A cluster allocation optimization method and system based on alliance game

Abstract

This invention discloses a cluster allocation optimization method and system based on coalition game theory. The method mainly includes: analyzing the task requirements and resource constraints of the cluster allocation scenario; establishing a mathematical model for cluster allocation to characterize the coupling relationship between clustering and allocation processes; initializing the cluster allocation; transforming the mathematical model into a coalition game-theoretic model for cluster allocation; designing an iterative optimization strategy based on the coalition game-theoretic model; and generating the optimized cluster allocation results through this strategy. This invention can quickly solve optimization problems where clustering and allocation are highly coupled, and is applicable to scenarios such as communication resource allocation, target allocation, and firepower allocation in large-scale clusters.

Description

Technical Field

[0001] This invention belongs to the field of cluster command and control technology, specifically relating to a cluster allocation optimization method and system based on alliance game theory. Background Art

[0002] Cluster task allocation technology has become a core support for fields such as industrial manufacturing and smart cities. For example, in the civilian sector, intelligent logistics robot clusters need to dynamically divide transportation subgroups based on different order volumes to optimize delivery efficiency.

[0003] To achieve rational resource allocation and collaborative task execution, clusters can assign different tasks to agents within the cluster through clustering. For example, in heterogeneous clusters, different amounts of resources can be allocated based on task complexity to improve the overall task execution efficiency of the cluster. In the face of sudden tasks or node failures, dynamic clustering can quickly reconstruct the cluster architecture to ensure task completion rates. Although the idea of ​​cluster allocation optimization is intuitive, the high coupling between the clustering and allocation processes involves a series of issues, such as analyzing the coupling mechanism of cluster clustering and allocation, and coordinating and optimizing the control of cluster clustering and allocation. Currently, the limitations of domestic research on cluster allocation optimization are mainly reflected in the following two aspects:

[0004] First, it is difficult to simultaneously obtain optimal results in dynamic clustering and task allocation. Traditional methods often employ static clustering or two-stage optimization (clustering first, then allocation), which severs the coupling relationship between clustering and allocation. For example, in a drone swarm, dynamic changes in target position can cause clustering structure failure, leading to a lag in task allocation strategies and reducing global resource utilization.

[0005] Secondly, it is difficult to guarantee the real-time performance of clustering and allocation. Existing algorithms rely on offline computation or fixed-period updates, making it difficult to cope with highly dynamic environments (such as a surge in logistics demand). The high computational complexity of complex optimization models leads to delays in clustering and allocation response, affecting task execution efficiency. Summary of the Invention

[0006] The purpose of this invention is to provide a clustering allocation optimization method and system based on alliance game theory, which solves the problems of uneven clustering and task allocation, low optimization quality and low computational efficiency in the current clustering allocation process.

[0007] The technical solution to achieve the purpose of this invention is as follows:

[0008] A clustering allocation optimization method based on coalition game theory includes the following steps:

[0009] Analyze the task requirements and resource constraints in cluster allocation scenarios, establish a mathematical model for cluster allocation, and characterize the coupling relationship between cluster allocation and the clustering process.

[0010] Perform cluster allocation initialization;

[0011] The cluster allocation mathematical model is transformed into a cluster allocation alliance game solution model.

[0012] Based on the cluster allocation alliance game solution model, an alliance iterative optimization strategy is designed, and the cluster allocation optimization result is generated through the alliance iterative optimization strategy.

[0013] Furthermore, the task requirements and resource constraints of cluster allocation scenarios are analyzed, and a mathematical model for cluster allocation is established, specifically including:

[0014] Suppose there exists This task, using Clustering is performed on groups of intelligent agents;

[0015] The utility function of each agent is established based on a weighted combination of the agent's energy consumption and task completion rate;

[0016] Based on the utility function, a reward function is designed for different agents to work together to complete a task after being clustered together, according to the cooperation achievement rate of each agent.

[0017] A mathematical model for cluster allocation is constructed based on the revenue function.

[0018] Furthermore, the utility function of each intelligent agent is:

[0019]

[0020] in, For intelligent agents For the task The benefits; For intelligent agents Execute the task Energy consumption status; For intelligent agents Execute the task Completion rate; These are the weighting coefficients.

[0021] Furthermore, the reward function for different intelligent agents to collaboratively complete a task after clustering together is:

[0022]

[0023] in, Representative cluster For the task The benefits; For clusters Any intelligent agent For the task The benefits; Cluster All agents are accessed through nonlinear functions Solution .

[0024] Furthermore, the nonlinear function for:

[0025]

[0026] in, To achieve the collaboration success rate.

[0027] Furthermore, the mathematical model for cluster allocation is as follows:

[0028]

[0029] In the formula, This represents the function used to calculate the total revenue of all clusters. The number of clusters; For decision variables related to cluster allocation, represents the cluster Should the task be executed? ,satisfy

[0030] ;

[0031] This means that an agent can only join one cluster. Both are positive integers, representing the cluster identifier. and They represent the first The cluster and the first A cluster; This means that all agents must participate in the clustering process and join a specific cluster; This means that each task can only be executed by one cluster; This means that each cluster can execute at most one task; This indicates that all tasks must be performed.

[0032] Furthermore, the cluster allocation initialization specifically includes: each agent in the initial cluster will allocate resources based on its maximum benefit for a particular task. To determine the task to be performed, if several agents choose the same task, they will form a cluster together. And calculate the cluster for the assigned task. Benefits .

[0033] Furthermore, the clustering allocation alliance game solution model is as follows:

[0034]

[0035] In the formula, , This means that the same agent cannot join different clusters. In the clustered allocation alliance game solution model, a cluster is the alliance partition. This means that any intelligent agent must join the cluster; This indicates that the number of stable alliance partitions formed is no less than the number of tasks. , indicating cluster Assign tasks The benefits.

[0036] Furthermore, the alliance iterative optimization strategy is as follows:

[0037] Each intelligent agent, according to its own task Maximum profit added to the initial alliance partition Afterwards, each intelligent agent By continuously performing three switching operations—leaving the alliance, remaining unchanged, and switching alliances—the alliance structure is updated, forming new alliance partitions. This gradually stabilizes the total alliance revenue in an increasing direction, ultimately resulting in a stable alliance partition, i.e., a stable total alliance revenue. The largest league division; Indicates the first Clusters.

[0038] A clustering allocation optimization system based on coalition game theory includes:

[0039] The clustering allocation mathematical model building unit analyzes the task requirements and resource constraints of the clustering allocation scenario, and is used to establish a clustering allocation mathematical model to characterize the coupling relationship between the clustering and allocation process.

[0040] The initialization unit is used to initialize cluster allocation.

[0041] The cluster allocation mathematical model transformation unit is used to transform the cluster allocation mathematical model into a cluster allocation alliance game solution model.

[0042] The iterative solution unit, based on the cluster allocation alliance game solution model, is used to design alliance iterative optimization strategies and generate cluster allocation optimization results through the alliance iterative optimization strategies.

[0043] Compared with the prior art, the present invention has the following advantages: 1) It analytically characterizes the coupling relationship between task allocation and agent clustering process, and solves the clustering and allocation problems at the same time, thereby improving computational efficiency; 2) It calculates the corresponding benefits of each cluster composed of different participants in advance, and can update the benefit situation in real time during the clustering allocation process without time-consuming calculation, thereby enhancing the real-time nature of the generation of clustering allocation results. Attached Figure Description

[0044] Figure 1 This is a schematic diagram illustrating the principle of the present invention.

[0045] Figure 2 This is a schematic diagram illustrating the application scenario of the present invention. Detailed Implementation

[0046] To better illustrate the purpose and function of the present invention, the present invention will be described in further detail below with reference to specific examples.

[0047] To address the problems of uneven clustering and task allocation, low optimization quality, and low computational efficiency in current cluster allocation processes, this invention discloses a cluster allocation optimization method that supports dynamic task scenarios. A schematic diagram of the principle is attached. Figure 1 As shown. This method controls the cooperative relationship of agents through alliance game theory, and simultaneously completes task allocation, achieving efficient resource utilization and balanced task distribution in dynamic scenarios. The specific steps are as follows:

[0048] First, we analyze the task requirements and resource constraints of cluster allocation scenarios and establish a mathematical model for cluster allocation.

[0049] Suppose there exists This task, using Clustering is performed on groups of intelligent agents, with specific scenario diagrams as follows: Figure 2 As shown. The utility function for each agent is established based on a weighted combination of the agent's energy consumption and task completion rate:

[0050]

[0051] in, For intelligent agents For the task The benefits; For intelligent agents Execute the task Energy consumption status; For intelligent agents Execute the task Completion rate; These are the weighting coefficients. Then, based on the collaboration achievement rate of each agent, a reward function is designed for different agents to collaboratively complete the task after clustering together:

[0052]

[0053] in, Representative cluster For the task The benefits; For clusters Any intelligent agent For the task The benefits; Cluster All agents are accessed through nonlinear functions Solution Its special case is However, it is not limited to this form; in this particular case... To improve the collaboration success rate, For agents in a cluster to perform tasks The total revenue. The constructed cluster allocation mathematical model is shown below:

[0054]

[0055] In the formula, The number of clusters; For decision variables related to cluster allocation, represents the cluster Should the task be executed? ,satisfy

[0056] ;

[0057] This means that an agent can only join one cluster; This means that all agents must participate in the clustering process and join a specific cluster; This means that each task can only be executed by one cluster; This means that each cluster can execute at most one task; This indicates that all tasks must be performed.

[0058] This step constructs a mathematical model for clustering and allocation in scenarios such as large-scale cluster communication resource allocation, target allocation, and firepower allocation. It analytically represents the coupling relationship between clustering and allocation processes, and can solve both clustering and allocation problems simultaneously.

[0059] Secondly, initial clustering is performed on the agents in the cluster. Initial clustering is a crucial step in the clustering optimization method; each agent in the initial cluster will be assigned a cluster based on its maximum benefit for a given task. To determine the task to be performed, if several agents choose the same task, they will form a cluster together. And calculate the assigned tasks for the cluster according to the profit function formula described in this invention. Benefits .

[0060] This step designs an initial clustering allocation strategy that can accelerate the solution of the clustering allocation optimization problem, transforming the clustering allocation model into a coalition game solution model, and providing a new approach for the reduction and solution of the strongly coupled clustering allocation problem.

[0061] Next, based on the principles of coalition game theory, the constructed clustering allocation mathematical model will be transformed into a coalition game model. Coalition game theory, a type of cooperative game, refers to the process by which game participants form stable alliances with other participants through alliances or cooperation. Here, "game" refers to a situation where several rational participants produce good or bad outcomes through complex interactions; "alliance" refers to a situation where all rational participants have the intention to cooperate and hope to achieve better results by forming a cooperative organization. Therefore, the main problem that coalition game theory aims to solve is how to form appropriate cooperative organizations to achieve the desired outcome. Coalition game theory contains two elements: one is the set of participants who need to form an alliance. First, alliances are formed based on the rules and constraints of a specific model. Second, the alliance payoffs are assessed, and their magnitude can be evaluated. Therefore, the mathematical model of a coalition game can be defined as follows: .

[0062] As can be seen from the above definition, the problems that need to be solved in coalition games and cluster allocation problems are the same. Considering individual agents as participants in a coalition game, and the resulting clusters as coalitions formed by these agents, the solution to the clustering allocation problem can be transformed into a problem of determining the coalition structure. Thus, the clustering allocation process is equivalent to the splitting or disintegration of coalitions, ultimately forming multiple disjoint coalitions through successive iterations. Therefore, coalition game theory is feasible for solving the clustering allocation problem in multi-agent systems.

[0063] Multiple disjoint alliances formed by intelligent agents are called alliance partitions, or clusters. Let... The set of participants in a coalition game consisting of [number] agents is [number]. Then the alliance partition is defined as a set. ,in Alliances in set П satisfy and .

[0064] As can be seen from the mathematical model of coalition games, coalition games include two elements: the set of participants that form the coalition. Alliance benefits and assessment of alliance value Coalition game model can be used This indicates the number of tasks. Determine the initial alliance task allocation. Each alliance partition Assigned to specific tasks The benefits to it are The game objective is to form stable alliance partitions and maximize the total benefit of all alliances. The transformed coalition game model, maximizing the potential of the outcome, is shown below:

[0065]

[0066] In the formula, , This means that the same agent cannot join different alliance partitions; This means that any intelligent agent must join the alliance partition; This indicates that the number of stable alliance partitions formed is no less than the number of tasks.

[0067] Finally, an iterative optimization strategy for alliance partitioning is designed, gradually iterating until a stable alliance partitioning is formed and the total benefit of all alliances is maximized. Maximizing this allows for the rapid generation of optimized cluster partitioning results. Based on the corresponding coalition game mathematical model and the initial coalition partitioning task allocation, the agent members in the initial coalition may not be the optimal composition. Therefore, a partitioning strategy is needed to continuously switch coalitions to obtain stable coalition partitions. The specific partitioning strategy definition is given below. Each agent, based on its own task... Maximum profit added to the initial alliance partition Afterwards, each intelligent agent The alliance structure is updated by continuously leaving the alliance, remaining unchanged, and switching alliances, forming new alliance partitions. The three behaviors of updating alliance partitions are called switching operations. The iterative strategy for the multi-agent clustering problem is to make the total alliance revenue gradually stabilize in the direction of increasing by continuously performing switching operations, and finally obtain a stable alliance partition.

[0068] The various agents in this alliance game model The three switching operations can be defined as expressions ,in Indicates a league partition Inner intelligent agents Leave the current alliance; Indicates a league partition Inner intelligent agents Remain in the current alliance; Indicates a league partition Inner intelligent agents Leave your current league and join another league .

[0069] In summary, to achieve the goal of splitting the system, the first step is to establish initial alliance partitions based on the number of tasks. Each agent joins the corresponding initial alliance based on its maximum benefit for each task. Subsequently, the agents will continuously switch between alliances, and the benefit of all alliance partitions will be calculated after each switch. If the total alliance revenue is greater than the previous total, then the alliance partition is updated. This continues in the following manner. The direction of increasing continuously is selected several times until... Stop the iteration when the changes cease. Simultaneously, to ensure rapid convergence of the results, [the following steps are taken]. The calculation is simplified to a predefined table query, which significantly speeds up the calculation compared to traditional dynamic programming or heuristic algorithms, thus improving computational efficiency.

[0070] The algorithm flow of the cluster allocation optimization method is as follows: First, establish an initial alliance partition based on the number of tasks and allocate tasks according to the maximum benefit of each agent. Agents with the same task are added to the corresponding alliance, and the total alliance benefit is calculated at this time. Then, starting with agent 1, the iteration proceeds sequentially from agent 1 to agent 2. Perform three switching operations:

[0071] Leaving the league: ;

[0072] Remain unchanged: ;

[0073] Switch alliances: ;

[0074] The total alliance revenue updated by the three operations is denoted as follows: , , Take the maximum of the three. Total revenue compared to the last alliance The comparison is performed; if the change increases, the alliance partition and total alliance revenue are updated accordingly; otherwise, the original alliance partition remains unchanged. After the update is completed, the next agent is evaluated until the next agent is evaluated. The judgment of each agent is considered as completing one round of alliance game. If multiple rounds of alliance game are conducted and the total payoff does not change, it means that the alliance partition composition has reached a relatively stable state, and the algorithm is complete.

[0075] A stable coalition partition refers to a partition in a coalition game where each participant has joined the optimal coalition that achieves the objective of the problem under study. In this case, if any participant in the resulting coalition switches coalitions, their payoff will not increase. Analysis shows that through continuous iteration, each agent, as a coalition participant, joins coalitions that maximize the overall coalition payoff. The largest alliance As the composition of members within each alliance gradually stabilizes, the resulting alliance partitions are stable. If an alliance partition were not stable at this point, it would mean that a switching operation was occurring, causing members within that partition to continue triggering switching operations. These two factors contradict each other; therefore, the final alliance partitions formed must be stable.

[0076] Based on the aforementioned method, the present invention also provides a clustering allocation optimization system based on coalition game theory, comprising:

[0077] The clustering allocation mathematical model building unit analyzes the task requirements and resource constraints of the clustering allocation scenario, and is used to establish a clustering allocation mathematical model to characterize the coupling relationship between the clustering and allocation process.

[0078] The initialization unit is used to initialize cluster allocation.

[0079] The cluster allocation mathematical model transformation unit is used to transform the cluster allocation mathematical model into a cluster allocation alliance game solution model.

[0080] The iterative solution unit, based on the cluster allocation alliance game solution model, is used to design alliance iterative optimization strategies and generate cluster allocation optimization results through the alliance iterative optimization strategies.

[0081] Example

[0082] Suppose that in a certain scenario, there are 8 drones that need to perform 4 tasks. According to the model description, clusters A, B, C, and D can be assigned to the four tasks. The solution strategy for multi-agent cluster allocation based on coalition game theory can be divided into two stages: In the first stage, tasks A, B, C, and D are initially allocated according to the maximum payoff of each drone. Drones that receive the same task are added to the cluster corresponding to the same task, and each cluster corresponds to a coalition.

[0083] To achieve rapid clustering and allocation, the potential alliances formed by each UAV are given according to the profit function formula, as shown in Table 1.

[0084] Table 1. Benefits of Alliances Composed of Different Members in This Invention

[0085]

[0086] During the switching of alliances, the process of repeatedly calculating alliance revenue is simplified to table lookup, eliminating the need for repeated calls to the revenue function and improving program execution efficiency. Furthermore, to quickly determine alliance members and obtain their corresponding revenues within the program, the row numbers of the revenues corresponding to alliances composed of different drones in Table 1 are determined according to the formula... Arrange the data, where n is the drone number. The columns represent the different rewards for each task. For example, the rewards for each task for the alliance of agents 2, 3, and 5 are shown in the corresponding row number of Table 1. .

[0087] Step 1: Analyze the case studies and establish a mathematical model for cluster allocation of UAVs.

[0088]

[0089] In the formula: For decision variables related to task assignment, let represent clusters. Should the task be executed? , ; This means that a drone can only join one cluster; This means that all drones must participate in the clustering process to join a cluster; This means that each task can only be executed by one cluster; This means that each cluster can execute at most one task; This indicates that all tasks must be performed.

[0090] Step 2: Perform initial cluster allocation. The drones are initially allocated according to their maximum potential reward, as shown in Table 2. Analysis of Table 2 shows that the alliance executing task A is... The alliance that performs task B is The alliance that performs task C is The alliance that executes task D is Corresponding benefits The values ​​are 6, 8, 9, and 8 respectively, at which point the alliance's total revenue is 31.

[0091] Table 2 Initial task allocation table for the present invention example

[0092]

[0093] Step 3: Transform the mathematical model of drone clustering and allocation into a cooperative game solution model.

[0094]

[0095] In the formula, , This means that the same drone cannot join different alliance partitions; This means that any drone must join the alliance's partition; This indicates that the number of stable alliance partitions formed is no less than the number of tasks.

[0096] Step 4: Run the alliance iterative optimization strategy to generate the cluster allocation optimization results. This involves continuously performing switching operations on a drone-by-drone basis. Each drone must select the switching operation that maximizes the total benefit of all alliances and update the alliance partitions accordingly.

[0097] (1) The switching operation for UAV 1 is shown in Table 3. Analysis indicates that the following should be adopted: Update the data for each alliance division and total revenue.

[0098] Table 3. Diagram of UAV 1 Switching Operation

[0099]

[0100] (2) The switching operation for UAV 2 is shown in Table 4. Analysis indicates that the following should be adopted: Update the data for each alliance division and total revenue.

[0101] Table 4. Diagram of UAV 2 Switching Operation

[0102]

[0103] (3) The switching operation for UAV 3 is shown in Table 5. Analysis indicates that the following should be adopted: Update the data for each alliance division and total revenue.

[0104] Table 5. Schematic diagram of UAV 3 switching operation

[0105]

[0106] (4) The switching operation for UAV 4 is shown in Table 6. Analysis shows that the following should be adopted. Update the data for each alliance division and total revenue.

[0107] Table 6. Diagram of UAV 4-way switching operation

[0108]

[0109] (5) The switching operation for UAV 5 is shown in Table 7. Analysis indicates that the following should be adopted: Update the data for each alliance division and total revenue.

[0110] Table 7. Instructions for UAV 5 Switching Operations

[0111]

[0112] (6) The switching operations for UAV 6 are shown in Table 8. Analysis indicates that the following should be adopted: Update the data for each alliance division and total revenue.

[0113] Table 8. Diagram of UAV 6-way switching operation

[0114]

[0115] (7) The switching operation for UAV 7 is shown in Table 9. Analysis indicates that the following should be adopted: Update the data for each alliance division and total revenue.

[0116] Table 9. Schematic diagram of UAV 7 switching operation

[0117]

[0118] (8) The switching operations for UAV 8 are shown in Table 10. Analysis indicates that the following should be adopted: Update the data for each alliance division and total revenue.

[0119] Table 10. Instructions for UAV 8-way Switching Operation

[0120]

[0121] The alliance partitions and corresponding revenues after the first iteration are shown in Table 11.

[0122] Table 11 shows the optimization results of the first iteration of the present invention's example.

[0123]

[0124] To determine the total revenue of the alliance Whether it remains unchanged multiple times is determined by multiple iterations. The optimization results after the second iteration are shown in Table 12, and the optimization results after the third iteration are shown in Table 13. The analysis shows that after the first iteration, the alliance partition and the total alliance profit are optimal and remain unchanged in subsequent iterations. This indicates that the alliance game has achieved a relatively optimal solution and formed a stable alliance partition.

[0125] Table 12 shows the optimization results of the second iteration of the present invention's example.

[0126]

[0127] Table 13 shows the optimization results of the third iteration of the present invention's example.

[0128]

[0129] Step 5: Obtain stable alliance partitions. The calculated allocation that maximizes the total alliance revenue and avoids conflicts is shown in Table 14. This completes the optimization of drone cluster allocation in the example using alliance game theory.

[0130] Table 14 Final Optimization Results of the Invention Example

[0131]

[0132] The optimization results show that the present invention can quickly solve the optimization problem of highly coupled clustering and allocation, and is applicable to scenarios such as communication resource allocation, target allocation, and firepower allocation in large-scale clusters.

[0133] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

[0134] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or make equivalent substitutions for some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A clustering allocation optimization method based on coalition game theory, characterized in that, Including the following steps: Analyze the task requirements and resource constraints in cluster allocation scenarios, establish a mathematical model for cluster allocation, and characterize the coupling relationship between cluster allocation and the clustering process. Perform cluster allocation initialization; The cluster allocation mathematical model is transformed into a cluster allocation alliance game solution model. Based on the cluster allocation alliance game solution model, an alliance iterative optimization strategy is designed, and the cluster allocation optimization result is generated through the alliance iterative optimization strategy. Analyze the task requirements and resource constraints in cluster allocation scenarios, and establish a mathematical model for cluster allocation, specifically including: Suppose there exists This task, using Clustering is performed on groups of intelligent agents; The utility function of each agent is established based on a weighted combination of the agent's energy consumption and task completion rate; Based on the utility function, a reward function is designed for different agents to work together to complete a task after being clustered together, according to the cooperation achievement rate of each agent. A mathematical model for cluster allocation is constructed based on the revenue function.

2. The clustering allocation optimization method based on coalition game theory according to claim 1, characterized in that, The utility function of each agent is: ； in, For intelligent agents For the task The benefits; For intelligent agents Execute the task Energy consumption status; For intelligent agents Execute the task Completion rate; These are the weighting coefficients.

3. The clustering allocation optimization method based on coalition game theory according to claim 2, characterized in that, The reward function for different intelligent agents to collaborate in completing a task is: ； in, Representative cluster For the task The benefits; For clusters Any intelligent agent For the task The benefits; Cluster All agents are accessed through nonlinear functions Solve .

4. The clustering allocation optimization method based on coalition game theory according to claim 3, characterized in that, The nonlinear function for: ； in, To achieve the collaboration success rate.

5. The clustering allocation optimization method based on coalition game theory according to claim 3, characterized in that, The mathematical model for cluster allocation is as follows: ； In the formula, This represents the function used to calculate the total revenue of all clusters. The number of clusters; For decision variables related to cluster allocation, represents the cluster Should the task be executed? ,satisfy: ； This means that an agent can only join one cluster. Both are positive integers, representing the cluster identifier. and They represent the first The cluster and the first A cluster; This means that all agents must participate in the clustering process and join a specific cluster; This means that each task can only be executed by one cluster; This means that each cluster can execute at most one task; This indicates that all tasks must be performed.

6. The clustering allocation optimization method based on coalition game theory according to claim 5, characterized in that, Cluster allocation initialization specifically includes: each agent in the initial cluster will allocate resources based on its maximum benefit for a particular task. To determine the task to be performed, if several agents choose the same task, they will form a cluster together. And calculate the cluster for the assigned task. Profit .

7. The clustering allocation optimization method based on coalition game theory according to claim 5, characterized in that, The clustering allocation alliance game solution model is as follows: ； In the formula, , This means that the same agent cannot join different clusters. In the clustered allocation alliance game solution model, a cluster is the alliance partition. This means that any intelligent agent must join the cluster; This indicates that the number of stable alliance partitions formed is no less than the number of tasks. , indicating cluster Assign tasks The benefits.

8. The clustering allocation optimization method based on coalition game theory according to claim 1, characterized in that, The alliance iterative optimization strategy is as follows: Each intelligent agent, according to its own task Maximum profit added to the initial alliance partition Afterwards, each intelligent agent By continuously performing three switching operations—leaving the alliance, remaining unchanged, and switching alliances—the alliance structure is updated, forming new alliance partitions. This gradually stabilizes the total alliance revenue in an increasing direction, ultimately resulting in a stable alliance partition, i.e., a stable total alliance revenue. The largest league division; Indicates the first Clusters.

9. A clustering allocation optimization system based on coalition game theory, implementing the method of any one of claims 1-8, characterized in that, include: The clustering allocation mathematical model building unit analyzes the task requirements and resource constraints of the clustering allocation scenario, and is used to establish a clustering allocation mathematical model to characterize the coupling relationship between the clustering and allocation process. The initialization unit is used to initialize cluster allocation. The cluster allocation mathematical model transformation unit is used to transform the cluster allocation mathematical model into a cluster allocation alliance game solution model. The iterative solution unit, based on the cluster allocation alliance game solution model, is used to design alliance iterative optimization strategies and generate cluster allocation optimization results through the alliance iterative optimization strategies.

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