing constraints by incorporating a packing module based on the skyline algorithm into the route planning optimization process, thereby ensuring both the optimal route and the feasibility of the goods loading method. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a multi-vehicle route planning method, system, device, and medium with packing constraints.

[0006] According to the present invention, a multi-vehicle route planning method, system, device, and medium with packing constraints are provided, the solution of which is as follows:

[0007] Firstly, a multi-vehicle path planning method with bin packing constraints is provided, the method comprising:

[0008] Step S1: Construct the main path planning model;

[0009] Step S2: Relax the master model into a relaxed model;

[0010] Step S3: Write the restricted relaxation model based on a set of initial solutions; where the initial solution is a set of path combinations, and a path can be represented by the order of stations visited by the vehicle;

[0011] Step S4: Write out the dual problem of the restricted relaxation model;

[0012] Step S5: Construct a sub-model based on the optimal solution to the dual problem;

[0013] Step S6: Solve the sub-model;

[0014] Step S7: Determine whether there is an optimal path based on the solution of the sub-model. If there is an optimal path, add the optimal path to the restricted relaxation model, update the restricted relaxation model, and start the loop from step S4; if there is no optimal path, end the loop.

[0015] Step S8: Obtain the solution space R′ according to the above steps, and solve the master model based on R′ to obtain the solution to the path planning problem.

[0016] Preferably, step S1 includes: in route planning with packing constraints, a penalty cost is set for each route. If all the goods at all stations on the route can be loaded, the penalty cost is 0; otherwise, the penalty cost is an arbitrarily large positive number.

[0017] The main model for path planning is as follows:

[0018]

[0019]

[0020] Here, r represents a path; R represents the set of all paths; and the decision variable x... r ∈{0,1} indicates whether path r is selected, if x r =1 indicates that path r is selected; P r P represents the binning penalty cost of path r; r ∈{0, M}, where M is an arbitrarily large positive number; N represents the set of all sites to be served; a ir This indicates whether station i is on path r; 1 indicates yes, 0 indicates no. r This represents the distance along path r.

[0021] Preferably, the relaxation in the restricted relaxation model in step S4 is reflected in relaxing the decision variables of the main model from 0-1 variables to continuous variables with values ​​between 0 and 1; while the restriction is reflected in the fact that the solution set of the relaxation model is a subset of the true solution set, and this solution set changes continuously as new paths are added during the solution process.

[0022] The dual problem refers to describing the original problem from different perspectives using methods that have the same meaning and symmetrical structure; every linear programming problem has a corresponding dual problem; the dual problems are as follows:

[0023]

[0024] Here, r represents a path; R represents the set of all paths; a ir Indicates whether station i is on path r; 1 indicates yes, 0 indicates no. i The dual variable of the relaxation problem in the master model; D r P represents the distance along path r; r P represents the binning penalty cost of path r; r ∈{0, M}, where M is an arbitrarily large positive number; N represents the set of all sites to be served.

[0025] Preferably, the sub-model for path planning is as follows:

[0026]

[0027]

[0028] Where, d ij λ represents the distance between station i and station j; p represents the packing penalty cost; i The dual variables of the relaxation problem in the main model; h represents the unloading bay; S represents the upper limit of the number of loading stations on a route; W represents the maximum load capacity of a vehicle; q i Indicates the total weight of the goods to be loaded at station i; u i Indicates the service order of site i on the path; v i The load of the vehicle after serving station i is represented; decision variable a i Indicates whether site i is selected.

[0029] Preferably, the bin packing algorithm is continuously called during the solution process in step S6, and the bin packing algorithm includes:

[0030] 1) Stack all the goods waiting to be loaded at all the service stations into pallets according to their dimensions to obtain different pallet sizes and quantities;

[0031] 2) Using the list as input, pack the boxes using the skyline algorithm;

[0032] 3) If the returned result indicates that the goods have been loaded, then p = 0; otherwise, p = M, where M is an arbitrarily large positive number.

[0033] 4) Return p to the path planning sub-model.

[0034] Secondly, a multi-vehicle routing system with packing constraints is provided, the system comprising:

[0035] Model M1: Construct the main path planning model;

[0036] Model M2: Relax the main model into a relaxed model;

[0037] Model M3: A restricted relaxation model is written based on a set of initial solutions;

[0038] Model M4: Write down the dual problem of the restricted relaxation model;

[0039] Model M5: A sub-model is constructed based on the optimal solution to the dual problem;

[0040] Model M6: Solve the aforementioned sub-model;

[0041] Model M7: Determine whether there is an optimal path based on the solution of the sub-model. If there is an optimal path, add the optimal path to the restricted relaxation model, update the restricted relaxation model, and start the loop from Model M4; if there is no optimal path, end the loop.

[0042] Model M8: The solution space R′ is obtained according to the above steps, and the main model is solved based on R′ to obtain the solution to the path planning problem.

[0043] Preferably, the module M1 includes: in route planning with packing constraints, setting a penalty cost for each route; if all the goods at all stations on the route can be loaded, the penalty cost is 0; otherwise, the penalty cost is an arbitrarily large positive number.

[0044] The main model for path planning is as follows:

[0045]

[0046] Here, r represents a path; R represents the set of all paths; and the decision variable x... r ∈{0,1} indicates whether path r is selected, if x r =1 indicates that path r is selected; P r P represents the binning penalty cost of path r; r ∈{0, M}, where M is an arbitrarily large positive number; N represents the set of all sites to be served; a ir This indicates whether station i is on path r; 1 indicates yes, 0 indicates no. r This represents the distance along path r;

[0047] The relaxation in the restricted relaxation model in module M4 is manifested in relaxing the decision variables of the main model from 0-1 variables to continuous variables with values ​​between 0 and 1; while the restriction is manifested in that the solution set of the relaxation model is a subset of the true solution set, and this solution set changes continuously as new paths are added during the solution process;

[0048] The dual problem refers to describing the original problem from different perspectives using methods that have the same meaning and symmetrical structure; every linear programming problem has a corresponding dual problem; the dual problems are as follows:

[0049]

[0050] Here, r represents a path; R represents the set of all paths; a ir Indicates whether station i is on path r; 1 indicates yes, 0 indicates no. i The dual variable of the relaxation problem in the master model; D r P represents the distance along path r; rP represents the binning penalty cost of path r; r ∈{0, M}, where M is an arbitrarily large positive number; N represents the set of all sites to be served.

[0051] Preferably, the sub-model for path planning is as follows:

[0052]

[0053]

[0054] Where, d ij λ represents the distance between station i and station j; p represents the packing penalty cost; i The dual variables of the relaxation problem in the main model; h represents the unloading bay; S represents the upper limit of the number of loading stations on a route; W represents the maximum load capacity of a vehicle; q i Indicates the total weight of the goods to be loaded at station i; u i Indicates the service order of site i on the path; v i The load of the vehicle after serving station i is represented; decision variable a i Indicates whether site i has been selected;

[0055] The bin packing algorithm is continuously invoked during the solution process of module M6. The bin packing algorithm includes:

[0056] 1) Stack all the goods waiting to be loaded at all the service stations into pallets according to their dimensions to obtain different pallet sizes and quantities;

[0057] 2) Using the list as input, pack the boxes using the skyline algorithm;

[0058] 3) If the returned result indicates that the goods have been loaded, then p = 0; otherwise, p = M, where M is an arbitrarily large positive number.

[0059] 4) Return p to the path planning sub-model.

[0060] Thirdly, an apparatus is provided, the apparatus comprising:

[0061] One or more processors;

[0062] Storage device for storing one or more programs.

[0063] When the one or more programs are executed by the one or more processors, the one or more processors perform the steps in the method.

[0064] Fourthly, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps of the method.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] This invention considers both path planning and packing constraints simultaneously when taking into account vehicle volume constraints, combining packing and path planning to effectively meet actual business needs, greatly enhance the application value of the algorithm, and increase the likelihood of the solution being implemented.

[0067] Other beneficial effects of the present invention will be explained in detail through the introduction of specific technical features and technical solutions in specific embodiments. Those skilled in the art should be able to understand the beneficial technical effects brought about by these technical features and technical solutions through the introduction of these technical features and technical solutions. Attached Figure Description

[0068] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0069] Figure 1 This is the overall flowchart of the present invention. Detailed Implementation

[0070] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0071] This invention provides a multi-vehicle route planning method with packing constraints. Route planning problems typically consider constraints such as vehicle volume, vehicle weight, and the number of service stations. When considering volume constraints, the cargo to be loaded is often treated as fluid components, meaning the total cargo volume only needs to be less than the vehicle volume. However, in practice, the actual dimensions of the cargo often prevent all cargo from being loaded as planned, leading to unrealistic route planning results. Therefore, packing constraints are crucial for the practicality of route planning problems. To address these issues, this invention aims to investigate how to incorporate packing constraints into the route planning problem based on a column generation algorithm.

[0072] The path planning problem we need to solve mainly includes the following constraints:

[0073] (1) The vehicle is required to depart from the warehouse, go to different stations in sequence to load goods, and finally return to the warehouse;

[0074] (2) The warehouse has a sufficient number of vehicles, and the models are all the same;

[0075] (3) The number of stations served by each vehicle is limited;

[0076] (4) The size, quantity and weight of the goods to be loaded at each station are known, and the vehicle must be able to load all the goods.

[0077] In constraint (4), we no longer treat the cargo to be loaded as a fluid component, but require the vehicle to load all the cargo. We use the skyline algorithm to determine whether the cargo can actually be loaded.

[0078] Reference Figure 1 As shown, the method specifically includes the following:

[0079] Step S1: Construct the path planning "master model".

[0080] Step S2: Relax the master model into a relaxed model, i.e., a linear model.

[0081] Step S3: Write out the restricted relaxation model based on a set of initial solutions.

[0082] Step S4: Write out the dual problem of the restricted relaxation model.

[0083] Step S5: Construct a sub-model based on the optimal solution of the dual problem.

[0084] Step S6: Solve the sub-model (the solution process will continuously call the bin packing algorithm).

[0085] Step S7: Determine whether there is an optimal path based on the solution of the sub-model. If there is an optimal path, add the optimal path to the restricted relaxation model, update the restricted relaxation model, and start the loop from step S4. If there is no optimal path, end the loop.

[0086] Step S8: Obtain the solution space R′ according to the steps, and solve the “master model” based on R′ to obtain the solution to the path planning problem.

[0087] Specifically, step S1 includes: When modeling the path planning problem (integer programming model) based on the column production algorithm, the granularity of the decision variables is a complete path. This allows us to handle nonlinear costs related to paths well in engineering. In path planning problems with bin packing constraints, it is only necessary to ensure that paths where goods cannot be loaded are not selected. Under this modeling approach, our solution is to set a penalty cost for each path. If all goods at all stations on the path can be loaded, the penalty cost is 0; otherwise, the penalty cost is an arbitrarily large (not infinite) positive number.

[0088] We use r to represent a path; R to represent the set of all paths; and x as the decision variable. r ∈{0,1} indicates whether path r is selected, if x r =1 indicates that path r is selected; Pr P represents the binning penalty cost of path r; r ∈{0, M}, where M is an arbitrarily large positive number; N represents the set of all sites to be served; a ir This indicates whether station i is on path r; 1 indicates yes, 0 indicates no. r This represents the distance along path r.

[0089] The path planning "main model" is as follows:

[0090]

[0091] The "main model" solves the path selection problem. However, we often don't know which paths are in the path set R, or the main model may be too large to solve directly. The column generation algorithm, on the other hand, uses a "sub-model" to continuously search for high-quality paths that satisfy the given constraints and adds them to the set R′. Therefore, R′ is a subset of R. We only need to select the optimal combination of paths from R′.

[0092] In step S4, the relaxation in the restricted relaxation model is reflected in relaxing the decision variables of the main model from 0-1 variables to continuous variables with values ​​between 0 and 1; while the restriction is reflected in the fact that the solution set of the relaxed model is a subset of the true solution set, and this solution set changes continuously as new paths are added during the solution process.

[0093] The dual problem refers to describing the original problem from different perspectives using methods that have the same meaning and symmetrical structure; every linear programming problem has a corresponding dual problem; the dual problems are as follows:

[0094]

[0095] Here, r represents a path; R represents the set of all paths; a ir Indicates whether station i is on path r; 1 indicates yes, 0 indicates no. i The dual variable of the relaxation problem in the master model; D r P represents the distance along path r; r P represents the binning penalty cost of path r; r ∈{0, M}, where M is an arbitrarily large positive number; N represents the set of all sites to be served.

[0096] The "sub-model" of path planning is as follows:

[0097]

[0098] Where, d ij λ represents the distance between station i and station j; p represents the packing penalty cost; iThe dual variables of the relaxation problem in the main model; h represents the unloading bay; S represents the upper limit of the number of loading stations on a route; W represents the maximum load capacity of a vehicle; q i Indicates the total weight of the goods to be loaded at station i; u i Indicates the service order of site i on the path; v i The load of the vehicle after serving station i is represented; decision variable a i Indicates whether station i is selected. The constraints of the sub-model guarantee that (1) the path is a loop from the warehouse to the warehouse; (2) each station is served once; (3) the number of stations on the path does not exceed S; and (4) the weight of the goods on the path does not exceed the vehicle's load capacity.

[0099] It should be noted that the packing penalty cost p for the path is a station-related function. Therefore, in practical applications, we need to define an additional function to calculate p, and use the skyline algorithm to determine whether the goods can be loaded based on the size and quantity of the goods to be loaded at the station and the size of the vehicle.

[0100] The bin packing algorithm is called repeatedly during the solution process in step S6. The bin packing algorithm includes:

[0101] 1) Stack all the goods waiting to be loaded at all the service stations into "pallets" according to their size, and obtain different pallet sizes and quantities;

[0102] 2) Using the "Takelist" as input, pack the boxes using the "Skyline Algorithm";

[0103] 3) If the result of the skyline algorithm indicates that the goods have been loaded, then p = 0; otherwise, p = M, where M is an arbitrarily large positive number.

[0104] 4) Return p to the path planning sub-model.

[0105] Here, "pallet" can be simply understood as a tray, and for each pallet, length, width, and quantity are required field attributes. The input "pallet list" to the packing algorithm refers to a list consisting of all pallets.

[0106] The "Skyline Algorithm" is a typical two-dimensional bin packing algorithm. In addition to the tray list mentioned above, the algorithm's input includes the dimensions of the vehicles to be packed. The "skyline" is a continuous polyline composed of a set of orthogonal line segments. Abstracting the vehicles into a two-dimensional coordinate system, the highest point of the currently placed tray is connected by the polyline segments to form the so-called "skyline." The algorithm stipulates that the trays to be packed can only be placed above the skyline, and the set of intersection points of the skyline polylines indicates the placement position of the tray's lower right or lower left corner. For each tray, the algorithm sequentially removes trays from the tray list and places them in the most suitable position, provided they can fit. The algorithm stops when no tray can fit or when all trays have been placed, returning a boolean value indicating whether all trays in the tray list have been packed.

[0107] This invention also provides a multi-vehicle routing system with container constraints. This system can be implemented by executing the steps of the multi-vehicle routing method with container constraints. That is, those skilled in the art can understand the multi-vehicle routing method with container constraints as a preferred embodiment of the multi-vehicle routing system with container constraints. Specifically, the system includes the following:

[0108] Module M1: Constructs the "master model" for path planning.

[0109] Module M2: Relaxes the main model into a relaxed model, i.e., a linear model.

[0110] Module M3: Restricted relaxation model is written based on a set of initial solutions.

[0111] Module M4: Write the dual problem of the restricted relaxation model.

[0112] Module M5: Constructs a sub-model based on the optimal solution of the dual problem.

[0113] Module M6: Solve the sub-model (the solution process will continuously call the bin packing algorithm).

[0114] Module M7: Determines whether an optimal path exists based on the solution of the sub-model. If an optimal path exists, it is added to the restricted relaxation model, the restricted relaxation model is updated, and the loop begins from module M4. If no optimal path exists, the loop ends.

[0115] Module M8: Obtain the solution space R′ according to the steps, and solve the “master model” based on R′ to obtain the solution to the path planning problem.

[0116] Specifically, module M1 includes: When modeling the path planning problem (integer programming model) based on the column production algorithm, the granularity of the decision variables is a complete path. This allows us to handle nonlinear costs related to paths well in engineering. In path planning problems with bin packing constraints, it is only necessary to ensure that paths where goods cannot be loaded are not selected. Under this modeling approach, our solution is to set a penalty cost for each path. If all goods at all stations on the path can be loaded, the penalty cost is 0; otherwise, the penalty cost is an arbitrarily large (not infinite) positive number.

[0117] We use r to represent a path; R to represent the set of all paths; and x as the decision variable. r ∈{0,1} indicates whether path r is selected, if x r =1 indicates that path r is selected; P r P represents the binning penalty cost of path r; r ∈{0, M}, where M is an arbitrarily large positive number; N represents the set of all sites to be served; a ir This indicates whether station i is on path r; 1 indicates yes, 0 indicates no. r This represents the distance along path r.

[0118] The path planning "main model" is as follows:

[0119]

[0120] The "main model" solves the path selection problem. However, we often don't know which paths are in the path set R, or the main model may be too large to solve directly. The column generation algorithm, on the other hand, uses a "sub-model" to continuously search for high-quality paths that satisfy the given constraints and adds them to the set R′. Therefore, R′ is a subset of R. We only need to select the optimal combination of paths from R′.

[0121] The "sub-model" of path planning is as follows:

[0122]

[0123]

[0124] Where, d ij λ represents the distance between station i and station j; p represents the packing penalty cost; i The dual variables of the relaxation problem in the main model; h represents the unloading bay; S represents the upper limit of the number of loading stations on a route; W represents the maximum load capacity of a vehicle; q i Indicates the total weight of the goods to be loaded at station i; u i Indicates the service order of site i on the path; vi The load of the vehicle after serving station i is represented; decision variable a i Indicates whether station i is selected. The constraints of the sub-model guarantee that (1) the path is a loop from the warehouse to the warehouse; (2) each station is served once; (3) the number of stations on the path does not exceed S; and (4) the weight of the goods on the path does not exceed the vehicle's load capacity.

[0125] It should be noted that the packing penalty cost p for the path is a station-related function. Therefore, in practical applications, we need to define an additional function to calculate p, and use the skyline algorithm to determine whether the goods can be loaded based on the size and quantity of the goods to be loaded at the station and the size of the vehicle.

[0126] The binning algorithm is called repeatedly during the solution process of module M6. This binning algorithm includes:

[0127] 1) Stack all the goods waiting to be loaded at all the service stations into pallets according to their dimensions to obtain different pallet sizes and quantities;

[0128] 2) Using the list as input, pack the boxes using the skyline algorithm;

[0129] 3) If the returned result indicates that the goods have been loaded, then p = 0; otherwise, p = M, where M is an arbitrarily large positive number.

[0130] 4) Return p.

[0131] Regarding the solution of all linear programming problems (including the dual problem and subproblems of the restricted relaxed master problem), the above problems are all standard linear programming problems. In the implementation of the algorithm, the optimal solution can be obtained by directly using the API of the pulp toolkit to call the standard solver. Optional solvers include CBC, GLPK, Gurobi, CPLEX, etc.

[0132] This invention provides a multi-vehicle route planning method, system, device, and medium with bin packing constraints, which can organically combine bin packing and route planning, effectively meeting the actual needs of business operations, greatly improving the application value of the algorithm, and increasing the possibility of implementing the solution results.

[0133] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0134] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A multi-vehicle path planning method with packing constraints, characterized in that, include: Step S1: Construct the main path planning model; Step S2: Relax the master model into a relaxed model; Step S3: Write the restricted relaxation model based on a set of initial solutions; where the initial solution is a set of path combinations, and a path can be represented by the order of stations visited by the vehicle; Step S4: Write out the dual problem of the restricted relaxation model; Step S5: Construct a sub-model based on the optimal solution to the dual problem; Step S6: Solve the sub-model; Step S7: Determine whether there is an optimal path based on the solution of the sub-model. If there is an optimal path, add the optimal path to the restricted relaxation model, update the restricted relaxation model, and start the loop from step S4; if there is no optimal path, end the loop. Step S8: Obtain the solution space based on the above steps. and based on Solve the master model to obtain the solution to the path planning problem; Step S1 includes: in route planning with packing constraints, a penalty cost is set for each route. If all the goods at all stations on the route can be loaded, the penalty cost is 0; otherwise, the penalty cost is an arbitrarily large positive number. The main model for path planning is as follows: Among them, using Indicates a path; The set representing all paths; decision variables Representing a path Whether it is selected, if Representing a path Selected; Representing a path Packing penalty costs; , It is an arbitrarily large positive number; This represents the set of all sites awaiting service. Indicates site Is it on the path? If yes, it is 1; otherwise, it is 0. Representing a path The distance; The relaxation in the restricted relaxation model in step S4 is reflected in relaxing the decision variables of the main model from 0-1 variables to continuous variables with values ​​between 0 and 1; while the restriction is reflected in the fact that the solution set of the relaxation model is a subset of the true solution set, and this solution set changes continuously as new paths are added during the solution process. The dual problem refers to describing the original problem from different perspectives using methods that have the same meaning and symmetrical structure; every linear programming problem has a corresponding dual problem; the dual problems are as follows: Among them, using Indicates a path; Represents the set of all paths; Indicates site Is it on the path? If yes, it is 1; otherwise, it is 0. The dual variables of the relaxation problem in the main model; Representing a path The distance; Representing a path Packing penalty costs; , It is an arbitrarily large positive number; This represents the set of all sites awaiting service. The sub-model for path planning is as follows: in, Indicates site and sites The distance between them; This indicates the cost of packing penalties; The dual variables of the relaxation problem in the main model; Indicates the unloading warehouse; This indicates the maximum number of loading stations on a route; Indicates the vehicle's maximum load capacity; Indicates site The total weight of the goods to be loaded; Indicates site The order of services along the path; Indicates that the service has been completed at the site. The load of the following vehicle; decision variables Indicates site Whether or not it was selected; The bin packing algorithm is called continuously during the solution process in step S6. The bin packing algorithm includes: 1) Stack all the goods waiting to be loaded at all the service stations into pallets according to their dimensions to obtain different pallet sizes and quantities; 2) Using the list as input, pack the boxes using the skyline algorithm; 3) If the returned result indicates that the goods have been loaded, then ,otherwise , It is an arbitrarily large positive number; 4) Return Provide a path planning sub-model.

2. A multi-vehicle route planning system with packing constraints, characterized in that, include: Model M1: Construct the main path planning model; Model M2: Relax the main model into a relaxed model; Model M3: A restricted relaxation model is written based on a set of initial solutions; Model M4: Write down the dual problem of the restricted relaxation model; Model M5: A sub-model is constructed based on the optimal solution to the dual problem; Model M6: Solve the aforementioned sub-model; Model M7: Determine whether there is an optimal path based on the solution of the sub-model. If there is an optimal path, add the optimal path to the restricted relaxation model, update the restricted relaxation model, and start the loop from model M4. If no optimal path is found, the loop ends. Model M8: The solution space is obtained according to the above steps. and based on Solve the master model to obtain the solution to the path planning problem; The module M1 includes: in route planning with packing constraints, a penalty cost is set for each route. If all the goods at all stations on the route can be loaded, the penalty cost is 0; otherwise, the penalty cost is an arbitrarily large positive number. The main model for path planning is as follows: Among them, using Indicates a path; The set representing all paths; decision variables Representing a path Whether it is selected, if Representing a path Selected; Representing a path Packing penalty costs; , It is an arbitrarily large positive number; This represents the set of all sites awaiting service. Indicates site Is it on the path? If yes, it is 1; otherwise, it is 0. Representing a path The distance; The relaxation in the restricted relaxation model in module M4 is manifested in relaxing the decision variables of the main model from 0-1 variables to continuous variables with values ​​between 0 and 1; while the restriction is manifested in that the solution set of the relaxation model is a subset of the true solution set, and this solution set changes continuously as new paths are added during the solution process; The dual problem refers to describing the original problem from different perspectives using methods that have the same meaning and symmetrical structure; every linear programming problem has a corresponding dual problem; the dual problems are as follows: Among them, using Indicates a path; Represents the set of all paths; Indicates site Is it on the path? If yes, it is 1; otherwise, it is 0. The dual variables of the relaxation problem in the main model; Representing a path The distance; Representing a path Packing penalty costs; , It is an arbitrarily large positive number; This represents the set of all sites awaiting service. The sub-model for path planning is as follows: in, Indicates site and sites The distance between them; This indicates the cost of packing penalties; The dual variables of the relaxation problem in the main model; Indicates the unloading warehouse; This indicates the maximum number of loading stations on a route; Indicates the vehicle's maximum load capacity; Indicates site The total weight of the goods to be loaded; Indicates site The order of services along the path; Indicates that the service has been completed at the site. The load of the following vehicle; decision variables Indicates site Whether or not it was selected; The bin packing algorithm is continuously invoked during the solution process of module M6. The bin packing algorithm includes: 1) Stack all the goods waiting to be loaded at all the service stations into pallets according to their dimensions to obtain different pallet sizes and quantities; 2) Using the list as input, pack the boxes using the skyline algorithm; 3) If the returned result indicates that the goods have been loaded, then ,otherwise , It is an arbitrarily large positive number; 4) Return Provide a path planning sub-model.

3. A device, characterized in that, The device includes: One or more processors; Storage device for storing one or more programs. When the one or more programs are executed by the one or more processors, the one or more processors perform the steps of the method as described in claim 1.

4. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method of claim 1.

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