A quantization communication optimization method for a multi-agent system in a communication-restricted situation, a storage medium and equipment

Abstract

The application discloses a kind of quantization communication optimization methods for multi-agent system under communication restricted situation, storage medium and equipment, comprising: according to the communication relationship between each agent in multi-agent system, communication topology graph is constructed, the communication decision variable of each communication node agent is differentially encoded, is sent to the agent on adjacent communication node, the communication decision variable estimation value of adjacent communication node agent is updated, and the communication decision variable cumulative value is updated in combination with the current communication decision variable of communication node agent communication decision variable estimation value update communication decision variable cumulative value;Introduce auxiliary variable that changes with time, in combination with the communication decision variable of corresponding communication node agent communication decision variable cumulative value updates the communication decision variable of communication node agent;Communication decision optimization model is constructed, to minimize communication decision optimization model as goal, determines the optimal communication decision variable of agent, can reduce network bandwidth, improve the operation efficiency of multi-agent system.

Description

Technical Field

[0001] This invention relates to the fields of multi-agent cooperative control and machine learning, and in particular to a quantitative communication optimization method, storage medium, and device for multi-agent systems under communication-constrained conditions. Background Technology

[0002] In recent years, multi-agent systems have been widely applied in fields such as smart grids, autonomous driving, and the Internet of Things. In these systems, agents typically achieve global goals and accomplish complex tasks by sharing local information and cooperating with each other. Distributed optimization algorithms play a crucial role in this process, enabling coordinated decision-making among agents and ensuring the system achieves global optimality without centralized control. For example, Nedic, Angelia, and Asuman Ozdaglar's paper "Distributed subgradient methods for multi-agent optimization" published in IEEE Transactions on Automatic Control successfully coordinated multiple agents. However, with the increase in the number of agents, the volume of communication and information exchange between them grows rapidly. How to effectively manage this information transmission, especially in bandwidth-constrained network environments, remains an important and urgent problem to be solved.

[0003] In the real world, many practical applications often face complex problems such as bandwidth constraints, asymmetric communication links, and dynamic changes in network topology. In such environments, traditional quantization communication and coding techniques often perform poorly. Although existing quantization methods, such as uniform and non-uniform quantization, can compress data volume to some extent, thereby reducing communication bandwidth usage, they often struggle to cope with complex topology changes and heterogeneous communication links in unbalanced directed graph communication topologies, leading to inefficient information transmission and potentially even information loss or transmission delays. Therefore, designing a more efficient quantization communication mechanism that can achieve efficient data exchange under limited bandwidth has become a major challenge in current technology.

[0004] Furthermore, existing distributed optimization methods typically rely on balancing communication networks and simple constraints, failing to adequately consider the variable network topologies and bandwidth limitations of the real world. In addition, many optimization problems involve set constraints, such as resource allocation and task scheduling, which further complicate the optimization process. Current optimization methods often fail to effectively balance bandwidth-constrained and dynamically changing network environments when dealing with these set constraints, resulting in a failure to guarantee global optimality and satisfy practical constraints in real-world applications. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a quantitative communication optimization method, storage medium, and device for multi-agent systems under communication constraints. This method can significantly reduce network bandwidth requirements while ensuring the computational efficiency of agents, thereby improving the overall operating efficiency of multi-agent systems.

[0006] To achieve the above objectives, this application provides the following technical solution:

[0007] A quantitative communication optimization method for multi-agent systems under communication constraints includes the following steps: Step S1: Establish a communication topology graph based on the communication relationships between agents in the multi-agent system, and construct a distributed optimization model for communication decision-making based on the communication topology graph. In the communication topology graph, each communication node corresponds to an agent. Step S2: Differentially encode the communication decision variables of the agents on each communication node in the communication topology diagram and send them to the agents on the adjacent communication nodes; Step S3: Agents on neighboring communication nodes accumulate and decode the received differentially encoded information, and update the estimated values ​​of the communication decision variables of agents on neighboring communication nodes; Step S4: Update the accumulated value of the communication decision variable using the current communication decision variable of the agent on the communication node and the updated estimated values ​​of the communication decision variable of the agents on neighboring communication nodes; Step S5: Introduce time-varying auxiliary variables on the communication node, and reconstruct the communication decision variables of the agent on the communication node by combining the accumulated values ​​of the communication decision variables of the agent on the corresponding communication node; Step S6: Input the communication decision variables reconstructed by the agent on the communication node into the distributed optimization model of communication decision, and determine the optimal communication decision variables of the agent with the goal of minimizing the distributed optimization model of communication decision.

[0008] Furthermore, the construction process of the distributed optimization model for communication decision-making is as follows:

[0009]

[0010]

[0011] in, This represents a distributed optimization model for communication decision-making. This indicates the number of communication nodes in the communication topology diagram. , All indicate index, Represents communication node Communication decision variables in the reconstruction of the agent Represents communication node The communication decision objective function, Represents communication node The set of constraints satisfied by the communication decision variables reconstructed by the agent; the distributed optimization model for communication decision needs to satisfy that the communication decision variables reconstructed by the agent on any communication node tend to be the same.

[0012] Furthermore, the specific process of differentially encoding the communication decision variables of agents on each communication node in the communication topology diagram is as follows: agents on each communication node in the communication topology diagram estimate communication decision variables based on historical communication information, calculate the difference information between the current communication decision variables of agents on the communication node and the communication decision variables estimated by the corresponding agents, and quantize and encode the difference information.

[0013] Furthermore, it also includes: compressing the differential information using quantizer scaling technology, and then quantizing and encoding the compressed differential information.

[0014] in, Represents communication node The intelligent agent at any time Differential coding information, Represents communication node The intelligent agent at any time The difference information, Represents the L2 norm, Represents a symbolic function. , This indicates the number of quantization levels. Represents communication node The intelligent agent at any time The random component of the quantization error.

[0015] Furthermore, the update process of the cumulative value of the communication decision variable of the agent on the communication node is as follows:

[0016] in, Represents communication node The intelligent agent at any time The cumulative value of the communication decision variables, Represents communication node The intelligent agent at any time The current communication decision variables, Represents communication node The intelligent agent at any time The estimated values ​​of communication decision variables, Represents communication node The number of adjacent communication nodes, express index, Indicates adjacent communication nodes The intelligent agent at any time Updated estimates of communication decision variables, Represents communication node With neighboring communication nodes The weighting coefficients between them.

[0017] Furthermore, the auxiliary variables that change over time are specifically:

[0018] in, Represents communication node The intelligent agent at any time Auxiliary variables, Represents communication node The number of adjacent communication nodes, express index, Represents communication node Adjacent communication nodes The intelligent agent at any time Auxiliary variables, A constant greater than 0; Represents communication node With neighboring communication nodes The weighting coefficients between them.

[0019] Furthermore, the reconstruction process of the communication decision variables of the agent on the communication node is as follows:

[0020] in, Represents communication node The intelligent agent at any time Reconstructed communication decision variables Represents communication node The intelligent agent at any time The cumulative value of the communication decision variables, Represents communication node The intelligent agent at any time Auxiliary variables, Represents communication node The set of constraints satisfied by the communication decision variables of the upper agent. Indicates in Projection on Indicates time The step size of the change, Indicates a constant step size. Represents communication node Gradient information on the surface.

[0021] Furthermore, the present invention also provides a computer-readable storage medium storing a computer program that causes a computer to execute the described quantitative communication optimization method for multi-agent systems under communication-constrained conditions.

[0022] Furthermore, the present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the aforementioned quantitative communication optimization method for multi-agent systems under communication-constrained conditions.

[0023] Compared with the prior art, the present invention has the following beneficial effects: (1) In the quantitative communication optimization method for multi-agent systems under communication constraints, the agents on the communication nodes do not directly transmit complete communication decision variables to the agents on the adjacent communication nodes. Instead, they generate differential coding information based on the difference between the current real communication decision variables and the communication decision variables estimated by the agents. Since the agents on the adjacent communication nodes only need to receive and accumulate the differential components to gradually reconstruct the communication decision variables of the agents on the communication nodes, the repeated transmission of complete communication decision variables or high-precision continuous variables in the traditional method is avoided, which effectively reduces the amount of redundant communication data. Even in scenarios where bandwidth or communication frequency is limited, it can significantly improve the communication efficiency of agents in multi-agent systems. It is especially suitable for application environments with limited communication resources such as wireless networks or edge computing. (2) The quantitative communication optimization method for multi-agent systems under communication constraints of this invention introduces time-varying auxiliary variables in the process of reconstructing the communication decision variables of agents at communication nodes. This allows for dynamic correction of information bias caused by inconsistencies between the in-degree and out-degree of communication in the communication topology graph, effectively overcoming the impact of communication asymmetry. The update mechanism of this auxiliary variable enables the multi-agent system to achieve effective propagation and fusion of communication decision variable information even when relying solely on row-random or non-double-random communication weights, thereby avoiding the dependence of existing methods on balanced communication graphs or global weight information. Therefore, this invention maintains good stability in dynamically changing, asymmetric communication network environments, significantly improving adaptability and robustness under actual complex network conditions. Attached Figure Description

[0024] Figure 1 This is a flowchart of the quantitative communication optimization method for multi-agent systems under communication constraints according to the present invention; Figure 2Here is a communication topology diagram for a multi-agent system, where, Figure 2 In a for Communication topology diagram at that time, Figure 2 In b for Communication topology diagram at that time, Figure 2 In c for Communication topology diagram at that time, Figure 2 In d This is a diagram of the overall communication topology of a multi-agent system. Figure 3 A graph showing the reconstructed communication decision variables for the agent; Figure 4 This is a convergence curve of the quantitative communication optimization method for multi-agent systems under communication constraints according to the present invention. Figure 5 This is a schematic diagram comparing the communication accuracy of the quantized communication optimization method and the non-quantized communication method of the present invention under different iteration numbers; Figure 6 This diagram illustrates a comparison of communication accuracy between the quantized and non-quantized communication methods of the present invention under different communication overheads. Detailed Implementation

[0025] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings.

[0026] like Figure 1 This is a flowchart of a quantitative communication optimization method for multi-agent systems under communication constraints, according to the present invention. The quantitative communication method includes the following steps: Step S1: Establish a communication topology graph consisting of communication nodes and edges based on the communication relationships between agents in the multi-agent system. In the communication topology diagram, each communication node corresponds to an agent. Represents a set of communication nodes. Represents the set of edges.

[0027] Constructing a distributed optimization model for communication decision-making based on the communication topology graph:

[0028]

[0029]

[0030] in, This represents a distributed optimization model for communication decision-making. This indicates the number of communication nodes in the communication topology diagram. , All indicate index, Represents communication node Communication decision variables in the reconstruction of the agent Represents communication node The communication decision objective function, Represents communication node The set of constraints satisfied by the communication decision variables reconstructed by the agent; the distributed optimization model for communication decision needs to satisfy that the communication decision variables reconstructed by the agent on any communication node tend to be the same.

[0031] Step S2: To reduce communication overhead, in the communication topology diagram of this invention, agents on each communication node do not directly transmit complete communication decision variables to agents on adjacent communication nodes. Instead, they differentially encode the communication decision variables and send them to agents on adjacent communication nodes, thereby significantly reducing the communication load. Specifically: In the communication topology diagram, agents at each communication node estimate communication decision variables based on historical communication information. They then calculate the difference between the current communication decision variable of each agent and its estimated value, and quantize and encode this difference. Since agents at adjacent communication nodes only need to receive and accumulate the difference components to gradually reconstruct the communication decision variables, this avoids the repeated transmission of complete communication decision variables or high-precision continuous variables as in traditional methods. This effectively reduces redundant communication data and significantly improves communication efficiency in multi-agent systems, even in scenarios with limited bandwidth or communication frequency.

[0032] The quantization encoding process in this invention is as follows:

[0033] in, Indicates the message node The intelligent agent at any time Differential coding information, Represents communication node The intelligent agent at any time Real communication decision variables, Represents communication node The intelligent agent at any time Communication decision variables estimated based on historical communication information This represents the quantization encoding operator.

[0034] In one technical solution of the present invention, the method further includes: compressing the differential information using quantizer scaling technology, and then quantizing and encoding the compressed differential information. In this invention, a random unbiased quantizer is used to compress the differential information under limited communication bit conditions, further reducing the communication volume between agents, while controlling the impact of quantization error on encoding performance. This enables agents to perform efficient data exchange under limited bandwidth, reducing network load and significantly improving the communication efficiency of multi-agent systems. Specifically, the quantization and encoding process is as follows:

[0035] in, Represents communication node The intelligent agent at any time Differential coding information, Represents communication node The intelligent agent at any time The difference information, Represents the L2 norm, Represents a symbolic function. , This indicates the number of quantization levels. Represents communication node The intelligent agent at any time The random component of the quantization error.

[0036] Step S3: Agents on adjacent communication nodes accumulate and decode the received differentially encoded information, and send it out according to the method in step S2 to update the estimated values ​​of communication decision variables of agents on adjacent communication nodes, thereby realizing the effective reconstruction of communication decision variable information between communication nodes.

[0037] In this invention, the update process of the estimated values ​​of the communication decision variables of agents on adjacent communication nodes is as follows:

[0038] in, Indicates adjacent communication nodes The intelligent agent at any time Updated estimates of communication decision variables, Indicates adjacent communication nodes The intelligent agent at any time Communication decision variables estimated based on historical communication information Indicates adjacent communication nodes The intelligent agent at any time The differentially encoded information sent.

[0039] Step S4: Update the cumulative value of the communication decision variables using the current communication decision variables of the agents on the communication nodes and the estimated values ​​of the updated communication decision variables of the agents on the neighboring communication nodes. By using the cumulative estimation and update method, the communication decision variables of the agents on the communication nodes are gradually optimized. This method can effectively solve the information asymmetry problem in multi-agent systems and improve the communication efficiency of multi-agent systems.

[0040] The update process of the cumulative value of the communication decision variable of the intelligent agent on the communication node of this invention is as follows:

[0041] in, Represents communication node The intelligent agent at any time The cumulative value of the communication decision variables, Represents communication node The intelligent agent at any time The current communication decision variables, Represents communication node The intelligent agent at any time The estimated values ​​of communication decision variables, Represents communication node The number of adjacent communication nodes, express index, Indicates adjacent communication nodes The intelligent agent at any time Updated estimates of communication decision variables, Represents communication node With neighboring communication nodes The weighting coefficients between them.

[0042] Step S5: Introduce time-varying auxiliary variables on the communication nodes, and reconstruct the communication decision variables of the agents on the corresponding communication nodes by combining the accumulated values ​​of the communication decision variables of the agents on the corresponding communication nodes. The update mechanism of this auxiliary variable enables the multi-agent system to achieve effective propagation and fusion of communication decision variable information even when relying only on row-random or non-double-random communication weights, thereby avoiding the dependence of existing methods on balanced communication graphs or global weight information. Therefore, this invention can maintain good stability in dynamically changing, asymmetric communication network environments, and significantly improves adaptability and robustness under actual complex network conditions. Specifically: Step S5.1: Construct time-varying auxiliary variables on the communication nodes to overcome the asymmetry of intelligent agent communication in the unbalanced communication topology graph, thereby ensuring the effective dissemination and updating of information.

[0043] The auxiliary variables that change over time in this invention are specifically as follows:

[0044] in, Represents communication node The intelligent agent at any time Auxiliary variables, Represents communication node The number of adjacent communication nodes, express index, Represents communication node Adjacent communication nodes The intelligent agent at any time Auxiliary variables, It is a constant greater than 0 to ensure the effective execution of subsequent iterations; Represents communication node With neighboring communication nodes The weighting coefficients between them.

[0045] Step S5.2: Let Proxy communication node The auxiliary state variables of the agent are effectively combined from two different sources through ratio calculation, ensuring the reasonable updating of the agent's communication decision variables. At the same time, in order to meet the constraints in the distributed optimization model of communication decision, a projection operation is adopted to ensure that the parameters of all communication nodes are always within the preset constraint set. Furthermore, a gradient update mechanism is designed to improve the computation speed and the optimization accuracy of the communication decision variables.

[0046] The reconstruction process of the communication decision variables of the agent on the communication node in this invention is as follows:

[0047] in, Represents communication node The intelligent agent at any time Reconstructed communication decision variables Indicates in Projection on Indicates time The step size of the change is used to adjust the impact of the constraint correction term on the variable update; Indicates a constant step size. Represents communication node Gradient information on the surface.

[0048] This invention, through the synergistic effect of auxiliary variables and projection operations, can not only handle simple unconstrained or single-constraint optimization problems, but also effectively address set-constraint situations commonly encountered in practical applications such as resource allocation and task scheduling. While ensuring the global convergence of multi-agent systems, this method improves the solution accuracy and stability in complex engineering application scenarios, enabling distributed optimization methods to better serve real-world engineering systems.

[0049] Step S6: Input the communication decision variables reconstructed by the agent on the communication node into the distributed optimization model of communication decision. With the goal of minimizing the distributed optimization model of communication decision, repeat steps S2-S6 to determine the optimal communication decision variables for the agent.

[0050] In the simulation environment, each agent has perception and communication capabilities. The simulation is conducted through a multi-agent system composed of agents to verify the effectiveness of the quantitative communication optimization method for multi-agent systems under communication-constrained conditions.

[0051] Set up communication nodes Communication decision objective function ,in, Indicates only communication nodes The constants known to the agent. Representing communication decision variables Dimensions express index, Representing communication decision variables The first dimension component, Representing communication decision variables The Dimensional components.

[0052] Based on the modulo function Selecting a multi-agent system at time The communication topology diagram, such as Figure 2 ,like Then select Figure 2 In a As a communication topology diagram, if Then select Figure 2 In b As a communication topology diagram, if Then select Figure 2 In c This serves as a communication topology diagram. Based on the above communication modes, The iteration interval contains all the communication network sequences. This ensures that all communication decision information of the agents can be transmitted throughout the entire communication topology network, such as... Figure 2 Ind As shown.

[0053] Under the given conditions, the quantitative communication optimization method for multi-agent systems under communication constraints of the present invention is simulated and verified. The communication decision variable curves reconstructed for each agent are shown in the figure below. Figure 3 As shown, with the increase of the number of iterations, the three dimensions of the communication decision variable reconstructed by each agent will eventually converge to the vicinity of the optimal communication decision variable, achieving consistent optimality. Figure 4 The quantitative communication optimization method of this invention can determine the optimal communication decision variables of an agent in just 600 iterations, and has the characteristic of fast convergence speed.

[0054] Furthermore, this invention uses a publicly available regression-based medical dataset to test a quantitative communication optimization method for multi-agent systems under communication-constrained conditions. This dataset contains multiple feature variables, with each sample having a 10-dimensional input feature. The dataset contains a total of 700 data samples, of which 600 are used for the distributed optimization process, and the remaining samples are used for performance evaluation. This invention constructs a distributed network structure with 5 communication nodes, each holding 120 data samples, and performs optimization and update operations under its own local constraints.

[0055] Specifically, the input data subsets and constraints of each communication node are different. The original dataset is divided evenly among the communication nodes, and the constraints of each communication node are described in the form of box constraints. For example... Figure 5 The diagram illustrates the communication accuracy of the 8-bit quantized communication method and the unquantized communication method of this invention at different iteration numbers. The communication accuracy of both increases with the number of iterations, and their accuracy curves match perfectly, indicating that the quantized communication method of this invention does not affect the convergence speed. Figure 6 The diagram illustrates the communication accuracy of the 8-bit quantized communication method and the non-quantized communication method of this invention under different communication overheads. The results show that although the quantized communication method of this invention introduces quantization error during the transmission of communication decision variables, it can still maintain fast convergence performance while significantly reducing communication overhead. This verifies the effectiveness and practicality of the method of this invention under constrained communication conditions. The communication accuracy is represented by the optimality error, which is specifically the difference between the reconstructed communication decision variable and the optimal communication decision variable.

[0056] In one embodiment of the present invention, a computer-readable storage medium is also provided, storing a computer program that enables a computer to execute the quantitative communication optimization method for multi-agent systems under communication-constrained conditions.

[0057] In one technical solution of the present invention, an electronic device is also provided, including: a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the quantitative communication optimization method of the present invention for multi-agent systems under communication-constrained conditions.

[0058] In the embodiments disclosed in this application, a computer storage medium may be a tangible medium that may contain or store programs for use by or in conjunction with an instruction execution system, apparatus, or device. The computer storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of computer storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, and portable compact disc read-only memory (CD). ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0059] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0060] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A quantitative communication optimization method for multi-agent systems under communication constraints, characterized in that, Includes the following steps: Step S1: Establish a communication topology graph based on the communication relationships between agents in the multi-agent system, and construct a distributed optimization model for communication decision-making based on the communication topology graph. In the communication topology graph, each communication node corresponds to an agent. Step S2: Differentially encode the communication decision variables of the agents on each communication node in the communication topology diagram and send them to the agents on the adjacent communication nodes; Step S3: Agents on neighboring communication nodes accumulate and decode the received differentially encoded information, and update the estimated values ​​of the communication decision variables of agents on neighboring communication nodes; Step S4: Update the accumulated value of the communication decision variable using the current communication decision variable of the agent on the communication node and the updated estimated values ​​of the communication decision variable of the agents on neighboring communication nodes; Step S5: Introduce time-varying auxiliary variables on the communication node, and reconstruct the communication decision variables of the agent on the communication node by combining the accumulated values ​​of the communication decision variables of the agent on the corresponding communication node; Step S6: Input the communication decision variables reconstructed by the agent on the communication node into the distributed optimization model of communication decision, and determine the optimal communication decision variables of the agent with the goal of minimizing the distributed optimization model of communication decision.

2. The quantitative communication optimization method for multi-agent systems under communication constraints according to claim 1, characterized in that, The construction process of the distributed optimization model for communication decision-making is as follows: in, This represents a distributed optimization model for communication decision-making. This indicates the number of communication nodes in the communication topology diagram. , All indicate index, Represents communication node Communication decision variables in the reconstruction of the agent Represents communication node The communication decision objective function, Represents communication node The set of constraints satisfied by the communication decision variables reconstructed by the agent; the distributed optimization model for communication decision needs to satisfy that the communication decision variables reconstructed by the agent on any communication node tend to be the same.

3. The quantitative communication optimization method for multi-agent systems under communication constraints according to claim 1, characterized in that, The specific process of differential encoding the communication decision variables of agents on each communication node in the communication topology diagram is as follows: agents on each communication node in the communication topology diagram estimate communication decision variables based on historical communication information, calculate the difference information between the current communication decision variables of agents on the communication node and the communication decision variables estimated by the corresponding agents, and quantize and encode the difference information.

4. The quantitative communication optimization method for multi-agent systems under communication constraints according to claim 3, characterized in that, It also includes: compressing the differential information using quantizer scaling technology, and then quantizing and encoding the compressed differential information. in, Represents communication node The intelligent agent at any time Differential coding information, Represents communication node The intelligent agent at any time The difference information, Represents the L2 norm, Represents a symbolic function. , This indicates the number of quantization levels. Represents communication node The intelligent agent at any time The random component of the quantization error.

5. The quantitative communication optimization method for multi-agent systems under communication constraints according to claim 1, characterized in that, The update process for the cumulative value of the communication decision variable of the agent on the communication node is as follows: in, Represents communication node The intelligent agent at any time The cumulative value of the communication decision variables, Represents communication node The intelligent agent at any time The current communication decision variables, Represents communication node The intelligent agent at any time The estimated values ​​of communication decision variables, Represents communication node The number of adjacent communication nodes, express index, Indicates adjacent communication nodes The intelligent agent at any time Updated estimates of communication decision variables, Represents communication node With neighboring communication nodes The weighting coefficients between them.

6. The quantitative communication optimization method for multi-agent systems under communication constraints according to claim 1, characterized in that, The auxiliary variables that change over time are as follows: in, Represents communication node The intelligent agent at any time Auxiliary variables, Represents communication node The number of adjacent communication nodes, express index, Represents communication node Adjacent communication nodes The intelligent agent at any time Auxiliary variables, A constant greater than 0; Represents communication node With neighboring communication nodes The weighting coefficients between them.

7. A quantitative communication optimization method for multi-agent systems under communication constraints as described in claim 1, characterized in that, The reconstruction process of the communication decision variables of the agent on the communication node is as follows: in, Represents communication node The intelligent agent at any time Reconstructed communication decision variables Represents communication node The intelligent agent at any time The cumulative value of the communication decision variables, Represents communication node The intelligent agent at any time Auxiliary variables, Represents communication node The set of constraints satisfied by the communication decision variables of the upper agent. Indicates in Projection on Indicates time The step size of the change, Indicates a constant step size. Represents communication node Gradient information on the surface.

8. A computer-readable storage medium storing a computer program, characterized in that, The computer program causes the computer to execute the quantitative communication optimization method for multi-agent systems under communication constraints as described in any one of claims 1-7.

9. An electronic device, characterized in that, include: The memory, the processor, and the computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the quantitative communication optimization method for multi-agent systems under communication constraints as described in any one of claims 1-7.

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