A method for multi-objective scheduling of AGVs based on ant colony algorithm

Abstract

The purpose of this invention is to provide a method for multi-objective scheduling of AGVs based on ant colony optimization. The optimization objectives are to minimize the delivery time window penalty, total running distance, and number of task groups, while constraints such as the AGV's maximum load capacity and time window limitations are used to construct a multi-task scheduling model. In the early stages of the algorithm, a saving algorithm is introduced to increase path pheromone levels and accelerate the search speed. To prevent ants from getting trapped in local optima due to excessively high pheromone concentration on a certain path, a minimax ant colony optimization algorithm is introduced. In summary, this method for multi-objective scheduling of AGVs based on ant colony optimization can solve the problems of slow initial convergence speed, susceptibility to local optima, and imbalance between the accuracy and time requirements of the algorithm search in multi-task AGV scheduling.

Description

[0001] Technology Neighborhood

[0002] This invention relates to the field of intelligent logistics, and in particular to a method for multi-objective scheduling of AGVs in manufacturing workshops. Background Technology

[0003] Currently, in the manufacturing sector, indirect production processes such as logistics and distribution consume more working time, leaving only a small portion for processing and assembly. Therefore, controlling logistics costs and time is crucial for enterprises to reduce costs and increase efficiency. The scheduling of AGV automated transportation and distribution systems refers to weighting transportation tasks and vehicles based on specific system parameters as optimization objectives, and determining a reasonable allocation scheme to improve overall system efficiency and reduce operating costs. To achieve efficient AGV scheduling and cost reduction, researchers have proposed and improved various intelligent algorithms to solve the AGV scheduling problem, such as evolutionary algorithms, hybrid immune algorithms, particle swarm optimization, variable neighborhood search algorithms, and simulated annealing algorithms.

[0004] For example, patent CN 115470651 A discloses a vehicle path optimization method based on ant colony optimization (ACO) with road and time window considerations. Ant colony optimization is a heuristic algorithm that, by simulating the behavior of ants searching for food, guides the entire colony towards a better direction through the deposition and evaporation of pheromones, ultimately finding the optimal solution. ACO has wide applications in combinatorial optimization and path planning. In the aforementioned patent, by designing the state transition rules and pheromone update parameters for ACO, and performing multiple state transitions and pheromone update operations on the obtained distance matrix, the feasible solution is gradually moved closer to the optimal solution through multiple iterations, thus obtaining the optimal path.

[0005] However, when planning the path, this algorithm tends to select the next node randomly, which takes a long time to generate positive feedback. This results in slow convergence in the early stages and makes the algorithm prone to getting stuck in local optima. This imbalance between the algorithm's search accuracy requirements and time cost requirements is particularly pronounced in applications that require scheduling AGVs with multiple tasks. Summary of the Invention

[0006] The purpose of this invention is to provide a method for multi-objective scheduling of AGVs based on ant colony algorithm, which solves the problems of slow initial convergence speed, easy getting trapped in local optima, and imbalance between the accuracy and time requirements of algorithm search when scheduling multi-task AGVs.

[0007] This invention is achieved through the following technical solution:

[0008] 1. A method for multi-target scheduling of AGVs based on ant colony algorithm, comprising the following steps:

[0009] S1. Create a raster map:

[0010] Establish a grid map, set the starting point, ending point, work points where materials need to be delivered, and the required workload for each work point, and mark obstacle areas and passable areas based on whether the AGV can pass through;

[0011] S2. Model Establishment:

[0012] A multi-objective task scheduling model is constructed, and a total cost function and constraints are established based on the grid map. The total cost function includes a path cost function, a fixed cost function, and a penalty cost function, and the constraints include the maximum load capacity of the AGV and time window limits.

[0013] S3, AGV cart scheduling:

[0014] The multi-objective task scheduling model is solved using the ant colony algorithm to obtain the optimal scheduling route.

[0015] Based on the actual working environment of the company's production workshop, the workshop's floor plan is divided into several grid graphics of the same size, and obstacle areas and passable areas are marked to create a grid map. The start and end points of each AGV (Automated Guided Vehicle) are defined: the start point is the warehouse location where materials are stored, and the end point is the storage point where the AGV is stored after all transportation is completed. The workstations within the workshop that require material delivery are determined as the AGV's waypoints, and the amount of material to be delivered at each workstation is defined as the task quantity. The path cost function, the fixed cost function, and the penalty cost function are then established, and these three cost functions are added together to obtain the total cost function.

[0016] The path cost function refers to the total running distance of all AGVs after completing all tasks; the fixed cost function refers to the optimization of the number of task groups. A task group refers to a group of AGVs that completes multiple material delivery tasks by passing through multiple workstations. Essentially, it aims to maximize the number of tasks within each task group and the number of production line points served. Under the same task load, the number of AGVs needed should be minimized, while the total amount of materials required by the planned production line points within the task group must meet the maximum load capacity of the AGVs. The penalty cost function refers to the optimal time window range for the AGV to arrive at each production line point, requiring material delivery to the corresponding production line point to be performed within a reasonable timeframe. If the arrival time is earlier or later than the set optimal time window range, a penalty will be imposed on the AGV.

[0017] This method, by setting the path cost function, the fixed cost function, and the penalty cost function, enables the ant colony algorithm to consider multiple optimization objectives during the search process, rather than simply finding the shortest path. This allows the algorithm to more comprehensively consider the overall cost and benefit, avoiding getting trapped in local optima. By establishing constraints based on the AGV's maximum load capacity and the time window limit, unrealistic path schemes can be eliminated during the search process, thus avoiding the generation of invalid solutions. This helps improve the accuracy of the algorithm's search and ensures that the generated path schemes meet the requirements of practical applications. By considering different cost factors and constraints, the algorithm can avoid premature convergence to local optima, while also better meeting practical requirements such as time and load. This solves the problems of slow initial convergence speed, susceptibility to local optima, and the imbalance between the accuracy and time requirements of the ant colony algorithm.

[0018] 2. As a preferred embodiment of the present invention, the path cost function is specifically as follows:

[0019]

[0020] ;

[0021] Wherein, 0 represents the starting point; V represents the set of work sites; V represents the set of nodes, that is, the set of the starting point and the work sites. This represents a collection of AGV (Automated Guided Vehicle) carts; This refers to a task group, where one vehicle completes material delivery tasks at multiple work sites; the aforementioned Indicates task group The number of groups; Distance for each task group; It is the value of the k-th vehicle from node i to node j, and the value can be 0 or 1; This represents the distance of the k-th vehicle from node i to node j;

[0022] The fixed cost function is specifically as follows:

[0023]

[0024] in, It is the value of the k-th vehicle from warehouse 0 to node j, and the value can be 0 or 1;

[0025] The penalty cost function is specifically as follows:

[0026]

[0027]

[0028] Where ti is the time point when the AGV reaches the i-th working point. Let the penalty cost function be... The penalty value per unit time for AGV carts to deliver materials to the workstation ahead of schedule; The unit time penalty value for AGV delivery of materials late to the workstation;

[0029] The total cost function is specifically as follows:

[0030] (5)

[0031] in, Indicates the target value to be optimized; This represents the cost per unit distance traveled. This represents a set of nodes, where 0 represents a repository; This represents a collection of AGVs (Automated Guided Vehicles). , Indicates different production line points; This refers to different types of AGVs (Automated Guided Vehicles). ; For nodes To the node The distance; Indicates the influence coefficient of the number of task groups; Represents the set of production line points; ; This is the penalty value function.

[0032] 3. As a preferred embodiment of the present invention, the constraint conditions are specifically as follows:

[0033]

[0034] In equation (6)

[0035] Indicates the execution of the production line point The required carrying capacity for delivery tasks.

[0036]

[0037] The maximum load capacity of each AGV.

[0038] In equation (7)

[0039] This indicates the maximum number of AGV vehicles allowed.

[0040] In equation (8)

[0041]

[0042] Indicates production line point , Production line points between them.

[0043] In equation (9)

[0044]

[0045]

[0046] In formula (10)

[0047] Represents a node To the node Delivery distance; This indicates the maximum range of the AGV transport vehicle.

[0048] In formula (11)

[0049]

[0050] In formula (12)

[0051] Represents a node Service hours; Represents a node Service hours; Represents a node The waiting time coefficient; node To the node The delivery time; where M is a sufficiently large positive number.

[0052] Equations (13) and (14) represent the properties of decision variables.

[0053] 4. As a preferred embodiment of the present invention, S3, AGV cart scheduling specifically includes:

[0054] S3.1, State Transition

[0055] Under the aforementioned constraints, the AGV needs to consider two factors when selecting the next work station:

[0056] First, from the currently mentioned node Select the next node. The length of the path and the pheromone concentration of that path segment,

[0057] Second, select the time window width of the next node and the degree of deviation from the time window width;

[0058] S3.2, Update pheromones

[0059] After an ant searches a path, the pheromone needs to be updated based on the search results to influence the ant's next choice. This pheromone updating includes: pheromone evaporation, where a certain proportion of the pheromone evaporates after each iteration to prevent excessive concentration and ant over-concentration on a particular path; and pheromone increase, where the pheromone concentration along the traversed path increases based on the success rate of the search, typically proportional to the optimization level of the path.

[0060] S3.3, Local Search

[0061] Optimize the search within the local neighborhood of a specific solution.

[0062] 5. As a preferred embodiment of the present invention, S3.1, the state transition specifically comprises:

[0063] Prioritize work sites with short paths and high pheromone concentrations.

[0064] The AGV vehicle starts from the current node. Select the next node. When the pheromone concentration is high, the pheromone will prioritize the shortest path and the highest concentration. Let the pheromone concentration on the path be... ;node To the node The visibility is ,and ; Represents a node To the node The distance; Pheromonium level factor, heuristic function The degree factor of the heuristic function;

[0065] Prioritize workstations with shorter waiting times or shorter time window spans.

[0066] AGV vehicle k from node To the node State transition probability formula for

[0067] (16)

[0068] (17)

[0069] (18)

[0070] in, Indicates the pheromone concentration along the path; Represents the node To the node The visibility, and ; The node represents To the node The distance; Pheromonium level factor, heuristic function The degree factor of the heuristic function; Indicates the cost savings of the path; This indicates the node that the AGV has not yet passed; This indicates that the AGV has reached the node. The degree of deviation from the time window of the node; Represents the node The degree of influence of the time window width; Represents the node The optimal service window range; This indicates that the AGV has reached the node. The time.

[0071] As a preferred embodiment of the present invention, a saving algorithm step is added to the S3.1 state transition step:

[0072] Place nodes on the two empty paths respectively. Then calculate the number of nodes simultaneously. and nodes The path value is calculated, and finally, nodes are also calculated. The path cost and the two nodes respectively, Difference in path costs The calculation formula is:

[0073] (15)

[0074] Indicates the distance from the starting point to the work site. distance, Indicates the work site to the work site The distance.

[0075] Because the ant colony algorithm starts with the same initial pheromone and has limited node path information, the random selection of nodes by ants leads to problems such as lengthy search time and slow convergence. Since this problem is related to path length, a saving algorithm is introduced to solve it. The larger the value, the more likely the node is to be affected. The greater the cost savings of the path formed after the connection, the higher the cost of that path segment. The larger it will be, the more likely you are to select the node. The greater the probability, the better. The cost-saving algorithm has the advantages of being easy to solve, short in time, and easy to integrate. In the practical problem of this invention, it involves saving costs on the path between the production line and the warehouse. Integrating the cost-saving algorithm into the state transition probability can improve the convergence speed and balance search accuracy and time.

[0076] As a preferred embodiment of the present invention, step S3.2, updating pheromones, specifically comprises:

[0077] A task group optimization function was superimposed during the pheromone update phase. To achieve the goal of minimizing task groups, the pheromone update formula is:

[0078] (19)

[0079] (20)

[0080] (twenty one)

[0081] In the formula, The factor representing the degree of pheromone volatility, and This indicates the persistence of pheromones, that is, the ability of ants to eliminate pheromones along that path. is a constant representing the total amount of pheromones released by the ant after traversing all nodes. This represents the total distance the ant travels through all paths. This represents the task group optimization function, which can provide feedback on the pheromone concentration based on the number of task groups solved in the current iteration.

[0082] As a preferred embodiment of the present invention, a pheromone restriction step is added to S3.2, the pheromone updating step:

[0083] The pheromone concentration on each path is limited to a threshold value, i.e. ,

[0084] like ,but ;

[0085] like ,but ,

[0086] in, Factors indicating the degree of pheromone volatility This represents the minimum cost of the current iteration.

[0087] The pheromone constraint step can prevent the search from stalling and getting stuck in a local optimum due to excessively high pheromone levels on a certain path.

[0088] As a preferred embodiment of the present invention, the S3.3 local search step specifically comprises:

[0089] S3.31, Given an initial solution And define q domain structures, denoted as {N} q},q=1,...,m, denoted as the initial solution The first step in performing a neighborhood search Each neighborhood structure;

[0090] S3.32, Using Neighborhood Structure Perform a search, if in Find a better solution Then let , ;

[0091] S3.33, If the neighborhood structure has been searched No comparison found A better solution would be to let ;

[0092] S3.34, if Proceed to step S3.32;

[0093] S3.34, Output the optimal solution.

[0094] As a preferred embodiment of the present invention, a neighborhood search structure is added to the local search step S3.3:

[0095] Delete the aforementioned warehouse node 0, and randomly select... Given a set of nodes, place the selected node at the forefront; then, re-add the warehouse node according to the constraints to obtain a new neighborhood solution. .

[0096] In summary, the present invention has the following beneficial effects:

[0097] 1. Setting multiple objective functions allows the ant colony algorithm to consider various optimization objectives during the search process, rather than just finding the shortest path. This enables the algorithm to more comprehensively consider the overall cost and benefit, avoiding getting trapped in local optima.

[0098] 2. By considering different cost factors and constraints, the algorithm can avoid premature convergence to a local optimum, while also better meeting practical requirements such as time and load.

[0099] 3. By incorporating a cost-saving algorithm into the state transition probability, the cost of the path between workstations and warehouses can be reduced, which can improve the convergence speed and solve the problem of the imbalance between search accuracy and time requirements.

[0100] 4. Adding a pheromone constraint step can prevent the search from stalling and getting stuck in a local optimum due to excessively high pheromone levels on a certain path.

[0101] 5. Enhance local search capabilities by designing an insertion operator-embedded variable neighborhood search algorithm. Attached Figure Description

[0102] Figure 1 This is a graph of the penalty function under time window constraints;

[0103] Figure 2 This is a schematic diagram of the saving algorithm;

[0104] Figure 3 This is a schematic diagram of neighborhood transformation;

[0105] Figure 4 This is a diagram illustrating an Insert search.

[0106] Figure 5 This is a flowchart of the improved ant colony algorithm;

[0107] Figure 6 It is a motion trajectory route map;

[0108] Figure 7 It is a graph showing the trend of the convergence curve. Detailed Implementation

[0109] The present invention will be further described in detail below with reference to the accompanying drawings.

[0110] S1. Create a raster map:

[0111] Based on the actual working environment of the company's production workshop, the workshop's floor plan is divided into several grid graphics of the same size, and obstacle areas and passable areas are marked to create a grid map. A start and end point are set for each AGV (Automated Guided Vehicle). The start point is the warehouse location where materials are stored, and the end point is the storage point where the AGV is stored after all transportation is completed. The workstations within the workshop that require material delivery are determined as the AGV's route points, and the amount of material to be delivered at each workstation is also identified, i.e., the task quantity. Multiple routes for the AGV are preset within the passable area. For example... Figure 6 As shown: Create a 20*20 grid map. Each small block represents a 1*1 grid cell. White areas are passable areas, and black areas are obstacles (impassable areas). The starting point coordinates are (0.5, 19.5), and the target point coordinates are (13.5, 4.5).

[0112] S2. Model Establishment:

[0113] Construct a multi-objective task scheduling model and establish objective functions and constraints, specifically including:

[0114] Path cost function establishment:

[0115] The path cost in the model refers to the total running distance of the AGV after completing all tasks. To obtain an accurate solution for the model, we convert the data to production line points, and the mathematical model is as follows:

[0116]

[0117] Establishing the fixed cost function:

[0118] To facilitate model calculations, the number of task groups needs to be converted, and a fixed cost needs to be designed. The mathematical model is as follows:

[0119]

[0120] Establishment of the penalty cost function:

[0121] It is a production line point The optimal time window for material delivery, and conducting logistics and delivery within a reasonable timeframe, can reduce costs for production line points. For example... Figure 1 The graph shown is a diagram of the penalty function under time window constraints, with the horizontal axis... Represents time, y-axis Let the penalty cost be represented. Design the penalty function; its mathematical model is as follows:

[0122]

[0123]

[0124] In the formula, For penalty value functions; The unit time penalty value for AGVs delivering materials to the production line ahead of schedule; The unit time penalty value for AGV delivery of materials that are late in arriving at the production line.

[0125] Establishing the total cost function

[0126]

[0127] Constraint Establishment

[0128] (6)

[0129] (7)

[0130] (8)

[0131] (9)

[0132] (10)

[0133] (11)

[0134] (12)

[0135] (13)

[0136] (14)

[0137] Wherein, Equation (5) represents the total cost, including path cost, fixed cost, and penalty cost; Equation (6) represents the AGV carrying capacity limit, each AGV cannot exceed its maximum carrying capacity; Equation (7) represents the limit on the number of AGV vehicles; Equation (8) represents the AGV transport vehicle... The number of vehicles entering and leaving the production line is equal; Equation (9) indicates that the AGV transport vehicle must return to the distribution center after completing the delivery; Equation (10) indicates that the total delivery distance of the AGV transport vehicle does not exceed its maximum range; Equation (11) indicates that each production line point can only be delivered by one AGV transport vehicle during the delivery process; Equation (12) indicates the service time limit, where M is a sufficiently large positive number; Equations (13) and (14) indicate the properties of the decision variables.

[0138] S3. Design an improved ACO algorithm to solve the model and obtain the optimal scheduling result, such as... Figure 5 As shown, it specifically includes:

[0139] S3.1 State Transition

[0140] Prioritize work sites with short paths and high pheromone concentrations.

[0141] The AGV (Automated Guided Vehicle) starts from the current node. Select the next node When the pheromone concentration is high, the pheromone will prioritize the shortest path and the highest concentration. Let the pheromone concentration on the path be... ;node To the node The visibility is ,and ; Represents a node To the node The distance; Pheromonium level factor, heuristic function The degree factor of the heuristic function;

[0142] Saving algorithm

[0143] like Figure 2 As shown, the saving algorithm first places nodes on two empty paths. Then calculate the number of nodes simultaneously. and nodes The path value is calculated, and finally, nodes are also calculated. The path cost and the two nodes respectively Difference in path costs The formula for calculating the savings value is:

[0144] (15)

[0145] In the formula, Indicates the distance from the distribution center to the node. distance, Represents a node To the node The distance. The larger the value, the more likely the node is to be affected. The greater the cost savings of the path formed after the connection, the higher the cost of that path segment. The larger it gets, the more nodes you need to select. The greater the chance, the more likely it is to succeed. In the practical problem addressed by this patent, it refers to cost savings in the path between the production line and the warehouse.

[0146] Prioritize workstations with shorter waiting times or shorter time windows.

[0147] AGV vehicle k from node To the node The state transition probability formula is:

[0148] (16)

[0149] (17)

[0150] (18)

[0151] in, Indicates the pheromone concentration along the path; Represents a node To the node The visibility, and ; Represents a node To the node The distance; Pheromonium level factor, heuristic function The degree factor of the heuristic function; Indicates the cost savings of the path; This indicates a node that the AGV has not yet passed; Indicates the AGV cart has reached the node. The degree of deviation from the time window of that node; Represents a node The degree of influence of the time window width; Represents a node The optimal service window range; This indicates that the AGV has reached the node. The time.

[0152] S3.2 Update Pheromones

[0153] A task group optimization function was superimposed during the pheromone update phase. The goal is to obtain the fewest task groups, maximizing the task load rate of each group. The pheromone update formula is:

[0154] (19)

[0155] (20)

[0156] In the formula, The factor representing the degree of pheromone volatility, and This indicates the persistence of pheromones, that is, the ability of ants to eliminate pheromones along that path. is a constant representing the total amount of pheromones released by the ant after traversing all nodes. This represents the total distance the ant travels through all paths. This represents the task group optimization function, which can provide feedback on the pheromone concentration based on the number of task groups solved in the current iteration.

[0157] (twenty one)

[0158] The pheromone concentration on each path is limited to a threshold value, i.e. .

[0159] like ,but ;

[0160] like ,but (twenty two)

[0161] (twenty three)

[0162] In the formula, Factors indicating the degree of pheromone volatility This represents the minimum cost of the current iteration.

[0163] S3.3 Local Search

[0164] Step 3.31: The Shaking phase generates an initial solution, and VND optimizes the initial solution, such as... Figure 3 As shown, the specific steps are as follows:

[0165] Step 3.311: Given an initial solution And define q domain structures, denoted as {N} q},q=1,...,m, denoted as the initial solution The first step in performing a neighborhood search Each neighborhood structure;

[0166] Step 3.312: Use neighborhood structure Perform a search, if in Find a better solution Then let , ;

[0167] Step 3.313: If the neighborhood structure has been searched No comparison found A better solution would be to let ;

[0168] Step 3.314: If Proceed to step 3.312;

[0169] Step 3.315: Output the optimal solution.

[0170] Step 3.32: The Insert search neighborhood structure was designed.

[0171] like Figure 4 As shown. First, delete the initial solution. The warehouse node in the middle is then randomly selected. Given a set of nodes, place the selected node at the forefront. Then, re-add the warehouse node according to the constraints to obtain a new neighborhood solution. The updated task groups are: Task Group 1: Warehouse 0 - Production Line Point 4 - Production Line Point 5 - Production Line Point 1 - Production Line Point 2 - Warehouse 0; Task Group 2: Warehouse 0 - Production Line Point 3 - Production Line Point 6 - Production Line Point 7 - Warehouse 0.

[0172] The final AGV trajectory diagram and convergence curve trend diagram are as follows: Figure 6 , 7 As shown.

Claims

1. A method for multi-target scheduling of AGVs based on ant colony algorithm, characterized in that, Includes the following steps: S1. Create a raster map: Establish a grid map, set the starting point, ending point, work points where materials need to be delivered, and the required workload for each work point, and mark obstacle areas and passable areas based on whether the AGV can pass through; S2. Model Establishment: A multi-objective task scheduling model is constructed, and a total cost function and constraints are established based on the grid map. The total cost function includes a path cost function, a fixed cost function, and a penalty cost function. The constraint is the maximum load capacity of the AGV. S3, AGV cart scheduling: The multi-objective task scheduling model is solved using the ant colony algorithm to obtain the optimal scheduling route result. The S3 and AGV cart scheduling specifically includes: S3.1, State Transition Under the aforementioned constraints, the AGV needs to consider two factors when selecting the next work station: First, from the current node Select the next node. The length of the path and the pheromone concentration of that path segment, Second, select the time window width of the next node and the degree of deviation from the time window width; S3.2, Update pheromones After the ants search for a path, the pheromones need to be updated based on the search results to influence the ants' choices in the next ant search. S3.3, Local Search Optimize the search within the local neighborhood of a specific solution; A savings algorithm step is added to the S3.1 state transition step: Place nodes on the two empty paths respectively. Then calculate the number of nodes simultaneously. and nodes The path value is calculated, and finally, nodes are also calculated. The path cost and the two nodes respectively, Difference in path costs The calculation formula is: Indicates the distance from the starting point to the work site. distance, Indicates the work site to the work site The distance; The S3.2 step of updating pheromones is as follows: A task group optimization function was superimposed during the pheromone update phase. To achieve the goal of minimizing task groups, the pheromone update formula is: In the formula, The factor representing the degree of pheromone volatility, and This indicates the persistence of the pheromone, that is, the ability of the ant's pheromone to disappear along that path; The constant represents the total amount of pheromone released by the ant after traversing all nodes; This represents the total distance the ant travels through all paths; This represents the task group optimization function, which can provide feedback on the pheromone concentration based on the number of task groups solved in the current iteration. The S3.2 step of updating pheromones includes an additional pheromone restriction step: The pheromone concentration on each path is limited to a threshold value, i.e. , like ,but ; like ,but , ; in, Factors indicating the degree of pheromone volatility This represents the minimum cost of the current iteration.

2. The method for multi-objective scheduling of AGV vehicles based on ant colony algorithm according to claim 1, characterized in that, The specific formula for the path cost function is as follows: Where V = {0} & U, 0 represents the starting point; V represents the set of work sites; V represents the set of nodes, that is, the set of the starting point and the work sites. This represents a collection of AGV (Automated Guided Vehicle) carts; This indicates a task group; a task group consists of a vehicle that completes material delivery tasks at multiple work sites. Indicates task group The number of groups; Distance for each task group; It is the value of the k-th vehicle from node i to node j, and the value can be 0 or 1; This represents the distance of the k-th vehicle from node i to node j; The specific formula for the fixed cost function is as follows: in, It is the value of the k-th vehicle from the starting point 0 to the node j, and the value can be 0 or 1; The specific formula for the penalty cost function is as follows: Among them, t i This refers to the time point when the AGV reaches the i-th working point. Let the penalty cost function be... The penalty value per unit time for AGV carts to deliver materials to the workstation ahead of schedule; The unit time penalty value for AGV material delivery to the workstation for late delivery, [et] i ,lt i [This refers to the optimal time window range for material delivery at production line point i;] The total cost function is specifically as follows: in, Indicates the influence coefficient of the number of task groups; This represents the cost per unit distance traveled.

3. The method for multi-objective scheduling of AGV vehicles based on ant colony algorithm according to claim 2, characterized in that, The constraints also include: limiting the total number of AGV vehicles; ensuring that the number of AGV vehicles entering and leaving the work site is equal; requiring AGV vehicles to return to the destination after completing delivery; ensuring that the total delivery distance of AGV vehicles does not exceed their maximum range; and allowing only one AGV vehicle to deliver to each work site during the delivery process.

4. The method for multi-objective scheduling of AGV vehicles based on ant colony algorithm according to claim 1, characterized in that, Specifically, S3.1, the state transition, is as follows: Prioritize work sites with short paths and high pheromone concentrations. The AGV vehicle starts from the current node. Select the next node. When the pheromone concentration is high, the pheromone will prioritize the shortest path and the highest concentration. Let the pheromone concentration on the path be... ;node To the node The visibility is ,and ; Represents a node To the node The distance; Pheromonium level factor, heuristic function The degree factor of the heuristic function; Prioritize workstations with shorter waiting times or shorter time window spans. AGV vehicle k from node To the node State transition probability formula for in, Indicates the pheromone concentration along the path; Represents the node To the node The visibility, and ; Represents the node To the node The distance; Pheromonium level factor, heuristic function The degree factor of the heuristic function; Indicates the cost savings of the path; This indicates the node that the AGV has not yet passed; This indicates that the AGV has reached the node. The degree of deviation from the time window of the node; Represents the node The degree of influence of the time window width; Represents the node The optimal service window range; This indicates that the AGV has reached the node. The time.

5. The method for multi-objective scheduling of AGV vehicles based on ant colony algorithm according to claim 1, characterized in that, The S3.3 local search step is as follows: S3.31, Given an initial solution And define q neighborhood structures, denoted as {N} q }, q=1,……,m, denoted as the initial solution The first step in performing a neighborhood search Each neighborhood structure; S3.32, Using Neighborhood Structure Perform a search, if in Find a better solution Then let , ; S3.33, If the neighborhood structure has been searched No comparison found A better solution would be to let ; S3.34, if Proceed to step S3.32; S3.35, Output the optimal solution.

6. The method for multi-objective scheduling of AGV vehicles based on ant colony algorithm according to claim 5, characterized in that, The S3.3 local search step adds a neighborhood search structure: Delete the starting point 0, and randomly select Select a node and place the selected node at the forefront. Re-add the starting point according to the constraints to obtain a new neighborhood solution. .

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