An AGV Scheduling and Quantity Joint Optimization Method Considering Conflicts

Abstract

The present invention discloses a method for jointly optimizing the scheduling and quantity of AGVs considering conflicts, which includes: S1. Obtaining the map data and task data of the automated unmanned warehouse; S2. Calculating the task execution order constraints according to the map data and task data; S3. Based on the execution order constraints, converting the constraints between tasks into a network structure and constructing an alternative network for AGV scheduling; S4. Based on the constructed alternative network for AGV scheduling, calculating the minimum path covering problem to obtain a set of candidate solutions, and taking the least non-overlapping scheduling sequences in the set of candidate solutions as the final scheduling plan. The advantages of the present invention are as follows: The solution quality is improved: By introducing the conflict average index for the scheduling plan, it is possible to select a scheduling plan with fewer conflicts during the actual execution of tasks from the top k theoretically optimal plans, reducing the average makespan by 10%.

Description

Technical Field

[0001] The present invention relates to the field of AGV scheduling and planning, and particularly relates to a method for jointly optimizing AGV scheduling and quantity considering conflicts. Background Art

[0002] An Automated Guided Vehicle (AGV) is a highly safe and powerful logistics transportation robot, commonly used for transporting goods in warehousing logistics. It can achieve unmanned operation, and by performing outbound and inbound tasks 24 hours a day, it can greatly shorten the overall time of warehousing logistics execution and improve the throughput of the entire warehouse. AGV scheduling mainly refers to allocating different tasks to multiple AGVs and having them execute the tasks respectively. It needs to consider the resource competition existing in the shared path network among AGVs. For example, two AGVs cannot pass through an edge simultaneously, and even for large AGVs, there may be collisions on two different edges. The existence of such conflict competition will cause the maximum task completion time to increase significantly when the conventional AGV scheduling scheme is actually executed, because when an AGV encounters a conflict, one vehicle must avoid and wait.

[0003] The most relevant technologies mainly focus on the field of AGV scheduling and quantity configuration. The existing AGV scheduling technologies are mainly divided into two categories: rule-based scheduling methods and model-based scheduling methods. Rule-based scheduling methods: The most typical one is first-come, first-served, which matches the AGV closest to the task to execute the task. 2. Model-based scheduling methods: Use mathematical programming models. For example, set the objective function to minimize the task completion time, set the decision variables as which AGV executes which task, and set the constraint conditions to ensure that the vehicle can reach the next task in time after completing the previous task, etc. For reference, see

[0004]

SINGH N, DANG Q V, AKCAY A, et al. A matheuristic for AGV scheduling with battery constraints[J]. European Journal of Operational Research, 2022, 298(3): 855 - 873.

[0005] In some existing technologies, a graph theory method is used to solve the urban minimum fleet problem. See the reference paper

[0006]

VAZIFEH M M, SANTI P, RESTA G, et al. Addressing the minimum fleet problem in on-demand urban mobility[J]. Nature, 2018, 557(7706): 534-538.

[0007] Problems or deficiencies of the prior art: Existing rule-based scheduling methods, such as first-come-first-served, are too inefficient and only optimize locally. Using the greedy idea, the current optimal AGV is matched to the task, but this may lead to a worse AGV being matched to subsequent tasks, resulting in a worse overall efficiency. Existing scheduling methods based on mathematical programming models are too complex, and the calculation time increases exponentially with the increase in the number of tasks and AGVs, making it difficult to adapt to large-scale scenarios in actual industrial applications. Once the task information changes or unexpected situations such as vehicle failures occur and a new scheduling scheme needs to be recalculated, a long waiting time is required.

[0008] Compared with the prior art, the technical solution of the present invention aims to solve the following problems:

[0009] Problem 1: Existing AGV scheduling methods often schedule under the condition of determining the number of AGVs. However, the configuration of the number of AGVs in the system will affect the overall system efficiency. When the number of AGVs is too small, it will be difficult to complete all tasks. When the number of AGVs is too large, it will cause congestion in the warehouse transportation area, increase the probability of path conflicts between AGVs, increase costs, but reduce the system efficiency. Therefore, it is necessary to consider configuring the corresponding number of AGVs during scheduling, determine the optimal scheduling scheme and the optimal number of AGVs that can complete the tasks according to the real-time number of tasks, and minimize costs and improve the throughput of the warehouse to the greatest extent.

[0010] Problem 2: After determining the AGV scheduling scheme and quantity, when AGVs execute tasks according to the given scheduling scheme, they will also encounter the problem of path conflicts between multiple AGVs, that is, affected by volume, when two AGVs are too close, there may be a collision or the anti-collision laser may be triggered. Conflicts between AGVs need to be resolved by delaying and waiting, which will affect the system operation efficiency. Therefore, it is necessary to consider path conflict problems in the scheduling scheme and select a scheduling scheme with fewer conflicts for subsequent AGV task execution as much as possible.

[0011] Problem 3: The existing scheduling method based on the mathematical programming model is too complex, and the calculation time will increase exponentially with the increase in the number of tasks and AGVs, making it difficult to adapt to large-scale scenarios in actual industrial applications. Once the task information changes or unexpected situations such as vehicle failures occur, a long waiting time is required when recalculating the scheduling plan. Therefore, a technical method for quickly and efficiently solving the scheduling plan is needed. Summary of the Invention

[0012] The object of the present invention is to provide a method for jointly optimizing AGV scheduling and quantity considering conflicts to solve the above problems according to the deficiencies of the above-mentioned existing technologies.

[0013] To achieve the above object, the present invention provides a method for jointly optimizing AGV scheduling and quantity considering conflicts, which includes:

[0014] S1. Obtain the map data and task data of the automated unmanned warehouse;

[0015] S2. Calculate the task execution sequence constraints according to the map data and task data;

[0016] S3. Based on the execution sequence constraints, convert the constraints between tasks into a network structure and construct an AGV scheduling alternative network;

[0017] S4. Based on the constructed AGV scheduling alternative network, calculate the minimum path coverage problem to obtain a candidate solution set; calculate the candidate solution with the least conflicts in the alternative solution set as the final scheduling plan.

[0018] A further improvement of the present invention is that the map data is the shelf positions, AGV parking spaces, AGV driving edges, conflict relationships between edges, and in-out ports of the unmanned warehouse; the task data includes the starting point of the task, the ending point of the task, the task arrival time, and the shortest path from the task starting point to the ending point.

[0019] A further improvement of the present invention is that step S2 specifically includes:

[0020] Based on the arrival time of the current task and the transportation time of the shortest path from the task starting point to the ending point, estimate the time when the task is completed. The shortest path from the task starting point to the ending point is pre-calculated by the A* algorithm of the path planning algorithm, and the transportation time is estimated according to the AGV driving speed and the shortest path length;

[0021] Based on the time when the current task is completed and the transportation time from the current task ending point to the next task starting point, calculate the time when the AGV arrives at the next task starting point after completing the current task. If the arrival time is earlier than the start time of the next task, the two tasks meet the execution sequence constraints.

[0022] A further improvement of the present invention lies in that: in step S3, each task is represented by a node, and the sequential connection is transformed into a directed connection between nodes to construct an AGV scheduling alternative network; two connected nodes in the network indicate that two tasks meet the execution order constraint and can be continuously executed by one AGV.

[0023] A further improvement of the present invention lies in that: step S4 specifically includes:

[0024] Based on the AGV scheduling alternative network, the AGV quantity configuration and scheduling problem are transformed into the minimum path covering problem in graph theory, and the bipartite graph maximum matching / minimum cost maximum flow algorithm is used to solve it to obtain several candidate solutions. The candidate solutions include the minimum number of AGVs and their corresponding scheduling schemes; calculate the number of conflict edges on the driving paths of AGVs in each candidate solution, and select the candidate solution with the fewest conflict edges as the final scheduling scheme.

[0025] The solution provided by the present invention has the following technical effects:

[0026] (1) The solution speed is significantly improved: as shown in the figure, compared with the solution speed of the mathematical programming model, an improvement at the order of magnitude level is achieved, and the solution speed is very stable, being little affected by the increase in the number of tasks;

[0027] (2) The solution quality is improved: by introducing the conflict average index for the scheduling scheme, a scheduling scheme with fewer conflicts during actual task execution can be selected from the top k theoretically optimal schemes, reducing the average makespan by 10%. Description of the Drawings

[0028] Figure 1 is a flowchart of the AGV scheduling and quantity joint optimization method considering conflicts of the present invention;

[0029] Figure 2 is a schematic diagram of the AGV scheduling alternative network;

[0030] Figure 3 is a schematic diagram of a candidate solution (the fewest non - overlapping scheduling sequences). Detailed Embodiments

[0031] The following specific examples illustrate the embodiments of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0032] It should be noted that the diagrams provided in the following embodiments only illustrate the basic concept of the present invention schematically. Therefore, only the components related to the present invention are shown in the diagrams, rather than being drawn according to the number, shape, and size of the components in actual implementation. The types, quantities, and proportions of the components in actual implementation can be arbitrarily changed, and the component layout type may also be more complex.

[0033] Some exemplary embodiments of the present invention are described for purposes of illustration. It is to be understood that the present invention can be implemented in other ways not specifically shown in the drawings.

[0034] An embodiment of the present invention includes a conflict-aware AGV scheduling and quantity joint optimization method. The "AGV scheduling alternative network" of the AGV system in the unmanned warehouse is designed, and the AGV quantity configuration and scheduling problem are transformed into a network minimum path coverage problem, which can simultaneously calculate the optimal quantity configuration and scheduling plan. At the same time, considering the characteristics of the AGV system, the competition conflict problem existing in the AGV shared path network is taken into account, and an evaluation index for the scheduling plan is designed. The final optimal (i.e., the minimum maximum completion time) scheduling plan is selected through index evaluation for actual operation.

[0035] As Figure 1 shown, the method of the present invention specifically includes:

[0036] 1. Obtain the map data and task data of the automated unmanned warehouse. The map data includes the shelf positions, AGV parking spaces, AGV driving edges, conflict relationships between the driving edges, and the in-out ports in the unmanned warehouse. The task data includes the starting shelf (in-port) of the task, the ending out-port (shelf) of the task, the task arrival time, and the shortest path from the task starting point to the ending point.

[0037] 2. Calculate the task execution order constraint according to the map data and task data. The task execution order constraint is used to determine which tasks can be continued after a certain AGV completes the current task, and the time feasibility needs to be considered. Specifically:

[0038] (2.1) Based on the arrival time of the current task and the transportation time of the shortest path from the task starting point to the ending point, estimate the time when the task is completed. The shortest path from the task starting point to the ending point is pre-calculated by the A* algorithm, a path planning algorithm, and the transportation time is estimated according to the AGV driving speed and the shortest path length.

[0039] (2.2) Based on the time when the current task is completed and the transportation time from the ending point of the current task to the starting point of the next task, calculate the time when the AGV arrives at the starting point of the next task after completing the current task. If the arrival time is earlier than the start time of the next task, the two tasks meet the task execution order constraint.

[0040] 3. Based on the execution order constraints, transform the constraints between tasks into a network structure to construct an alternative network for AGV scheduling, as Figure 2 shown below:

[0041] (3.1) The left side is a schematic diagram of a conventional unmanned warehouse, including an inbound port, an outbound port, an AGV parking lot, and shelves arranged in sequence. Use labeled black directed arrows to represent tasks. In the figure, T1 to T6 are inbound / outbound tasks. The arrow starts from the task starting point and points to the task end point along the specified shortest path. According to the sequential execution constraints, it can be judged whether T j can be executed by the same AGV after T i . The unlabeled black directed arrows in the left figure indicate sequential connections. Starting from the end point of the previous task, it points to the starting point of the next task along the specified shortest path, indicating that these two tasks can be sequentially executed by the same AGV. Thus, the sequential execution constraints between tasks can be obtained;

[0042] (3.2) Represent each task with a node and transform the sequential connection into a directed connection between nodes, then an intuitive alternative network for AGV scheduling can be constructed, as shown on the right side of the figure.

[0043] In this step, when constructing the alternative network for AGV scheduling, the condition for adding edges ensures that each edge is directed, and the non-cyclic nature of time can ensure that there are no loops. Therefore, any alternative network for AGV scheduling is a directed acyclic graph, which can be transformed into a bipartite graph maximum matching problem to be solved effectively and optimally. The bipartite graph maximum matching problem can be transformed into a network maximum flow problem for solution, so as to obtain a solution that is optimal for both AGV scheduling and quantity.

[0044] 4. Based on the constructed alternative network for AGV scheduling, solve the minimum path cover problem to obtain a set of candidate solutions. The set of candidate solutions includes multiple candidate solutions, and each candidate solution is a combination of the fewest non-overlapping scheduling sequences in the alternative network for AGV scheduling, which can give the fewest AGV quantities and the corresponding scheduling plans.

[0045] (4.1) Connecting two nodes in the alternative network for AGV scheduling indicates that two tasks can be continuously executed by one AGV, and the paths in the network correspond to a series of tasks that one vehicle can execute, that is, the scheduling sequences that can be sequentially executed by a single AGV. Therefore, all scheduling sequences that can be executed by a single AGV can be obtained according to the alternative network for AGV scheduling; by solving the minimum path cover problem, multiple solutions can be obtained, and each solution includes multiple non-overlapping scheduling sequences that cover all nodes of the alternative network for AGV scheduling.

[0046] (4.2) In each candidate solution, the scheduling sequences do not intersect, thus ensuring that each task is executed by only one AGV. The solution method adopted by this method can minimize the number of scheduling sequences in the candidate solution, thereby minimizing the number of AGVs required to execute the tasks. Figure 3 An example of a candidate solution is shown. From the constructed alternative network for AGV scheduling, the minimum non-intersecting scheduling sequences (the combination of scheduling sequences with the fewest conflicting edges on the AGV travel paths) are solved, and 4 paths can be obtained. The minimum number of AGVs required to execute all tasks is 4, and the 4 paths are the scheduling task sequences for each AGV.

[0047] 5. According to the above calculation method, multiple candidate solutions can be obtained. In practice, the conflict problem between AGVs during task execution also needs to be considered. By considering the number of conflicts between the paths corresponding to the scheduling sequences, a scheduling scheme with fewer conflicts during actual task execution can be obtained, reducing the vehicle waiting delay time caused by conflicts.

[0048] (5.1) Assume that the travel route of AGV 1 is R ij = [a i , …, a j , and the travel route of AGV 2 is R pm = [a p , …, a m . If there is a conflict relationship between the edge a i′ ∈ R ij and the edge a p′ ∈ R pm , that is, a p′ ∈ C(i′), where C(i′) is the conflict edge set of the edge a i′ , then a i′ ∈ R ij and the edge a p′ ∈ R pm are a pair of conflict edges.

[0049] (5.2) It can be seen that the above calculation method can be completed offline, and only needs to be calculated once for a map. According to the above calculation method, the number of conflicts can be calculated for the top k optimal scheduling schemes obtained for the minimum path covering problem, that is, calculate the possible number of conflicts between each path (representing the travel of one AGV) in the solution, and select the solution with the minimum number of conflicts as the final optimal scheduling scheme.

[0050] (5.3) According to the above method, the total number of conflicts between different scheduling sequences in the scheduling scheme can be calculated. Calculate and evaluate multiple scheduling schemes, and select the scheduling scheme (candidate solution) with the minimum total number of conflicts as the final scheduling

[0051] To evaluate the performance of the method of the present invention for the AGV quantity and scheduling problem in an unmanned warehouse, the algorithm is tested using the real map and task data of an enterprise. The map contains 1,800 shelf storage locations, 8 in-out ports, AGV parking spaces, 8,421 edges, etc. A conventional multi-objective optimization model for AGV quantity and scheduling is used as a comparison model, and its objective functions are to minimize the number of vehicles and to minimize the completion time of the last task;

[0052] As shown in Table 1, as the number of tasks increases, both methods can obtain the minimum number of AGVs required to execute the tasks and the scheduling scheme. Among them, the solution time of the graph theory method is always within 4 seconds, while the calculation time of using Gurobi to solve the comparison model increases significantly with the increase in the number of tasks. The solution time for 50 tasks has exceeded 1,000 seconds. In terms of solution efficiency, the graph theory method not only has a fast solution speed but also can maintain a stable solution speed and is little affected by the problem scale.

[0053] Table - 1

[0054]

[0055] As shown in Table 2, the maximum completion times obtained by inputting the scheduling sequences obtained by using Gurobi to solve the comparison optimization model and by using the graph theory method under different numbers of tasks into the conflict-free planning algorithm are listed. Here, the conflict-free planning algorithm is completed based on the time window algorithm. Among them, Gap refers to the percentage difference between the conflict-free maximum completion time of the scheduling sequence obtained by the algorithm and the estimated maximum completion time calculated when generating the scheduling sequence, and Dev refers to the percentage difference between the conflict-free maximum completion times obtained by the two algorithms.

[0056] Table 2

[0057]

[0058] As can be seen from Table 2, compared with the results obtained by the comparison optimization method, the graph theory algorithm can better consider the conflict situation, narrow the gap between the scheduling calculation and the actual conflict-free planning, and can reduce the time by more than 10% on average. Therefore, the evaluation index considering the number of conflicts can enable each task to depart as punctually as possible and arrive on time, and the total delay time is relatively shorter.

[0059] In summary, compared with the results obtained by the comparison optimization method, the graph theory algorithm can better consider the conflict situation, narrow the gap between the scheduling calculation and the actual conflict-free planning, and can reduce the time by more than 10% on average. Therefore, the evaluation index considering the number of conflicts can enable each task to depart as punctually as possible and arrive on time, and the total delay time is relatively shorter.

[0060] The above embodiments are only illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Any person familiar with this technology can modify or change the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or changes made by those with ordinary knowledge in the technical field without departing from the spirit and technical idea disclosed by the present invention should still be covered by the claims of the present invention.

Claims

1. A method for jointly optimizing AGV scheduling and quantity considering conflicts, characterized in that Including: S1. Obtain the map data and task data of the automated unmanned warehouse; S2. Calculate the task execution sequence constraints based on the map data and task data; S3. Based on the execution sequence constraints, transform the constraints between tasks into a network structure to construct an alternative AGV scheduling network; S4. Based on the constructed alternative AGV scheduling network, calculate the minimum path covering problem to obtain a set of candidate solutions; Calculate the candidate solution with the fewest conflicts in the set of alternative solutions as the final scheduling plan; Step S2 specifically includes: Estimate the task completion time based on the arrival time of the current task and the transportation time of the shortest path from the task start point to the end point. The shortest path from the task start point to the end point is pre-calculated by the A* algorithm, a path planning algorithm, and the transportation time is estimated based on the AGV driving speed and the shortest path length; Based on the current task completion time and the transportation time from the current task end point to the next task start point, calculate the time when the AGV arrives at the next task start point after completing the current task. If the arrival time is earlier than the start time of the next task, the two tasks meet the execution sequence constraints; In step S3, each task is represented by a node, and the sequential connection is transformed into a directed connection between nodes to construct an alternative AGV scheduling network; two connected nodes in the network indicate that the two tasks meet the execution sequence constraints and can be continuously executed by one AGV; Step S4 specifically includes: Based on the alternative AGV scheduling network, transform the AGV quantity configuration and scheduling problem into a minimum path covering problem, and use the bipartite graph maximum matching / minimum cost maximum flow algorithm to solve it to obtain several candidate solutions. The candidate solutions include the fewest AGV quantities and their corresponding scheduling plans; Calculate the number of conflicting edges on the AGV driving paths of each candidate solution, and select the candidate solution with the fewest conflicting edges as the final scheduling plan.

2. The method for jointly optimizing AGV scheduling and quantity considering conflicts according to claim 1, characterized in that: The map data is the shelf positions, AGV parking spaces, AGV driving edges, conflict relationships between edges, and loading / unloading ports of the unmanned warehouse; the task data includes the start point of the task, the end point of the task, the task arrival time, and the shortest path from the task start point to the end point.

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