Lightweight federated learning aggregation method based on genetic algorithm

Abstract

The invention relates to the technical field of knowledge maps, in particular to a lightweight federated learning aggregation method based on a genetic algorithm. The invention provides a lightweight federated learning aggregation method based on a genetic algorithm, which performs lightweight improvement on an existing aggregation method by introducing a genetic learning theory and reconstructing an aggregation mechanism of a server side in a federated learning process so as to better solve the problems occurring when the prior art is applied to the field of Internet of Things. According to the method, the client model which is excellent in performance in each round of training is selected to participate in aggregation, so that the convergence process of the global model is remarkably accelerated, the resource consumption in the training process is reduced, and the final performance of the model is improved. Compared with an existing federated learning algorithm, the selective aggregation scheme can effectively reduce or avoid interference from malicious clients and reduce negative effects of malicious attacks on federated learning performance when dealing with unreliable or heterogeneous clients, so that robustness and reliability of the model are further improved.

Description

Technical Field

[0001] The present invention relates to the technical field of federated learning, and in particular to a lightweight federated learning aggregation method based on genetic algorithm. Background Art

[0002] With the continuous development of the Internet of Things technology, various devices in life are becoming more and more intelligent. These devices can exchange data through the Internet, thereby realizing data sharing and resource integration. Such interconnected devices are called Internet of Things (IoT) devices. The amount of data generated by IoT devices is huge, and these data are called big data. Big data refers to data that cannot be effectively processed and analyzed by traditional data processing technologies due to the characteristics of data size, speed and complexity. Big data has the following characteristics: 1. Large scale: The scale of big data can reach TB or even PB level; 2. Fast speed: Big data is generated very quickly and needs to be processed in real time; 3. High complexity: The information types and structures contained in big data are very diverse.

[0003] In the context of IoT big data, federated learning technology has been widely used. Federated learning is a distributed machine learning technology that allows multiple parties to collaboratively train models while maintaining data privacy and security. The core advantage of this technology lies in the local processing of data, that is, the data does not need to leave its original storage location, so it can reduce the risk of data leakage and meet the requirements of privacy protection-related laws and regulations. The traditional federated learning framework includes the following three processes: 1. The server randomly selects the clients participating in the aggregation in this round and sends the global model to them. 2. The client that receives the global model updates its own model and conducts several rounds of training to obtain a new local model and send it back to the server. 3. The server uses all the received local models to aggregate a new round of global models.

[0004] Federated learning aggregation algorithm,The aggregation process is an important link that occurs on the server side in the federated learning framework. The quality of the aggregation algorithm will directly affect the training effect. In the field of federated learning, the aggregation process mainly includes two types of aggregation methods: synchronous aggregation and asynchronous aggregation.

[0005] Asynchronous federated learning allows the client to asynchronously upload locally updated model parameters, and the server asynchronously aggregates these parameters to form a global model. The main purpose of this asynchronous update is to prevent the server from waiting for clients with slow training speeds, causing the training process to become abnormally slow. In other words, this method can speed up the training speed of federated learning to a certain extent and enhance the overall flexibility and scalability of the system. However, this may lead to the problem of updating the global model with outdated models. In order to solve this problem, researchers have proposed a variety of strategies, such as discarding outdated models, dynamically adjusting the number of local training rounds, and performing time-weighted aggregation updates on the model. However, this phenomenon can only be alleviated and cannot be completely solved, which will have a relatively large impact on the performance of the final global model. Therefore, the present invention chooses to improve the federated learning framework from the perspective of non-federated learning.

[0006] Synchronous federated learning requires that the client must receive a sufficient number of client models to perform a round of model aggregation, so there is a problem of waiting for slow clients. To address this problem, a large number of researchers have explored solutions to speed up the training process while maintaining model performance by introducing more efficient update mechanisms. The FedPA design requires that the server only wait for a number of device models pre-specified by the agent in each round, and then use these models for aggregation. Under similar considerations, an adaptive selection mechanism was developed to determine the time threshold and the client queue participating in the training iteration. However, both methods ignore the value of low-performance client data, which may have a negative impact on model performance. Other researchers believe that better models can be obtained by selecting more suitable participating clients or screening the models aggregated in each round according to certain strategies. Eiffel assigns a priority index based on client performance, and the scheduling algorithm randomly selects participating clients with this priority as the weight. MS screens the models to be aggregated based on momentum, and only selects clients with a Euclidean distance to more than half of the other clients within a certain range to participate in the average aggregation. FedAU adaptively uses a total weight inversely proportional to the average participation rate of the client, thereby improving the accuracy of the model. The above scheme of client aggregation based on evaluation filtering is very unfair to some clients. Moreover, some external attackers may attack some key clients, resulting in a decrease in the overall training effect. At the same time, in the evaluation-based selection scheme, the number of client models screened in each round is fixed and close to each other, which may cause some valid client data to be lost, resulting in slow training.

[0007] Genetic algorithm is a search and optimization method based on the principles of natural selection and genetics. In genetic algorithms, feasible solutions to the problem to be solved are usually encoded as "genes" represented by one-dimensional vectors. At the beginning, the program generates a large number of random genotypes as the initial population. Subsequently, the "environment" scores the fitness of each solution in the population according to its quality, and selects high-quality solutions based on the scores to participate in the crossover and mutation process to form a new round of population. Repeat the above process until a set of high-quality solutions with fitness scores that meet certain standards are obtained. Summary of the invention

[0008] The purpose of the present invention is to solve the problems of slow training speed, high resource consumption and susceptibility to extreme customers when federated learning is applied to the field of Internet of Things in the prior art, and to propose a lightweight federated learning aggregation method based on genetic algorithm.

[0009] On the one hand, the present invention proposes a lightweight federated learning aggregation method based on genetic algorithm, characterized in that it includes a server side, the server side specifically includes a communication interface module, a model selection module and a model aggregation module, and the server side implements the aggregation of the global model of the Internet of Things by the following steps:

[0010] S1, the server randomly selects a set amount of IoT device data from the global verification set to supplement the data of the client that sends the data supplement request;

[0011] S2. The server implements the client selection function through the communication interface module and distributes the current global model of the Internet of Things device to the client.

[0012] S3, the server receives through the communication interface module the global model returned after training by the client

[0013] S4, the server side selects the global model through the model selection module Fitness scoring is performed based on the performance in the global validation set;

[0014] S5. The server selects the top performance rankings based on the fitness score using a binary heap data structure. t the global model of

[0015] S6: The server aggregates the selected global models to form a new global model through the model aggregation module.

[0016] Preferably, the lightweight genetic algorithm-based federated learning aggregation method further requires looping steps S2 to S7, and ends the loop when the global model reaches a set accuracy or the total number of communication rounds is exhausted.

[0017] Preferably, the server needs to wait for a fixed set time t after receiving the data supplement request sent by the client. wait After completing the data transmission, the server needs to wait for a fixed set time t wait .

[0018] Preferably, the server randomly selects a set amount of IoT device data from the global verification set to supplement data for the client that sends a data supplement request, which only happens once.

[0019] Preferably, the global validation set is an introduced public data set, and the global validation set provides a model evaluation benchmark for the client training in step S4; the global validation set also serves as a benchmark for fitness scoring in step S5.

[0020] Further preferably, the global validation set needs to satisfy that the server can fairly characterize the client's environment; the global validation set also needs to satisfy that the server can evaluate the model returned by the client according to the fitness scoring benchmark established by the global validation set, and select the model participating in the aggregation according to the fitness scoring standard.

[0021] Preferably, the scores obtained in step S5 are ranked first t Add the global model of middle, and The following relationship exists:

[0022]

[0023] Where: Represents the set of clients selected to participate in this communication round.

[0024] Preferably, the new global model in step S6 uses the new set Perform aggregation as follows:

[0025]

[0026] Where: representing the new global model; The global model returned by the server according to the client; represents the new set; p irepresents the aggregate weight of the model from client i.

[0027] Preferably, the number of the global models participating in the aggregation in step S6 is ρ t , ρ t It can be set according to different situations, as follows:

[0028] The first setting method is to maintain the number of aggregations at a constant value, denoted as:

[0029] ρ t =ρ max

[0030] Where: t is the number of the global models involved in the aggregation; ρ max Indicates the maximum number of aggregations during the experiment;

[0031] The second setting method uses a power function, and the aggregate quantity change process can be expressed as:

[0032] ρ t =ρ max *(1-b t )+1while b∈(0,1)

[0033] Where: t is the number of the global models involved in the aggregation; ρ max Indicates the maximum number of aggregations during the experiment; b is the base number that needs to be set before the experiment;

[0034] The third setting method is based on the linear change of the number of aggregations, as follows:

[0035]

[0036] Where: t is the number of the global models involved in the aggregation; ρ max represents the maximum value of the number of aggregations during the experiment; c represents the maximum number of iterations of the maximum change in the number of aggregations;

[0037] The fourth design method is based on a sinusoidally varying aggregate quantity. The first sinusoidally varying aggregate quantity model follows a period of The sine function is:

[0038]

[0039] Another model uses a complete π cycle of the sine function, written as:

[0040]

[0041] Where:t is the number of the global models involved in the aggregation; ρ max Indicates the maximum number of aggregations during the experiment.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] The present invention provides a lightweight federated learning aggregation method based on genetic algorithm. By introducing genetic learning theory, the aggregation mechanism of the server side in the federated learning process is reconstructed, and the existing aggregation method is lightweight improved by using the data structure of binary heap and applied to the field of Internet of Things. On the basis of ensuring communication efficiency and computing power of the device side, the training of the distributed learning mechanism optimization model is realized. The present invention selects the client model with excellent performance in each round of training to participate in the aggregation, which significantly accelerates the convergence process of the global model, reduces resource consumption during the training process, and improves the final performance of the model. Compared with the existing federated learning algorithm, the selective aggregation scheme of the present invention can effectively reduce or avoid interference from malicious clients when dealing with unreliable or heterogeneous clients, reduce the negative impact of malicious attacks on the performance of federated learning, and further improve the robustness and reliability of the model. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a block diagram of a lightweight federated learning aggregation method based on genetic algorithm in an embodiment of the present invention.

[0045] Figure 2 These are experimental results obtained on different data sets in the embodiments of the present invention.

[0046] Figure 3 These are the experimental results of different numbers of clients on the CIFAR-10 dataset in an embodiment of the present invention.

[0047] Figure 4 These are the experimental results of different Dirichlet parameter scenarios on the CIFAR-10 dataset in an embodiment of the present invention.

[0048] Figure 5 These are the experimental results under different attack modes in the embodiments of the present invention.

[0049] Figure 6 is the accuracy change curve of each method on the CIFAR-10 dataset in the embodiment of the present invention. DETAILED DESCRIPTION

[0050] The present invention is further described in detail below in conjunction with test examples and specific implementation methods. However, this should not be understood as the scope of the above subject matter of the present invention being limited to the following embodiments, and all technologies realized based on the content of the present invention belong to the scope of the present invention.

[0051] Example 1

[0052] A lightweight federated learning aggregation method based on genetic algorithm proposed in the present invention can produce relatively good application effects in the IoT neighborhood where data is extreme and some high-quality public data sets currently exist. The genetic algorithm (GenFed method) can optimize model training through a distributed learning mechanism on the basis of ensuring communication efficiency and device-side computing power. It is suitable for large-scale IoT application scenarios such as smart homes, smart cities, and smart manufacturing. The performance verification of a specific lightweight federated learning aggregation method based on genetic algorithm is as follows.

[0053] In order to evaluate this plug-and-play and easily scalable federated learning design, the present invention integrates the GenFed method into the existing federated algorithm to explore the practical utility of the genetic mechanism in the federated framework. Specifically, the present invention selects the classic federated method FedAvg[3], the federated training acceleration method FedUmf

[30] , and the latest federated learning method FedAU

[18] based on weight design as comparison schemes to explore the performance of these methods in different task scenarios before and after integrating the GenFed mechanism. The specific steps are as follows:

[0054] S1, the server randomly selects a set amount of IoT device data from the global verification set to supplement the data of the client that sends the data supplement request;

[0055] S2. The server implements the client selection function through the communication interface module and distributes the current global model of the Internet of Things device to the client.

[0056] S3, the server receives through the communication interface module the global model returned after training by the client

[0057] S4, the server side selects the returned global model through the model selection module Fitness scoring is performed based on the performance in the global validation set;

[0058] S5. The server selects the top performance rankings based on the fitness score using a binary heap data structure. t The returned global model

[0059] S6: The server aggregates the selected returned global models to form a new global model through the model aggregation module.

[0060] The lightweight genetic algorithm-based federated learning aggregation method also requires looping steps S2 to S7, and ends the loop when the global model reaches a set accuracy or the total number of communication rounds is exhausted.

[0061] In step S1, the server needs to wait for a fixed set time t after receiving the data supplement request sent by the client. wait After completing the data transmission, the server needs to wait for a fixed set time t wait , reserving time for the client to receive data.

[0062] From the perspective of the client, first of all, non-malicious clients will actively participate in data supplementation. Clients with limited data can significantly improve the performance of the model obtained by local training by using the data provided by the server. In contrast, for clients with a large amount of data, the contribution of server-side data to the enhancement of model performance is negligible, and may even lead to an increase in the demand for the client's own local computing resources. Therefore, for these clients, deceiving the server in this process will have a negative impact on their own training. Secondly, malicious clients may regard the data distribution on the server as an opportunity to launch an attack and use the data obtained in this stage to carry out attacks. However, the process of distributing data on the server side is to randomly select a part of the data and send it to the client. Therefore, for any client i, j that issues a data support request, the supplementary data they receive and global data The following relations are satisfied:

[0063]

[0064] This means that malicious clients cannot obtain not only complete global verification data, but also any data that is the same as that obtained by other clients. This brings a certain degree of difficulty to their attack behavior at this stage. At the same time, the initialization stage only occurs once and only accounts for a small proportion in the framework of the present invention, so the attack and defense behavior at this stage is not the focus of the present invention.

[0065] The global validation set must meet the following key requirements: (1) the server must be able to fairly characterize the client's environment; (2) the server needs to evaluate the model returned by the client based on the characterization, and select the model to participate in the aggregation accordingly. Based on these requirements, the present invention introduces a public dataset for use as a global validation set. This dataset has the characteristics of balanced distribution and privacy independence, and provides a standardized model evaluation benchmark for the client during the training phase. The server uses this dataset to evaluate the model returned by the client in each round of training, and selects the models with excellent performance to participate in the aggregation, thereby building a new global model.

[0066] The scores obtained in step S5 are ranked first t Add the global model of middle, and The following relationship exists:

[0067]

[0068] Where: Represents the set of clients selected to participate in this communication round.

[0069] The new global model in step S6 uses the new set Perform aggregation as follows:

[0070]

[0071] Where: representing the new global model; The global model returned by the server according to the client; represents the new set; p i represents the aggregate weight of the model from client i.

[0072] 8. A lightweight federated learning aggregation method based on genetic algorithm according to claim 1, characterized in that the number of the global models participating in the aggregation in step S6 is p t , ρ t It can be set according to different situations, as follows:

[0073] The first setting method is to maintain the number of aggregations at a constant value, denoted as:

[0074] ρ t =ρ max

[0075] Where: t is the number of the global models involved in the aggregation; ρ max Indicates the maximum number of aggregations during the experiment;

[0076] The second setting method uses a power function, and the aggregate quantity change process can be expressed as:

[0077] ρ t =ρ max *(1-b t )+1while b∈(0,1)

[0078] Where: tis the number of the global models involved in the aggregation; ρ max Indicates the maximum number of aggregations during the experiment; b is the base number that needs to be set before the experiment;

[0079] The third setting method is based on the linear change of the number of aggregations, as follows:

[0080]

[0081] Where: t is the number of the global models involved in the aggregation; ρ max represents the maximum value of the number of aggregations during the experiment; c represents the maximum number of iterations of the maximum change in the number of aggregations;

[0082] The fourth design method is based on a sinusoidally varying aggregate quantity. The first sinusoidally varying aggregate quantity model follows a period of The sine function is:

[0083]

[0084] Another model uses a complete π cycle of the sine function, written as:

[0085]

[0086] Where: t is the number of the global models involved in the aggregation; ρ max Indicates the maximum number of aggregations during the experiment.

[0087] To evaluate the performance of the model, the present invention uses three widely used datasets in the field of federated learning: MNIST

[31] , Fashion-MNIST

[32] , and CIFAR-10

[23] for experiments. Unless otherwise specified, the Dirichlet distribution

[33] with parameter is used in the experiment to simulate the data heterogeneity of 100 clients, and the CIFAR-10 dataset is used for performance evaluation. Since the research focus is on the design of the federated framework, the present invention only uses a simple convolutional neural network (CNN model) for training. For the experiments on the MNIST and Fashion-MNIST datasets, the present invention performed 2000 training rounds; in contrast, due to the greater difficulty of training the CIFAR-10 dataset, 4000 training rounds were performed. In addition, in each communication round, 10 clients are selected to participate in the training, and each client performs 5 rounds of local training.

[0088] To verify the effect of GenFed in improving training efficiency and model performance in different tasks, the present invention conducted experiments on multiple data sets. The results are as follows: Figure 2As shown. After the introduction of the GenFed mechanism, the performance of several traditional methods has been improved to varying degrees. In addition, the application of the GenFed mechanism significantly reduces the number of communication rounds required to achieve high performance. Specifically, on the MNIST dataset, GenFed only needs 1 / 15 of the FedAvg training cycle to achieve 97% accuracy; on the FashionMNIST dataset, GenFed only needs 1 / 35 of the FedAvg training cycle to achieve 80% accuracy; and on the CIFAR-10 dataset, GenFed only needs 1 / 10 of the FedAvg training rounds to achieve 45% accuracy. The above results fully demonstrate the actual effect of GenFed in significantly improving model performance while accelerating the training process.

[0089] At the same time, in order to verify the effectiveness of the GenFed method under different client numbers, the present invention conducted the following Figure 3 The experiment shown in Figure 2 shows that the GenFed method is always better than the traditional method in various application scenarios with different numbers of clients. It is particularly noteworthy that when the number of clients exceeds 140, GenFed can still maintain a stable and high performance level. In contrast, the performance of the traditional method gradually deteriorates with the increase in the number of clients, and the accuracy decreases significantly. This experimental result shows that the GenFed method shows excellent robustness and effectiveness in an environment with a large number of clients, making up for the insufficient performance of the traditional method under a large client base.

[0090] In order to verify the influence of different Non-IID levels on the performance of the GenFed method, the present invention conducted experiments based on different Dirichlet distribution parameters. Figure 4 As shown in the figure. In most cases, the GenFed method shows better performance than the traditional method. Especially under extreme conditions, due to the highly unbalanced data distribution among clients, it is difficult for the traditional method to maintain a high accuracy rate on all clients. However, the average client accuracy of the method of the present invention under this condition is 11% higher than that of the traditional method, which fully demonstrates the robustness of GenFed in dealing with severe data imbalance problems.

[0091] In order to evaluate the effectiveness of the GenFed method in the presence of malicious clients, the present invention conducted an attack experiment based on the CIFAR-10 dataset. The specific malicious client implementation is as follows:

[0092] 1) Label Flipping (LF)

[34] : The malicious client modifies the labels of local training data and flips the labels from 0 to 9, that is, label x becomes 9-x.

[0093] 2) Inner Product Manipulation Attack (IPM)

[35] : The malicious client submits the negative vector of the normal client’s average gradient to the server, thereby causing destructive effects on the model update process.

[0094] 3) MimicAttack

[36] : A malicious client submits a randomly selected copy of a normal client’s gradient to the server to mimic the behavior of a benign client.

[0095] The experimental results are as follows Figure 5 As shown in Figure 2, in three different attack scenarios, the performance degradation of the GenFed method is significantly lower than that of the FedAvg method. This shows that the integration of the GenFed mechanism effectively enhances the robustness of the federated learning algorithm in dealing with malicious client attacks.

[0096] Figure 2 The results show that the GenFed method achieves higher accuracy with fewer training rounds and converges significantly faster than traditional algorithms. To further analyze the impact of different parameter settings on the federated learning training process, Figure 6 The accuracy trends of various methods on the CIFAR-10 dataset during the training process are shown in detail. Among the different specific implementation methods, the GenFed models with dynamically changing parameters (including GenFed(2), GenFed(3), GenFed(4) and GenFed(5)) are better than the fixed GenFed(1) method in accelerating the training process and improving the final model accuracy. However, it should be noted that GenFed(5) showed great instability in the later stages of training, which affected its overall reliability.

[0097] In view of the above findings, it is recommended to give priority to the GenFed (3) and GenFed (4) methods. These two methods show an excellent balance between fast convergence and final model performance, and have both high efficiency and excellent results, so they are widely applicable in various application scenarios.

[0098] The expected practical effects that can be obtained by deploying the GenFed method in the above process are as follows:

[0099] 1. Significantly improve the convergence speed of the model: By introducing the genetic mechanism, GenFed can accelerate the convergence speed of model training, making the training time shorter than the traditional federated learning method in an environment with strong data heterogeneity. For example, in the case of a large number of IoT data sets, the number of communication rounds required for training is reduced, which greatly improves the deployment efficiency of the model.

[0100] 2. Enhanced accuracy and model performance: GenFed optimizes the model aggregation strategy to achieve higher prediction accuracy on different types of datasets.

[0101] 3. Improve robustness against malicious attacks: In federated learning, some participants may submit malicious updates, affecting the performance of the global model. GenFed effectively suppresses the negative impact of malicious participants on the global model through adaptive weight adjustment in the genetic mechanism, improves the system's robustness against attacks, and is suitable for scenarios facing security risks, such as the Internet of Things.

[0102] 4. Support for the expansion of large-scale client environments: As the number of participating clients increases, the performance of traditional federated learning methods will drop significantly, while GenFed, through reasonable scheduling and balancing of resources, will only slightly reduce its performance even when large-scale clients participate. This enables GenFed to maintain efficient and stable operation in large-scale distributed systems of the Internet of Things.

[0103] In short, the GenFed framework has a wide range of applications, especially for distributed systems such as the Internet of Things that involve multiple clients, highly heterogeneous data, and limited resources. Its efficiency and robustness provide strong technical support for large-scale practical scenarios.

Claims

1. A lightweight federated learning aggregation method based on genetic algorithm, characterized in that: The system comprises a server side, which specifically comprises a communication interface module, a model selection module based on a genetic algorithm and a model aggregation module. The server side implements the aggregation of the global model of the Internet of Things by the following steps: S1, the server randomly selects a set amount of IoT device data from the global verification set to supplement the data of the client that sends the data supplement request; S2. The server implements the client selection function through the communication interface module and distributes the current global model of the Internet of Things device to the client. S3, the server receives through the communication interface module the global model returned after training by the client S4, the server side selects the returned global model through the model selection module Fitness scoring is performed based on the performance in the global validation set; S5. The server selects the top ρ in performance ranking according to the fitness score using a binary heap data structure. t The returned global model S6: The server aggregates the selected returned global models to form a new global model through the model aggregation module.

2. A lightweight genetic algorithm-based federated learning aggregation method according to claim 1, characterized in that: The lightweight genetic algorithm-based federated learning aggregation method also requires looping steps S2 to S7, and ends the loop when the global model reaches a set accuracy or the total number of communication rounds is exhausted.

3. According to claim 1, a lightweight federated learning aggregation method based on genetic algorithm, characterized in that: In step S1, the server needs to wait for a fixed set time t after receiving the data supplement request sent by the client. wait After completing the data transmission, the server needs to wait for a fixed set time t wait .

4. The lightweight genetic algorithm-based federated learning aggregation method according to claim 1, characterized in that: The server randomly selects a set amount of IoT device data from the global verification set to supplement data for the client that sends a data supplement request, which only happens once.

5. The lightweight genetic algorithm-based federated learning aggregation method according to claim 1, characterized in that: The global validation set is an introduced public data set, which provides a model evaluation benchmark for the client training in step S4; the global validation set also serves as a benchmark for fitness scoring in step S5.

6. A lightweight genetic algorithm-based federated learning aggregation method according to claim 1, characterized in that: The scores obtained in step S5 are ranked first t Add the global model of middle, and The following relationship exists: Where: Represents the set of clients selected to participate in this communication round.

7. The lightweight federated learning aggregation method based on genetic algorithm according to claim 1, characterized in that: The new global model in step S6 uses the new set Perform aggregation as follows: Where: representing the new global model; The global model returned by the server according to the client; represents the new set; p i represents the aggregate weight of the model from client i.

8. The lightweight genetic algorithm-based federated learning aggregation method according to claim 1, characterized in that: The number of the global models participating in the aggregation in step S6 is ρ t , ρ t It can be set according to different situations, as follows: The first setting method is to maintain the number of aggregations at a constant value, denoted as: r t =ρ max Where: t is the number of the global models involved in the aggregation; ρ max Indicates the maximum number of aggregations during the experiment; The second setting method uses a power function, and the aggregate quantity change process can be expressed as: r t =ρ max *(1-b t )+1 while b∈(0,1) Where: t is the number of the global models involved in the aggregation; ρ max Indicates the maximum number of aggregations during the experiment; b is the base number that needs to be set before the experiment; The third setting method is based on the linear change of the number of aggregations, as follows: Where: t is the number of the global models involved in the aggregation; ρ max represents the maximum value of the number of aggregations during the experiment; c represents the maximum number of iterations of the maximum change in the number of aggregations; The fourth design method is based on a sinusoidally varying aggregate quantity. The first sinusoidally varying aggregate quantity model follows a period of The sine function is: Another model uses a complete π cycle of the sine function, written as: Where: t is the number of the global models involved in the aggregation; ρ max Indicates the maximum number of aggregations during the experiment.

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