Network robustness evaluation method for multi-agent systems based on convolutional neural networks

Abstract

The present invention discloses a method for evaluating the network robustness of a multi-agent system based on a convolutional neural network. First, for a multi-agent system network set, the in-degree distribution statistics of each node in the adjacency matrix are used as basic features, and the nodes of the adjacency matrix are rearranged according to the in-degree information; then, a data set with the same number of nodes is submitted to the convolutional neural network for feature learning to obtain a weight matrix and a bias vector; finally, the features learned from the adjacency matrix of the same data set are predicted by a convolutional neural network model to obtain the final classification result. This method uses a convolutional neural network model that is more suitable for learning the features of the adjacency matrix, and learns features that can better express the graph structure from the adjacency matrix, so that the accuracy and precision of the convolutional neural network after learning are better. This solves the problem that the time complexity of the prior art increases exponentially when the number of nodes in the network increases, and the algorithm complexity is extremely high, so it cannot be effectively evaluated.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-agent systems, and in particular relates to a multi-agent system network robustness evaluation method based on convolutional neural networks. Background Art

[0002] Multi-agent systems are a new concept formed with the development of embedded systems, control systems and network technologies. They usually refer to a network system formed by a group of agents with certain perception, communication, computing and execution capabilities connected through perception, communication and other means. This type of system composed of multiple agents can complete complex tasks that a single agent cannot complete, and improve the ability to perform tasks and work efficiency. Therefore, multi-agent system technology has been widely used in various fields, such as smart grids, space exploration, wireless sensor networks, air traffic control, etc. In multi-agent systems, network robustness refers to the ability of the system's communication network to tolerate the failure of some nodes or even the recovery ability when encountering network attacks. Therefore, it is necessary to analyze and evaluate the network robustness during the operation of the multi-agent system, and quantify the system's ability to tolerate malicious network attacks from the evaluation results.

[0003] Measuring and evaluating the robustness of the communication network of a multi-agent system with the help of deep learning technology is an effective way to ensure that the system operates safely and efficiently in the event of network attacks or node failures. In 2013, in the paper "Resilient Asymptotic Consensus in Robust Networks", Heath J. LeBlanc and other scholars proposed a concept called (r, s)-robustness or network robustness. Network robustness is a property of a network that measures the redundancy of directed information flows or directed edges between non-empty non-intersecting node subsets in the network. Compared with the use of connectivity in traditional graph theory to measure the redundancy of such information and the ability of the network to tolerate attacks, it has better pertinence and effectiveness. However, Heath J. LeBlanc and other scholars subsequently used an algorithm based on the exhaustive idea in the paper "Algorithms for Determining Network Robustness" to solve the r and s values ​​in the (r, s)-robustness of a given directed graph, and pointed out that the time complexity of this solution is related to the number of nodes, reaching an exponential level and is essentially an NP-hard problem. Therefore, for large-scale distributed multi-agent systems with a large number of nodes and complex communication edge relationships, there is still no precedent for using traditional algorithms to accurately evaluate their (r,s)-robustness. Summary of the invention

[0004] In order to solve the problem that traditional algorithms cannot be effectively evaluated because the time grows exponentially and the algorithm complexity is high when the number of nodes in the network increases, the present invention provides a multi-agent system network robustness evaluation method based on convolutional neural networks. The method can be applied to networks with a massive number of nodes, and quickly and accurately evaluate the r and s values ​​in the (r, s)-robustness of the network topology, thereby inferring the system's ability to tolerate partial node failures or maintain normal operation after suffering a network attack.

[0005] The network robustness evaluation method of a multi-agent system based on a convolutional neural network specifically includes the following steps:

[0006] Step (1). For a system network set G = G1, G2, ..., G consisting of multiple agents N , using its corresponding adjacency matrix set A=A1,A2,…,A N The in-degree distribution statistics of each node in the adjacency matrix are used as the basic features, and then each node in each adjacency matrix is ​​rearranged one by one according to its in-degree value. The rearranged adjacency matrix set is A′=A′1,A′2,…,A′ N Represented. And the convolutional layer of the neural network automatically extracts the valid feature vector set F=f1,f2,…,f from the rearranged adjacency matrix. N , and then the representation features are learned in a supervised manner through a fully connected network, and finally the evaluation and solution of different (r, s)-robust graphs are realized through the classifier.

[0007] Step (2). Construct a convolutional neural network model, input the rearranged adjacency matrix with the same number of nodes into the convolutional neural network model for feature extraction, and obtain the weight matrix Θ and bias vector b after learning. Then input the extracted features into the convolutional neural network model for prediction to obtain the final classification result.

[0008] Furthermore, the step (1) of rearranging the nodes in the adjacency matrix includes the following steps:

[0009] (1.1). Use a double loop to obtain the in-degree of all nodes in the adjacency matrix A. The nodes with larger in-degree are prioritized in the front. The nodes with the same in-degree are arranged in the order of traversal and stored in the variable list;

[0010] (1.2). Obtain the new labels newLables of the rearranged node sequence from the variable list;

[0011] (1.3). Use the obtained new labels newLables to rearrange the rows of the original input adjacency matrix A, transpose it, and then use the obtained new labels newLables to rearrange the columns of the transposed matrix;

[0012] (1.4). Finally, the matrix output by (1.3) is restored to its original state by transposing, completing the rearrangement of the adjacency matrix.

[0013] Furthermore, the method for constructing a convolutional neural network model in step (2) comprises the following steps:

[0014] (2.1). Construct an input layer, three convolutional layers, one fully connected layer, and two classifier layers. The two classifiers are used to output the r value and s value in the robustness value respectively. Considering that the pooling layer will cause information loss during compression, the pooling layer after the convolutional layer is discarded;

[0015] (2.2). Set the eigenvector sets of different adjacency matrices F = f1, f2, ..., f N After normalization, the data is input into the input layer of the convolutional neural network model;

[0016] (2.3) Input the adjacency matrix A′ after the rearrangement in step 1 into the convolutional layer of the convolutional neural network model. The operation performed by the convolutional layer is x = σ(W·A′ [i:i+h-1,i:h-1] +b), where σ is the activation function, W is the convolution kernel, and b is the bias vector;

[0017] Preferably, the activation function σ is a RELU nonlinear activation function.

[0018] (2.4) The first convolutional layer is used to extract edge-to-edge features, which is specifically set as i and j are the i-th row and j-th column of the adjacency matrix, respectively. and They are the convolution kernels of the h-th row and h-th column respectively, and the number of convolution kernels in the first layer is f1.

[0019] (2.5) The second convolutional layer is used to extract edge-to-node features, which is specifically set as and They are the convolution kernels of the h-th row and h-th column respectively, and the number of convolution kernels in the second layer is f2.

[0020] (2.6) The third convolutional layer is used to extract node-to-graph features, which is specifically set as in is the convolution kernel of the hth row.

[0021] (2.7). Then, the vector output by the fully connected layer is input into the r and s classifiers respectively. The r and s classifiers use the softmax function to normalize the input, calculate their cross entropy loss function, and obtain the difference between the actual output value and the real network (r, s)-robustness. Then, the adam optimization algorithm is used to update the weights of the convolutional neural network model.

[0022] (2.8). The calculation ends when and only when the error of the output results of the r and s classifiers meets the set requirements or the number of iterations reaches the upper limit. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is a flow chart of the network robustness evaluation method for multi-agent systems.

[0024] Figure 2 Schematic diagram of the convolutional neural network model constructed in the embodiment. DETAILED DESCRIPTION

[0025] The present invention is further described below in conjunction with the accompanying drawings:

[0026] Step (1). Figure 1 As shown, for a system network set G=G1,G2,…,G N , using its corresponding adjacency matrix set A=A1,A2,…,A N The in-degree distribution statistics of each node in the adjacency matrix are used as the basic features, and then each node in each adjacency matrix is ​​rearranged one by one according to its in-degree value. The rearranged adjacency matrix set is A′=A′1,A′2,…,A′ N Represented. And the convolutional layer of the neural network automatically extracts the valid feature vector set F=f1,f2,…,f from the rearranged adjacency matrix. N , and then learn the representation features in a supervised manner through a fully connected network, and finally evaluate and solve different (r, s)-robust graphs through a classifier, where the specific method of matrix rearrangement is:

[0027] (1.1). Directed graphs with the same structure have very different adjacency matrices due to different node orders. First, the algorithm input is the adjacency matrix A. A double loop is used to obtain the in-degree of all nodes. The nodes with large in-degree are prioritized. The nodes with the same in-degree are arranged in the order of traversal and stored in the variable list.

[0028] (1.2). Obtain the new labels newLables of the rearranged node sequence from the variable list;

[0029] (1.3). Use the obtained new labels newLables. Rearrange the rows of the original input adjacency matrix A, transpose it, and then use the obtained new labels newLables to rearrange the columns of the adjacency matrix A;

[0030] (1.4).Finally, the matrix A output by (1.3) is restored to its original state by transposing.

[0031] Step (2). Construct a convolutional neural network model and submit the adjacency matrix with the same number of nodes to the convolutional neural network model for feature extraction. After learning, the weight matrix Θ and the bias vector b are obtained, as shown in Figure 2 As shown, the specific method of constructing a convolutional neural network model is:

[0032] (2.1). Construct an input layer, three convolutional layers, one fully connected layer, and two parallel classifier layers. The two classifier layers are used to output the r value and s value in the robustness value respectively. Considering that the pooling layer will cause information loss during compression, the pooling layer after the convolutional layer is discarded;

[0033] (2.2). Set the eigenvector sets of different adjacency matrices F = f1, f2, ..., f N After normalization, input the data into the input layer;

[0034] (2.3) Input the rearranged adjacency matrix A′ into the convolutional layer. The operation performed by the convolutional layer is x = σ(W·A′ [i:i+h-1,i:h-1] +b), where σ is the activation function, RELU nonlinear activation function is selected, W is the convolution kernel, and the bias vector is b;

[0035] (2.4) The first convolutional layer is used to extract edge-to-edge features, which is specifically set as i and j are the i-th row and j-th column of the adjacency matrix, respectively. and They are the convolution kernels of the h-th row and h-th column respectively, and the number of convolution kernels in the first layer is f1.

[0036] (2.5) The second convolutional layer is used to extract edge-to-node features, which is specifically set as and They are the convolution kernels of the h-th row and h-th column respectively, and the number of convolution kernels in the second layer is f2.

[0037] (2.6) The third convolutional layer is used to extract node-to-graph features, which is specifically set as in is the convolution kernel of the hth row.

[0038] (2.7). Then, the vectors output by the fully connected layer are input into the r and s classifiers respectively, normalized using the softmax function, and the cross entropy loss function is calculated to obtain the difference between the actual output value and the true network (r, s)-robustness. Then, the adam optimization algorithm is used to update the weights of the convolutional neural network model.

[0039] In this example, the initial learning rate is set to 0.0001, the Dropout rate is set to 0.2, the number of training iterations is set to 500, the batch size is set to 1024, and the initial weights and biases satisfy the Gaussian distribution N(0,0.1)

[0040] (2.8). The calculation ends when and only when the error of the output result meets the set requirements or the number of iterations reaches the upper limit.

[0041] Any details not mentioned in the specific embodiments of the present invention belong to the known technologies in the art and can be implemented with reference to the known technologies.

[0042] The above specific implementation methods are specific support for the technical idea of ​​the multi-agent system network robustness method based on convolutional neural network proposed in the present invention, and cannot be used to limit the protection scope of the present invention. Any equivalent changes or equivalent modifications made on the basis of the technical solution of the present invention in accordance with the technical idea proposed in the present invention still fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for evaluating the network robustness of a multi-agent system based on a convolutional neural network, characterized by: The specific steps include: Step 1: For the system network set G=G1,G2,…,G consisting of multiple agents N , calculate the corresponding adjacency matrix set A=A1,A2,…,A N The in-degree distribution statistics of each node in the network are then rearranged according to the in-degree of the node from large to small. The rearranged adjacency matrix set A′=A′1,A′2,…,A′ N ; Step 2: Construct a convolutional neural network model. The first convolution layer is used to extract edge-to-edge features. The number of convolution kernels is f1, which is specifically set as: Where i and j are the i-th row and j-th column of the rearranged adjacency matrix A′, respectively. and are the convolution kernels of the h-th row and h-th column respectively; The second convolutional layer is used to extract edge-to-node features. The number of convolution kernels is f2, which is specifically set as: in, and are the convolution kernels of the h-th row and h-th column respectively; The third convolutional layer is used to extract node-to-graph features, and the specific settings are: in is the convolution kernel of the hth row; The adjacency matrices with the same number of nodes in the adjacency matrix set A′ after the rearrangement in step one are input into the convolutional neural network model for feature extraction. After the learning is completed, the weight matrix Θ and the bias vector b of the convolutional neural network model are obtained. Then the extracted features are input into the learned convolutional neural network model for prediction, so as to solve the r and s values ​​of the robustness of the system network (r, s).

2. The method for evaluating network robustness of a multi-agent system based on a convolutional neural network as claimed in claim 1, characterized in that: The specific steps to rearrange the neighbor matrix are: s1.

1. Use a double loop to obtain the in-degrees of all nodes in the adjacency matrix, and arrange the nodes in descending order according to the size of the in-degrees; for two nodes with the same in-degree, arrange them in the order of traversal; store the rearranged nodes in the variable list; s1.2 obtains the labels newLables of the rearranged node sequence from the variable list; s1.3 uses the label newLables obtained in s1.2; rearranges the rows of the original adjacency matrix A, transposes it, and then uses the label newLables to rearrange the columns of the transposed matrix; S1.4 finally restores the matrix output by S1.3 to its original state by transposing, and obtains the rearranged adjacency matrix A′.

3. The method for evaluating network robustness of a multi-agent system based on a convolutional neural network as claimed in claim 1, characterized in that: The convolutional neural network model includes an input layer, three convolutional layers, a fully connected layer and two classifier layers; the convolutional layer is x=σ(W·A′ [i:i+h-1,i:h-1] +b), where σ is the activation function, W is the convolution kernel, and b is the bias vector; the two classifiers are used to output the r value and s value in the robustness value respectively.

4. The method for evaluating network robustness of a multi-agent system based on a convolutional neural network as claimed in claim 1 or 3, characterized in that: Input the rearranged adjacency matrix A′ from step 1 into the convolutional layer of the convolutional neural network model and extract the corresponding feature vector set F = f1, f2, …, f N ; Then, the vectors output by the fully connected layer are input into the r and s classifiers respectively. The r and s classifiers are normalized using the softmax function, and the cross entropy loss function is calculated to obtain the difference between the actual output value of the convolutional neural network model and the (r, s) robustness of the real system network. Then, the adam optimization algorithm is used to update the weights of the convolutional neural network model to complete the learning of the convolutional neural network model.

5. The method for evaluating network robustness of a multi-agent system based on a convolutional neural network as claimed in claim 3, characterized in that: The activation function σ is a RELU nonlinear activation function.

6. The method for evaluating network robustness of a multi-agent system based on a convolutional neural network as claimed in claim 1, characterized in that: If and only if the error of the output result of the convolutional neural network model meets the set requirements or the number of iterations reaches the upper limit, the convolutional neural network model learning is completed, and the weight matrix Θ and the bias vector b are fixed.

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