A method and system for constrained multi-objective collaborative optimization
By generating initial paths and iteratively optimizing them using the LaCAM algorithm, a compromise graph and maximum weight matching are constructed, which solves the conflict and computational efficiency problems in multi-AGV path planning and improves the path quality and efficiency of port logistics.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- QINGDAO PORT INT CO LTD
- Filing Date
- 2026-03-25
- Publication Date
- 2026-07-07
AI Technical Summary
In port logistics scenarios, multi-AGV path planning suffers from frequent path conflicts, high computational load, and difficulty in meeting real-time requirements, resulting in low path efficiency and increased energy consumption.
The LaCAM algorithm is used to generate initial path solutions, and a compromise graph is constructed through iterative optimization. The maximum weight matching is solved to determine the modification set, and the path is replanned. The path quality is optimized by combining time-space constraints and dynamic priority mechanisms.
It improves the path quality of multi-AGV systems, reduces conflicts and path deviations, enhances overall operational efficiency, and ensures computational efficiency and path feasibility.
Smart Images
Figure CN121920635B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of port logistics technology, specifically relating to a constrained multi-objective collaborative optimization method and system guided by shared knowledge. Background Technology
[0002] In modern industry and logistics, Automated Guided Vehicles (AGVs) are playing an increasingly crucial role. As a type of battery-powered, driverless vehicle equipped with electromagnetic or optical automatic guidance devices, AGVs can travel along preset paths to complete tasks such as material handling. Their applications are extremely wide-ranging, covering numerous industries including manufacturing, warehousing, ports, post offices, libraries, food, and chemicals.
[0003] In manufacturing, AGVs can efficiently, accurately, and flexibly transport materials between production lines. Multiple AGVs can also form a flexible logistics and handling system, which can change the transport route in a timely manner according to the adjustment of the production process, thereby improving production efficiency.
[0004] In port logistics scenarios, there is a frequent problem of multiple AGV path conflicts. Current algorithm-planned paths, when multiple AGVs are working simultaneously in the workshop, fail to fully consider the priorities and conflicts between AGVs, causing AGVs to frequently stop and avoid each other in narrow passages or near workstations, affecting the normal order of port logistics and causing delays to high-priority tasks.
[0005] Moreover, in ports, there are many AGVs and frequent cargo storage and retrieval. Although global replanning algorithms can find better paths, the computational load is large and it is difficult to meet real-time requirements. Local replanning may result in limited improvement in path quality due to the selection of unreasonable optimization objects, resulting in excessively long redundant paths for some AGVs, increasing energy consumption and operation time, and leading to low overall path efficiency. Summary of the Invention
[0006] This invention provides a constrained multi-objective collaborative optimization method. The method ensures computational efficiency and path feasibility through iterative optimization, reduces anomalies and path deviations, and improves overall operational efficiency.
[0007] The methods include:
[0008] S101: Use the LaCAM algorithm to generate initial path solutions for multiple AGVs;
[0009] S102: Determine whether the iteration termination condition is met. The iteration termination condition includes, but is not limited to, exceeding the given time limit, reaching the maximum number of iterations, or being unable to continue improving the solution. If met, output the current path solution. If not met, proceed to step S103.
[0010] S103: Construct a compromise diagram based on the compromises made by each AGV in path planning;
[0011] In the compromise graph, the nodes are each AGV, the edges are AGV pairs with compromises, and the edge weight is the sum of all compromise numbers among the AGVs; the compromise number is the deviation between the distance from the actual selected path node to the destination and the distance from the better path node to the same destination.
[0012] S104: Solve the maximum weight matching of the compromise graph, and determine each pair of AGVs in the matching result as a modification set M;
[0013] S105: Fix the current path of the AGV in the non-modification set as an obstacle, and replan the path of the AGV in the modification set M;
[0014] S106: Update the current path solution with the replanned path and return to step S102 to continue determining the iteration termination condition.
[0015] It should be further noted that S103 specifically includes the following steps:
[0016] Real-time data collection of the actual path selection nodes of each AGV in each single step of the path planning process is recorded as follows: The current position node at the corresponding time is denoted as u, and the target position node is denoted as gi;
[0017] In each single-step planning of each AGV, extract all neighboring nodes of the current position node u and u itself to form a candidate node set;
[0018] For each node in the candidate node set, obtain its shortest path distance to the target location node gi; then select the actual path node. Using the shortest path distance to gi as the benchmark, select candidate nodes whose distance is less than the benchmark and mark them as nodes with better paths, denoted as v;
[0019] If there is a better path node v, and the reason why the node is not selected is due to an anomaly with other AGVs, denoted as aj, then the compromise recording method is triggered to record the AGV pair (ai, aj) involved in this compromise.
[0020] For each recorded compromise event, calculate the compromise number, which is the actual path node. The difference between the shortest path distance to gi and the shortest path distance from the better path node v to gi is calculated, and the value is associated with the corresponding AGV pair (ai, aj).
[0021] Each AGV is treated as a node in the graph; for AGV pairs with compromise records, an edge is established between the two nodes, and the sum of the compromise counts of all compromise events of the AGV is used as the weight of the edge to form a compromise graph.
[0022] It should be further explained that S104 specifically includes the following steps:
[0023] Read the node information, edge information, and edge weight data of the compromise graph, and convert the node identifier, the two end node identifiers of the edge, and the edge weight into a preset data format;
[0024] Mark all nodes as unmatched and create an empty list of matching results to record the edges that were finally matched;
[0025] Sort all edges in the data in descending order of weight to generate a sorted edge sequence; if there are edges with the same weight, prioritize retaining the edges whose two endpoints have not participated in other high-weight edges;
[0026] Process each edge sequentially according to the sorted edge sequence: extract the two endpoints of the current edge and check whether both nodes are in an unmatched state; if both are unmatched, add the edge to the matching result list and update the status of the two nodes to matched.
[0027] When one or both ends of an edge are already matched, skip the edge, record the error information, and continue processing the next edge.
[0028] After all edges have been processed, extract the two endpoints of each edge from the matching result list, determine the AGV corresponding to each pair of nodes as the modification set M, and output the AGV number list of the modification set M.
[0029] It should be further explained that S102 specifically includes:
[0030] The system compares the real-time clock with a preset time limit. If the current time exceeds the preset time limit, the termination condition is triggered.
[0031] An iteration counter is set up. The counter value is incremented after each complete iteration, which is the execution cycle of steps S101 to S106. When the counter value reaches the preset maximum number of iterations, the termination condition is triggered.
[0032] After each iteration, the total path length and number of anomalies of the current path solution are recorded and compared with the historical best solution. If the optimization index of the total path length does not change by less than 1% in multiple consecutive iterations, it is determined that the solution cannot be improved further and the termination condition is triggered.
[0033] The status register indicates whether the current iteration has successfully generated a valid path solution; if a valid solution is not generated in multiple consecutive iterations, it is determined to be a no-solution state, triggering the termination condition.
[0034] The threshold for the change of optimization indicators is dynamically adjusted based on historical iteration data; if the change of the current optimization indicator is lower than the preset indicator threshold, it is determined that the solution cannot be improved further, and the termination condition is triggered.
[0035] The system integrates the results of judgments such as time limit exceeding limit, iteration number exceeding limit, optimization stagnation, continuous occurrence of invalid solutions, and preset index thresholds by using a logical OR gate. A termination signal is output when any of these conditions are met.
[0036] It should be further explained that step S105 specifically includes:
[0037] Traverse the current path of all AGVs in the non-modified set, mark each node on the path as an obstacle, and record its time step information to form an obstacle mapping table;
[0038] Separate the AGVs from the modification set M in the global path planning system and create independent path planning instances for them;
[0039] In the independent planning instance, the obstacle map is used as the input parameter, and the priority of the AGV in the modification set M is set to the highest priority of the current system.
[0040] Based on the obstacle identification map and priority configuration, a new local path is generated for each AGV in the modification set M;
[0041] The new paths of the AGVs in the modification set M are merged into the global path solution, the obstacle identification map is updated, and the independent planning instances of the AGVs in the modification set are released.
[0042] It should be further noted that S105 also includes the following steps:
[0043] Extract the path time-space trajectory of the non-modified AGVs, record the position node of each AGV at the historical time step, and mark the starting point of its future planning time window;
[0044] The trajectory of the non-modified AGV is divided into executed segments and unexecuted segments, and only the time-space nodes of the unexecuted segments are used as the set of obstacles.
[0045] For each AGV in the modified set M, calculate the remaining execution steps of its original path and adjust the search range of its replanned path;
[0046] During the replanning process of the modified set AGV, configure time-space buffer constraints: for each unexecuted segment path node of the non-modified set AGV, extend the buffer area around it to constrain the path nodes of the modified set AGV to not overlap with the buffer area.
[0047] The path planning task is started simultaneously for all AGVs in the modification set M, and constraints are executed in the planning task of each AGV. Finally, the new paths of all AGVs are merged as the update result.
[0048] It should be further noted that S101 also includes the following steps:
[0049] Collect obstacle distribution data in the AGV operating area and generate an environmental topology map containing node, edge, and obstacle attributes;
[0050] Extract the starting position, target position, and task priority label of each AGV, convert the task priority into path planning weight parameters, and associate them with the corresponding AGV;
[0051] The upper-level search module based on the LaCAM algorithm configures the initial parameters of the constraint tree;
[0052] The joint state space exploration task of the upper-level search is assigned to the first computing unit, and the local path planning task of the lower-level search is assigned to the second computing unit. The two units synchronize node information and constraints in real time through a data interaction interface.
[0053] It receives each AGV path segment generated collaboratively by the upper-level search and the lower-level search. The upper-level search first configures the path constraints, and then passes the constraints to the lower-level search. The lower-level search completes the calculation of the remaining paths under the premise of satisfying the path constraints, and gives a feasible solution or no solution.
[0054] This application also provides a constrained multi-objective collaborative optimization system, the system comprising:
[0055] The initial path generation module is used to generate initial path solutions for multiple AGVs using the LaCAM algorithm;
[0056] The termination determination module is used to determine whether the iteration termination conditions are met. The iteration termination conditions include, but are not limited to, exceeding the given time limit, reaching the maximum number of iterations, or being unable to continue improving the solution. If the conditions are met, the current path solution is output; if the conditions are not met, the compromise graph construction module is executed.
[0057] The compromise graph construction module constructs a compromise graph based on the compromises made by each AGV in path planning;
[0058] In the compromise graph, the nodes are each AGV, the edges are AGV pairs with compromises, and the edge weight is the sum of all compromise numbers among the AGVs; the compromise number is the distance deviation between the path node actually selected by the AGV and the better path node.
[0059] The maximum weight matching module is used to solve the maximum weight matching of the compromise graph and determine each pair of AGVs in the matching result as a modification set M;
[0060] The local replanning module is used to fix the current path of the AGV in the non-modification set as an obstacle and replan the path of the AGV in the modification set M.
[0061] The path update module is used to update the current path solution with the replanned path and return to the termination decision module.
[0062] As can be seen from the above technical solutions, the present invention has the following advantages:
[0063] The constrained multi-objective collaborative optimization method provided by this invention utilizes the LaCAM algorithm to generate initial path solutions, ensuring solution completeness and providing feasible initial paths for large-scale AGVs. By judging iteration termination conditions from multiple dimensions, it avoids excessive iteration and resource waste, balancing optimization effect and efficiency. Constructing a compromise graph can locate AGV pairs whose path quality deteriorates due to conflicts. Determining a modification set M allows for the optimization of AGV pairs with high potential, improving the efficiency of single-iteration optimization. Replanning paths for the modification set reduces computational load and ensures compatibility of new paths with other paths. Updating the path solutions and iterating continuously improves path quality. This method ensures computational efficiency and path feasibility, improves path quality in multi-AGV systems, reduces conflicts and path deviations, and enhances overall operational efficiency. Attached Figure Description
[0064] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0065] Figure 1 Flowchart of a constrained multi-objective collaborative optimization method;
[0066] Figure 2 This is a schematic diagram of the iterative improvement algorithm based on the compromise number applied to the map random-32-32-20.
[0067] Figure 3 This is a schematic diagram of the iterative improvement algorithm based on the compromise number applied to map room-32-32-4;
[0068] Figure 4 A schematic diagram of a multi-objective collaborative optimization system constrained by rules. Detailed Implementation
[0069] The constrained multi-objective collaborative optimization method involved in this invention employs the heuristic algorithm LaCAM to generate an initial solution and iteratively improves the current solution within time constraints. The iterative improvement algorithm iteratively improves the solution from the entire AGV set each time. Select a subset ,gather It is called a modification set, which is fixed. The path of the AGV, and the... The path of the AGV is recalculated, and the new path is merged with the original path to obtain an improved solution. This process of selecting AGV and recalculating can be performed iteratively until the termination condition is met.
[0070] For the PIBT and LaCAM algorithms, the LaCAM algorithm consists of two layers of search: the upper layer is responsible for global search, and the lower layer is responsible for local planning. The two work together to achieve efficient solution.
[0071] The upper-level search of the algorithm is similar to that of the A* algorithm. It unfolds in a joint state space, uses a stack structure (OPEN) to manage search nodes, and follows a modified depth-first search (DFS) paradigm. Upper-level nodes remain in OPEN after being visited, and different successor nodes are generated by dynamically adjusting the constraints stored in the nodes. A node is only removed from OPEN after all possible successor states have been explored, ensuring the completeness of the LaCAM algorithm.
[0072] Each upper-level node Save the following information:
[0073] Layout (configuration): Records the position information of all AGVs at a specific time. ,in express Current node position.
[0074] The priority array `order`: a non-negative real number `order[i]` specifies the priority. Priority.
[0075] The parent pointer: maintains path backtracking information.
[0076] Dynamic constraint tree: A tree structure is used to manage the movement constraints of (some) AGVs, while the movement of the remaining AGVs is determined by the lower-level search (PIBT).
[0077] The constraint tree is managed according to the following principles: initially, it contains only the root node, which contains no constraints. Non-root nodes at each level represent the movement constraints of an AGV. A movement constraint specifies that an AGV must move to a certain node in the next time step. For example, in the constraint tree of the first column, " "and" "respectively represent" The node must be moved to in the next moment. or The constraint tree is traversed and expanded using a breadth-first search strategy, and maintained using a queue structure.
[0078] Each time the current parent node is visited, the following constraint tree-related operations need to be performed: extract the head constraint node; if the depth of the constraint tree is less than 10 ... (If the root node depth is specified as 0), then new constraints are generated based on the next level AGV of the current node and added to the tail of the queue. All constraints on the path from the selected node to the root node are collected and input into the next level search.
[0079] The lower-level search of the algorithm is responsible for expanding the upper-level nodes and generating feasible successor states that satisfy the constraints provided by the current upper-level nodes using a specific algorithm. LaCAM uses the PIBT algorithm to implement this task, performing fast local path planning.
[0080] The LaCAM hierarchical architecture consists of two layers: the upper-layer search covers the entire solution space through depth-first search and constraint tree expansion, ensuring solution completeness; the lower-layer search uses the PIBT algorithm to achieve fast local layout planning, ensuring computational efficiency and basic solution quality. This combination enables LaCAM to achieve both solution capability and efficiency when dealing with large-scale MAPF problems.
[0081] PIBT (Priority Inheritance with Backtracking) was originally designed for iteratively solving the MAPF problem. It is a layout generator that starts with an initial layout ( As input, generate a feasible adjacent layout ( By iteratively executing this process, PIBT can quickly generate complete feasible solutions to the MAPF problem. The PIBT algorithm is implemented based on a dynamic priority mechanism, as well as priority inheritance and backtracking strategies.
[0082] PIBT prioritizes AGVs that have not yet reached the target node or are far from the target node through a dynamic priority mechanism. This embodiment uses non-negative real numbers. express Priority.
[0083] The specific implementation is as follows:
[0084] Priority initialization: for each Set its initial priority to .in, Represents a node The shortest distance between them This refers to the number of AGVs.
[0085] Dynamic adjustment: in the new layout After generation, for each Adjust priority:
[0086] Reaching the goal, that is Set its priority to the lowest level. .
[0087] If the target has not been reached, increase its priority. .
[0088] This design is particularly useful in lifelong MAPF problems, where AGVs are immediately assigned to a new target location after reaching one. This is because, in lifelong scenarios, not all AGVs are simultaneously at the target location; dynamic prioritization ensures task continuity and efficiency.
[0089] PIBT effectively solves this problem through a priority inheritance mechanism in planning. Towards After the location is moved, the algorithm briefly makes inherit Priority, actually according to The sequential planning scheme was successfully used to generate a feasible solution.
[0090] In the specific implementation of the algorithm, the priority inheritance mechanism needs to be combined with recursion and backtracking strategies to provide opportunities to escape deadlock and seek other feasible solutions. In the example of this embodiment, because lie in Mobile candidate nodes The above needs to be based on The planning results are to be finalized. Towards Is relocation feasible? If so... Planning failure, through backtracking Select another movement option.
[0091] The constrained multi-objective cooperative optimization method involved in this application will be described in detail below. Specific details such as particular system structures and techniques are presented for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application can also be implemented in other embodiments without these specific details.
[0092] It should be understood that, when used in this specification, terms include indicating the presence of a described feature, integral, step, operation, element, and / or component, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or collections thereof. The terms include, encompass, have, and variations thereof mean including but not limited to, unless otherwise specifically emphasized.
[0093] The statements such as "one embodiment" or "some embodiments" described in this application mean that one or more embodiments of this application include the specific features, structures, or characteristics described in that embodiment. Therefore, the statements such as "in one embodiment," "in some embodiments," "in other embodiments," and "in still other embodiments" in this application do not necessarily refer to the same embodiment, but rather mean one or more, but not all, embodiments, unless otherwise specifically emphasized.
[0094] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0095] Please see Figure 1 The diagram shows a flowchart of a constrained multi-objective cooperative optimization method in a specific embodiment. The method includes:
[0096] S101: Use the LaCAM algorithm to generate initial path solutions for multiple AGVs.
[0097] In some embodiments, the LaCAM algorithm works collaboratively through a global search at the upper level and local planning at the lower level. The upper-level search unfolds in the joint state space using an improved depth-first search approach, managing nodes with a stack structure. Each node records the positions of all AGVs, their priority array, predecessor pointers, and a dynamic constraint tree. The constraint tree expands using a breadth-first strategy, with each node recording the movement constraints of a particular AGV—the node it must reach in the next time step. The lower-level search, based on the PIBT algorithm, quickly generates locally feasible paths for the AGVs according to the constraints provided by the upper level, ensuring that the constraints are met and there are no anomalies. Finally, the local paths of each AGV are concatenated to form a complete initial path solution.
[0098] As can be seen, the upper-level search expands the constraint tree to cover all possible solution spaces, ensuring the completeness of the solution; the lower-level search, with the help of PIBT's dynamic priority and backtracking mechanism, quickly generates local paths that satisfy the constraints, balancing global exploration with local efficiency. The collaboration of the two ensures that the initial solution is both feasible and of basic quality.
[0099] In some specific embodiments, S101 further includes the following steps:
[0100] S1011: Collect obstacle distribution data in the AGV operating area and generate an environmental topology map containing node, edge and obstacle attributes, where each node is associated with its passable time period information.
[0101] The environmental topology graph involved in this embodiment can be configured as a grid to represent the operating area. Each node includes attributes such as coordinates and passable time periods, and the weight of the edges is set according to the distance between nodes and the difficulty of passage. In this way, the physical environment is transformed into a computable graphical model.
[0102] S1012: Extract the starting position, target position, and task priority label of each AGV, convert the task priority into path planning weight parameters, and associate them with the corresponding AGV.
[0103] S1013: The upper-level search module based on the LaCAM algorithm configures the initial parameters of the constraint tree, including the unconstrained state of the root node and the maximum depth threshold for constraint expansion.
[0104] In this embodiment, the upper-level computing unit is mainly used for generating the global path framework, and the lower-level computing unit refines the local path based on this framework. By synchronizing constraints and node states through interfaces, the unit works collaboratively to achieve a combination of global optimization and local fine-grained planning.
[0105] S1014: Assign the joint state space exploration task of the upper-level search to the first computing unit, and assign the local path planning task of the lower-level search to the second computing unit. The two units synchronize node information and constraints in real time through a data interaction interface.
[0106] S1015: Receives each AGV path segment generated collaboratively by the upper-level search and the lower-level search. The upper-level search first configures the path constraints, and then passes the constraints to the lower-level search. The lower-level search completes the calculation of the remaining paths under the premise of satisfying the path constraints, and gives a feasible solution or no solution.
[0107] In this embodiment, the position and time of each AGV path are compared. If there is an overlap at the same time and position, it is determined to be abnormal. The uniqueness check of spatiotemporal coordinates ensures that there are no abnormal paths.
[0108] Therefore, step S101 constructs an environment model containing spatiotemporal attributes, combines the AGV task priority configuration algorithm constraint parameters, and adopts a hierarchical computing architecture to achieve the coordination of global and local path planning, generating an initial path solution without anomalies. In this way, the feasibility and adaptability of the initial solution are ensured through environment modeling, task adaptation, and hierarchical coordination.
[0109] Optionally, the urgency of the task is converted into the probability of constraint tree expansion. The constraints of high-priority AGVs are given a higher probability when expanding, and they are given priority to obtain path resources. An environmental adaptability adjustment module is added to adjust the node exploration range of the upper-level search according to the congestion index of the operating area. The exploration range is narrowed in congested areas to reduce invalid calculations, and the range is expanded in sparse areas to find better paths, thus balancing efficiency and solution quality.
[0110] S102: Determine whether the iteration termination condition is met. The iteration termination condition includes, but is not limited to, exceeding the given time limit, reaching the maximum number of iterations, or being unable to continue improving the solution. If it is met, output the current path solution. If S102 is not met, execute S103.
[0111] In some embodiments, three core metrics are monitored in real time: first, the cumulative iteration time, recorded by a clock module from startup to the current time and compared with a preset maximum allowable time threshold; second, the number of iterations, recorded by a counter and compared with a maximum number threshold; and third, the improvement in solution, calculated as the quality difference between the current path solution and the previous solution. Optionally, the reduction in total path length is compared with a minimum improvement threshold. If any metric meets the target, the process terminates. This embodiment ensures that iterative optimization has sufficient time to improve solution quality, prevents excessive iteration from consuming resources, and balances optimization effectiveness and efficiency.
[0112] In some specific embodiments, S102 specifically includes:
[0113] Step S1021: Compare the real-time clock with the preset time limit. If the current time exceeds the preset time limit, trigger the termination condition.
[0114] Step S1022: Set an iteration counter. The counter value increments after each complete iteration, i.e., the execution cycle of steps S101 to S106. When the counter value reaches the preset maximum number of iterations, the termination condition is triggered.
[0115] Step S1023: After each iteration, record the total path length, number of anomalies, etc. of the current path solution, and compare it with the historical best solution; if the optimization index of the total path length does not change by less than 1% in multiple consecutive iterations, it is determined that the solution cannot be improved further and the termination condition is triggered.
[0116] Step S1024: Mark whether the current iteration has successfully generated a valid path solution by using the status register; if a valid solution is not generated in multiple consecutive iterations, it is determined to be a no-solution state and the termination condition is triggered.
[0117] Step S1025: Dynamically adjust the change threshold of the optimization index based on historical iteration data; if the change of the current optimization index is lower than the preset index threshold, it is determined that the solution cannot be improved further, and the termination condition is triggered.
[0118] Step S1026: Combine the judgment results of logic OR gate exceeding time limit, exceeding iteration limit, optimization stagnation, continuous occurrence of invalid solutions, and preset index threshold, and output a termination signal when any condition is met.
[0119] It can be seen that by monitoring time, iteration count, solution quality, and system status, the termination timing of the iteration process can be determined, avoiding the waste of ineffective computational resources. The path planning system is configured with time monitoring, iteration counters, solution quality assessment, and threshold adjustment, combined with status registers and logic gates to achieve a comprehensive determination of termination conditions. Here, time monitoring compares the real-time clock with a preset time limit and outputs an over-limit signal; solution quality assessment compares the optimization metrics of the current solution with historical solutions and outputs a stall signal; threshold adjustment dynamically adjusts the judgment threshold based on historical data, improving the adaptability of termination conditions.
[0120] S103: Construct a compromise graph based on the compromises made by each AGV in path planning. The nodes of the compromise graph are each AGV, the edges are pairs of AGVs with compromises, and the edge weight is the sum of all compromise numbers between those pairs of AGVs. The compromise number is the deviation between the distance from the actually selected path node to the destination and the distance from the better path node to the same destination.
[0121] In some embodiments, the path selection of AGVs is recorded: when an AGV abandons a better path node (i.e., a node closer to the target) due to an anomaly with a higher-priority AGV and chooses a suboptimal node, the distance deviation between the two is calculated, i.e., the compromise number. Then, the compromise records of all AGV pairs are counted: each AGV is treated as a node in the graph. If there is a compromise between two AGVs, an edge is established between the nodes, with the edge weight being the sum of all compromise numbers between the two, forming a compromise graph.
[0122] This embodiment identifies AGV pairs whose path quality deteriorates due to mutual anomalies, providing data support for subsequent selection of optimization and modification sets, and improving the targeted nature of iterative improvements.
[0123] S103 also includes the following steps:
[0124] S1031: Real-time collection of the actual path selection nodes of each AGV during each planning cycle in the path planning process, denoted as... The current position node at the corresponding time is denoted as u, and the target position node is denoted as g. i And store.
[0125] S1032: For each planning cycle of each AGV, extract all neighboring nodes of the current location node u and u itself to form a candidate node set.
[0126] S1033: For each node in the candidate node set, obtain its distance to the target location node g. i The shortest path distance; the actual selected path nodes to g i Using the shortest path distance as a benchmark, select candidate nodes whose distance is less than the benchmark and mark them as nodes with better paths, denoted as v.
[0127] Optionally, AGVa is set. i The actual path nodes are The better path node is v, and both paths lead to the target node g. i The shortest path distances are d( ,g i ) and d(v,g i If ), then the compromise number C = d( ,g i )-d(v,g i ).
[0128] S1034: If a better path node v exists, and the reason this node was not selected is due to other AGVs, denoted as a. j If an anomaly is detected, the compromise recording method is triggered, recording the AGV pairs (a) involved in the compromise. i ,a j ).
[0129] S1035: For the recorded compromise events, calculate the compromise number, i.e., the actual path nodes. to g i Shortest path distance and better path node v to g i The difference in the shortest path distance is used to associate this value with the corresponding AGV pair (a i ,a j ).
[0130] S1036: Treat each AGV as a node in the graph; for AGV pairs with compromise records, establish an edge between the two nodes, and use the sum of the compromise counts of all compromise events of the AGV as the weight of the edge to form a compromise graph.
[0131] In step S103 of this embodiment, the path selection behavior of AGVs is tracked in real time to identify suboptimal path selection states caused by abnormalities. The deviation between the actual path of the AGV and the optimal path in this selection state is quantified as a compromise number. Then, a graph structure is used to map the compromise relationship nodes between AGVs to represent AGVs, the edges represent the existence of compromise relationships, and the edge weights represent the total deviations. Finally, a compromise graph that can quantify the degree of mutual influence between the paths of AGVs is formed.
[0132] S104: Solve for the maximum weight matching of the compromise graph, and determine each pair of AGVs in the matching result as the modification set M.
[0133] In some embodiments, the node, edge, and edge weight data of the compromise graph are parsed and sorted in descending order of edge weight. A greedy strategy is used to match edges sequentially: the edge with the largest weight is selected first, ensuring that the nodes at both ends of the edge are not matched by other edges, until all matchable high-weight edges are selected. Each pair of matched nodes corresponds to a modification set M. This embodiment optimizes the highest-performing AGV pair, enabling targeted path improvement in each iteration. Compared to randomly selecting modification sets, this improves the optimization efficiency of a single iteration and accelerates the improvement of solution quality.
[0134] S104 specifically includes the following steps:
[0135] S1041: Read the node information, edge information and edge weight data of the compromise graph, and convert the node identifier, the two end node identifiers of the edge and the edge weight into a preset data format.
[0136] Optionally, a bubble sort logic is adopted, which compares the weights of edges pair by pair and swaps the edges with larger weights to the front of the sequence to achieve sorting from largest to smallest; for edges with equal weights, the edge with higher unmatching degree is selected first by calculating the node unmatching degree to ensure that the matching covers more potential optimization objects.
[0137] S1042: Mark all nodes as unmatched and create an empty list of matching results to record the edges that were finally matched.
[0138] S1043: Sort all edges in the data in descending order of weight to generate a sorted edge sequence; if there are edges with the same weight, prioritize retaining the edges whose two endpoints have not participated in other high-weight edges.
[0139] S1044: Process each edge sequentially according to the sorted edge sequence: extract the two endpoints of the current edge, check whether both nodes are in an unmatched state; if both are unmatched, add the edge to the matching result list and update the status of the two nodes to matched.
[0140] S1045: When one or both ends of an edge are already matched, skip the edge, record the error information, and continue processing the next edge.
[0141] S1046: After all edges have been processed, extract the two endpoints of each edge from the matching result list, determine the AGV corresponding to each pair of nodes as the modification set M, and output the AGV number list of the modification set M.
[0142] Optionally, the matching verification method is to calculate the number of overlapping nodes in the current paths of the two AGVs on the initially matched edges. If the proportion of overlapping nodes to the total number of nodes in their respective paths exceeds 30%, it is determined to be an optimizable area and the edge is retained; otherwise, it is discarded. AGV pairs that are easier to reduce anomalies through replanning are selected based on the path overlap.
[0143] As can be seen, in step S104 of this embodiment, by parsing the data of the compromise graph, and taking edge weight as the core basis, the edge with the largest weight and the node not being matched is selected first for matching, so as to ensure that each AGV only participates in matching once, and obtains the AGV pair set that can reflect the maximum optimization potential, namely the modification set M.
[0144] S105: Fix the current paths of AGVs in the non-modification set as obstacles, and replan the paths of AGVs in the modification set M. The non-modification set refers to the current paths of all AGVs except those in the modification set M as obstacles.
[0145] In some embodiments, the path data of the modified set and the non-modified set AGVs are first separated, and the path of the non-modified set is converted into a path containing path nodes and corresponding passage times; then the current path of the modified set AGV is cleared, the path planning module is called, and the path from the current position to the target is replanned for the modified set AGV while avoiding these spatiotemporal obstacles; finally, it is verified whether the new path is abnormal from the non-modified set path, and if it is abnormal, it is replanned.
[0146] This embodiment replans some AGVs to reduce computational load. Spatiotemporal obstacle constraints ensure the new path is compatible with other paths, preventing global anomalies caused by local modifications.
[0147] S106: Update the current path solution with the replanned path and return to step S102 to continue determining the iteration termination condition.
[0148] In some embodiments, the new path of the modified AGV replaces its original path, all non-modified AGVs are retained, the modified set is updated, and a new current path solution is formed. The new solution is then passed to step S102 to start the next iteration loop, repeating the process of determining termination, constructing a compromise graph, selecting a modified set, replanning, and updating. Through iterative loops, the parts of the path with high optimization potential are continuously improved, gradually accumulating optimization effects, causing the path solution to approach a better state from the initial state, ultimately obtaining a better feasible solution that meets the AGV system's requirement for efficient and low-abnormal paths.
[0149] In one embodiment of the present invention, based on step S105, the following will provide a possible embodiment and its specific implementation will be described in a non-limiting manner. Step S105 specifically includes:
[0150] Traverse the current path of all AGVs in the non-modified set, mark each node on the path as an obstacle, and record its time step information to form an obstacle mapping table.
[0151] Separate the AGVs from the modification set M in the global path planning system and create independent path planning instances for them.
[0152] In the independent planning instance, the obstacle map is used as the input parameter, the priority of the AGV in the modification set M is set to the highest priority of the current system, and the path update function of other AGVs is disabled.
[0153] Based on the obstacle mapping table and priority configuration, the optimal algorithm such as SIPP is called to generate a new local path for each AGV in the modification set M, ensuring that the new path does not deviate from the identified obstacles.
[0154] The new paths of the AGVs in the modification set M are merged into the global path solution, the obstacle identification map is updated, and the independent planning instances of the AGVs in the modification set are released.
[0155] This embodiment optimizes path quality locally by fixing the paths of non-modified AGVs to marked obstacles, thus limiting the path planning space of modified AGVs. An obstacle mapping table reflects environmental changes in real time, and independent planning instances avoid the complexity of global path planning.
[0156] Furthermore, in this embodiment, the obstacle mapping table records the path nodes of non-modified AGVs in real time, providing local environmental constraints for modified AGVs. Finally, through an incremental update mechanism, only local path data is modified, maintaining the integrity of the global path solution.
[0157] In some specific embodiments, S105 further includes the following steps:
[0158] S2051: Extract the path time-space trajectory of the non-modified AGV, record the position node of each AGV in the historical time step, and mark the starting point of its future planning time window;
[0159] S2052: Divide the trajectory of the non-modified AGV into executed segments and unexecuted segments, and only use the time-space nodes of the unexecuted segments as the set of identified obstacles;
[0160] S2053: Calculate the remaining number of execution steps for each AGV in the modified set M on its original path, i.e., the total number of steps on the original path minus the number of steps already executed, and adjust the search range of its replanned path.
[0161] S2054: During the replanning process of the modified set AGV, configure time-space buffer constraints: for each unexecuted segment path node of the non-modified set AGV, extend the buffer area around it, and constrain the path nodes of the modified set AGV to not overlap with the buffer area.
[0162] S2055: Simultaneously start the path planning task for all AGVs in the modification set M, and independently execute the constraints of S2051 to S2054 in the planning task of each AGV, and finally merge the new paths of all AGVs as the update result.
[0163] In this embodiment, step S105 uses dynamic constraint isolation and parallel optimization to avoid anomalies with non-modified AGVs with already determined paths when replanning the modified set AGV path, thereby improving planning efficiency and solution quality.
[0164] This embodiment treats only the unexecuted segments of the non-modified AGV's path as obstacles, preventing the modified AGV from being unable to utilize areas left by the non-modified AGV due to fixed executed paths, thus expanding the available space for replanning. The search range is adjusted based on the remaining steps of the original path of the modified AGV, avoiding redundant calculations caused by global searches. By expanding the buffer area around the unexecuted path nodes of the non-modified AGV, potential spatial anomalies are avoided in advance, reducing the need for minor adjustments to the path after replanning.
[0165] Furthermore, as a refinement and extension of the specific implementation of the constrained multi-objective collaborative optimization method described above, the heuristic algorithm of the constrained multi-objective collaborative optimization method for the MAPF problem can provide feasible solutions to the MAPF problem relatively efficiently, but the quality of the solutions is often difficult to guarantee. When the solution time is much less than the given time limit, in order to make full use of the remaining time, it can be used to recalculate the (partial / all) paths of the AGVs to iteratively refine the initial solution. Currently, there are two main iterative refinement strategies: Global replanning: recalculating the paths of all AGVs. Local replanning: optimizing only the paths of some AGVs while keeping other paths unchanged.
[0166] Based on the real-time requirements in practical applications, local replanning is a relatively feasible solution. This embodiment uses a heuristic algorithm, LaCAM, to generate an initial solution and iteratively improves the current solution within the time constraint.
[0167] The iterative improvement algorithm iterates through the entire AGV set each time. Select a subset ,gather This is called a modification set, which fixes the path of the AGV in A / M and... The path of the AGV is recalculated, and the new path is merged with the original path to obtain an improved solution. This process of selecting AGV and recalculating can be performed iteratively until the termination condition is met, such as exceeding the given time limit or failing to obtain an improvement in the solution.
[0168] Specifically, given a MAPF instance, the execution flow of the iterative improvement algorithm is as follows:
[0169] Generate an initial solution using the fast MAPF solver. The fast MAPF solver uses the LaCAM algorithm.
[0170] The improvement process involves the following steps:
[0171] (1) Based on the current solution Constructing Modification Sets .
[0172] (2) Fixed The paths of the AGVs are treated as dynamic obstacles, and the optimal algorithm is used to replan their routes. The path of the AGV.
[0173] (3) Update with the new path .
[0174] (4) Repeat steps (1)-(3) until the termination condition is met. Stop iterating when the condition is met, such as timeout, reaching the maximum number of iterations, or inability to continue improvement.
[0175] One of the core aspects of iterative improvement algorithms lies in the modification set. The choice of determines the theoretical upper limit that the current solution can reach in one iteration.
[0176] The modification set is constructed based on the compromise number. The compromise number is used during the PIBT layout generation phase of LaCAM, where AGVs perform path planning according to priority order. Located at node When, use represent In the actual selection of this plan, if any better option that was not selected exists... It satisfies ,represent Moving it will result in a collision with another higher priority AGV. The conflict led to a compromise in this planning process, with a suboptimal node being chosen. .
[0177] For the above situation, the Compromise Number for this plan is defined as follows:
[0178]
[0179] Reflecting AGV The degree of deviation between the actual path selection and the optimal path selection in a planning process.
[0180] The compromise diagram is based on the compromise number, which actually associates a pair of AGVs in a planning operation. And another AGV that forced it to compromise in this planning Multiple compromises occur between each pair of AGVs, and a compromise graph is constructed. To record all compromise information.
[0181] Specifically, AGVs are considered as nodes in the graph, and the sum of the compromises between a pair of AGVs is the "edge weight" between them. Conditions met:
[0182] Node set In the graph, each node corresponds to an AGV. (Edges) If and only if A "compromise" occurred between them. Denotes the edge weight, for any , Defined as and The sum of all compromises.
[0183] The following section constructs the modification set based on the compromise graph. To avoid redundant calculations and for efficiency considerations, this embodiment specifies... Each AGV is limited to being selected at most once. Since the compromise number represents the degree of deviation between the actual path and the optimal path, the larger the compromise number (edge weight) between a pair of AGVs, the greater the optimization potential of the pair, and they should be selected first.
[0184] Therefore, constructing the modification set by finding the maximum weight matching (MWM) on the compromise graph is a reasonable approach.
[0185] The specific algorithm is as follows: Find the compromise graph. Maximum weight matching For each matched edge Construct a binary modification set .
[0186] This embodiment presents the experimental results of the iterative improvement algorithm based on the compromise number, as shown in Table 1. The experiment uses SOC (Sum of Cost, total time) as the objective function, and the LaCAM algorithm is used to obtain an initial solution. An iterative improvement algorithm for randomly selected AGVs is used as a control, as shown in Table 1. Figure 2 As shown, the iterative improvement algorithm based on the compromise number was tested on maps random-32-32-20 and such. Figure 3 The average improvement rate of the solution shown in the room-32-32-4 diagram is defined as having an iterative improvement time of 1.
[0187] Experiments show, as shown in Table 1, that compared with the iterative improvement algorithm that randomly selects AGVs, the iterative improvement algorithm based on compromise numbers has significantly improved the solution improvement capability. The iterative improvement algorithm that randomly selects AGVs has an average improvement rate of 6.64% on all MAPF test instances, while the iterative improvement algorithm based on compromise numbers further utilizes the hidden information in the planning process of the LaCAM algorithm, increasing the improvement rate to an average of 15.49%.
[0188] Table 1: Experimental Results of the Iterative Improvement Algorithm
[0189]
[0190] This embodiment addresses the iterative improvement problem of MAPF solutions. By capturing compromise information during the planning process of the LaCAM and PIBT algorithms, it presents a modification set construction scheme based on the compromise number and an iterative improvement algorithm. Given the initial solution provided by the LaCAM algorithm, this iterative improvement scheme significantly enhances the quality of the solution, complementing the high efficiency of the LaCAM algorithm.
[0191] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.
[0192] The following are embodiments of the constrained multi-objective cooperative optimization system provided in this disclosure. This system and the constrained multi-objective cooperative optimization methods in the above embodiments belong to the same inventive concept. For details not described in detail in the embodiments of the constrained multi-objective cooperative optimization system, please refer to the embodiments of the constrained multi-objective cooperative optimization methods described above.
[0193] like Figure 4 As shown, the system includes:
[0194] The initial path generation module 201 is used to generate initial path solutions for multiple AGVs using the LaCAM algorithm;
[0195] The termination determination module 202 is used to determine whether the iteration termination condition is met. The iteration termination condition includes, but is not limited to, exceeding the given time limit, reaching the maximum number of iterations, or being unable to continue improving the solution. If the condition is met, the current path solution is output. If the condition is not met, the compromise graph construction module is executed.
[0196] The compromise graph construction module 203 constructs a compromise graph based on the compromise situation of each AGV in path planning;
[0197] In the compromise graph, the nodes are each AGV, the edges are AGV pairs with compromises, and the edge weight is the sum of all compromises between the AGV pairs.
[0198] Maximum weight matching module 204 is used to solve the maximum weight matching of the compromise graph and determine each pair of AGVs in the matching result as a modification set M;
[0199] The local replanning module 205 is used to fix the current path of the AGV in the non-modification set as an obstacle and replan the path of the AGV in the modification set M.
[0200] The path update module 206 is used to update the current path solution with the replanned path and return to the termination decision module.
[0201] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims
1. A constrained multi-objective collaborative optimization method, characterized in that, The methods include: S101: Use the LaCAM algorithm to generate initial path solutions for multiple AGVs; S102: Determine whether the iteration termination condition is met. The iteration termination condition includes, but is not limited to, exceeding the given time limit, reaching the maximum number of iterations, or being unable to continue improving the solution. If met, output the current path solution. If not satisfied, proceed to step S103; S103: Construct a compromise diagram based on the compromises made by each AGV in path planning; In the compromise graph, the nodes are each AGV, the edges are AGV pairs with compromises, and the edge weight is the sum of all compromise numbers among the AGVs; the compromise number is the deviation between the distance from the actual selected path node to the destination and the distance from the better path node to the same destination. S104: Solve the maximum weight matching of the compromise graph, and determine each pair of AGVs in the matching result as a modification set M; S105: Fix the current path of the AGV in the non-modification set as an obstacle, and replan the path of the AGV in the modification set M; S106: Update the current path solution with the replanned path and return to step S102 to continue determining the iteration termination condition.
2. The constrained multi-objective cooperative optimization method according to claim 1, characterized in that, S103 also includes the following steps: Real-time data collection of the actual path selection nodes of each AGV in each single step of the path planning process is recorded as follows: The current position node at the corresponding time is denoted as u, and the target position node is denoted as g. i ; In each single-step planning of each AGV, extract all neighboring nodes of the current position node u and u itself to form a candidate node set; For each node in the candidate node set, obtain its distance to the target location node g. i The shortest path distance; the actual selected path nodes to g i Using the shortest path distance as the benchmark, select candidate nodes whose distance is less than the benchmark and mark them as nodes with better paths, denoted as v; If a better path node v exists, and the node was not selected because of other AGVs, let's call it a. j If an anomaly is detected, the compromise recording method is triggered, recording the AGV pairs (a) involved in the compromise. i ,a j ); For each recorded compromise event, calculate the compromise number, which is the actual path node. to g i Shortest path distance and better path node v to g i The difference in the shortest path distance is used to associate the value with the corresponding AGV pair (a i ,a j ); Each AGV is treated as a node in the graph; for AGV pairs with compromise records, an edge is established between the two nodes, and the sum of the compromise counts of all compromise events of the AGV is used as the weight of the edge to form a compromise graph.
3. The constrained multi-objective cooperative optimization method according to claim 1, characterized in that, S104 specifically includes the following steps: Read the node information, edge information, and edge weight data of the compromise graph, and convert the node identifier, the two end node identifiers of the edge, and the edge weight into a preset data format; Mark all nodes as unmatched and create an empty list of matching results to record the edges that were finally matched; Sort all edges in the data in descending order of weight to generate a sorted edge sequence; if there are edges with the same weight, prioritize retaining the edges whose two endpoints have not participated in other high-weight edges; Process each edge sequentially according to the sorted edge sequence: extract the two endpoints of the current edge and check whether both nodes are in an unmatched state; if both are unmatched, add the edge to the matching result list and update the status of the two nodes to matched. When one or both ends of an edge are already matched, skip the edge, record the error information, and continue processing the next edge. After all edges have been processed, extract the two endpoints of each edge from the matching result list, determine the AGV corresponding to each pair of nodes as the modification set M, and output the AGV number list of the modification set M.
4. The constrained multi-objective cooperative optimization method according to claim 1, characterized in that, S102 specifically includes: The system compares the real-time clock with a preset time limit. If the current time exceeds the preset time limit, the termination condition is triggered. An iteration counter is set up. The counter value is incremented after each complete iteration, which is the execution cycle of steps S101 to S106. When the counter value reaches the preset maximum number of iterations, the termination condition is triggered. After each iteration, the total path length and number of anomalies of the current path solution are recorded and compared with the historical best solution. If the optimization index of the total path length does not change by less than 1% in multiple consecutive iterations, it is determined that the solution cannot be improved further and the termination condition is triggered. The status register indicates whether the current iteration has successfully generated a valid path solution; if a valid solution is not generated in multiple consecutive iterations, it is determined to be a no-solution state, triggering the termination condition. The threshold for the change of optimization indicators is dynamically adjusted based on historical iteration data; if the change of the current optimization indicator is lower than the preset indicator threshold, it is determined that the solution cannot be improved further, and the termination condition is triggered. The system integrates the results of judgments such as time limit exceeding limit, iteration number exceeding limit, optimization stagnation, continuous occurrence of invalid solutions, and preset index thresholds by using a logical OR gate. A termination signal is output when any of these conditions are met.
5. The constrained multi-objective cooperative optimization method according to claim 1, characterized in that, Step S105 specifically includes: Traverse the current path of all AGVs in the non-modified set, mark each node on the path as an obstacle, and record its time step information to form an obstacle mapping table; Separate the AGVs from the modification set M in the global path planning system and create independent path planning instances for them; In the independent planning instance, the obstacle map is used as the input parameter, and the priority of the AGV in the modification set M is set to the highest priority of the current system. Based on the obstacle identification map and priority configuration, a new local path is generated for each AGV in the modification set M; The new paths of the AGVs in the modification set M are merged into the global path solution, the obstacle identification map is updated, and the independent planning instances of the AGVs in the modification set are released.
6. The constrained multi-objective cooperative optimization method according to claim 1, characterized in that, S105 also includes the following steps: Extract the path time-space trajectory of the non-modified AGVs, record the position node of each AGV at the historical time step, and mark the starting point of its future planning time window; The trajectory of the non-modified AGV is divided into executed segments and unexecuted segments, and only the time-space nodes of the unexecuted segments are used as the set of obstacles. For each AGV in the modified set M, calculate the remaining execution steps of its original path and adjust the search range of its replanned path; During the replanning process of the modified set AGV, configure time-space buffer constraints: for each unexecuted segment path node of the non-modified set AGV, extend the buffer area around it to constrain the path nodes of the modified set AGV to not overlap with the buffer area. The path planning task is started simultaneously for all AGVs in the modification set M, and constraints are executed in the planning task of each AGV. Finally, the new paths of all AGVs are merged as the update result.
7. The constrained multi-objective cooperative optimization method according to claim 1, characterized in that, S101 also includes the following steps: Collect obstacle distribution data in the AGV operating area and generate an environmental topology map containing node, edge, and obstacle attributes; Extract the starting position, target position, and task priority label of each AGV, convert the task priority into path planning weight parameters, and associate them with the corresponding AGV; The upper-level search module based on the LaCAM algorithm configures the initial parameters of the constraint tree; The joint state space exploration task of the upper-level search is assigned to the first computing unit, and the local path planning task of the lower-level search is assigned to the second computing unit. The two units synchronize node information and constraints in real time through a data interaction interface. It receives each AGV path segment generated collaboratively by the upper-level search and the lower-level search. The upper-level search first configures the path constraints, and then passes the constraints to the lower-level search. The lower-level search completes the calculation of the remaining paths under the premise of satisfying the path constraints, and gives a feasible solution or no solution.
8. A constrained multi-objective cooperative optimization system, characterized in that, The system is used to implement the constrained multi-objective collaborative optimization method as described in any one of claims 1 to 7; The system includes: The initial path generation module is used to generate initial path solutions for multiple AGVs using the LaCAM algorithm; The termination determination module is used to determine whether the iteration termination conditions are met. The iteration termination conditions include, but are not limited to, exceeding the given time limit, reaching the maximum number of iterations, or being unable to continue improving the solution. If the conditions are met, the current path solution is output; if the conditions are not met, the compromise graph construction module is executed. The compromise graph construction module constructs a compromise graph based on the compromises made by each AGV in path planning; In the compromise graph, the nodes are each AGV, the edges are AGV pairs with compromises, and the edge weight is the sum of all compromise numbers among the AGVs; the compromise number is the distance deviation between the path node actually selected by the AGV and the better path node. The maximum weight matching module is used to solve the maximum weight matching of the compromise graph and determine each pair of AGVs in the matching result as a modification set M; The local replanning module is used to fix the current path of the AGV in the non-modification set as an obstacle and replan the path of the AGV in the modification set M. The path update module is used to update the current path solution with the replanned path and return to the termination decision module.