All-terminal network reliability estimation using convolutional neural networks

Abstract

Estimating the all-terminal network reliability by using artificial neural networks (ANNs) has emerged as a promissory alternative to classical exact NP-hard algorithms. Approaches based on traditional ANNs have usually considered the network reliability upper bound as part of the inputs, which implies additional time-consuming calculations during both training and testing phases. This paper proposes the use of Convolutional Neural Networks (CNNs), without the reliability upper-bound as an input, to address the all-terminal network reliability estimation problem. The present study introduces a multidimensional matrix format to embed the topological and link reliability information of networks. The unique contribution of this article is the method to capture the topology of a network in terms of its adjacency matrix, link reliability, and topological attributes providing a novel use of CNN beyond image classification. Since CNNs have been successful for image classification, appropriate modifications are needed and introduced to use them in the estimation of network reliability. A regression output layer is proposed, preceded by a sigmoid layer to achieve predictions within the range of reliability characteristic, a feature that some previous ANN-based works lack. Several training parameters together with a filter multiplier (CNN architecture parameter) were investigated. The actual values and the ones predicted with the best trained CNN were compared in the light of RMSE (0.04406) and p-value (0.3) showing non-significant difference. This study provides evidence supporting the hypothesis that the network reliability can be estimated by CNNs from its topology and link reliability information, embedded as an image-like multidimensional matrix. Another important result of the proposed approach is the significant reduction in computational time. An average of 1.18 ms/network was achieved by the CNN, whereas backtracking exact algorithm took around 500 s/network.

A Graph Convolution Neural Network-Based Framework for Communication Network K-Terminal Reliability Estimation

“…With network topology and link reliability vector, the k-terminal reliability can be computed. To improve the precision of the estimation model, instead of the Monte Carlo simulation method as presented in [33][34][35][36][37], in this paper we use the exact method to calculate the target reliability value. One of the most widely-used exact methods for network k-terminal reliability is the contraction-deletion method [54][55][56][57].…”

“…Although in the ANN models, the adjacency matrix flattened into a long vector can sorely determine the network topology, this type of node-level feature is inadequate for network-level representations because it overlooks the potential correlation between nodes and links that are close to one another. Stemming from this idea, in [37] Alex Davila-Frias and Om Prakash Yadav proposed to make use of the Convolution Neural Network (CNN) for the all-terminal reliability estimation for homogeneous networks. e network topology is processed as a n × n pixel image determined by its adjacency matrix, and several convolution layers are stacked to extract the high-level structure feature of the network.…”

“…e network topology represented by the graph is, in essence, non-Euclidean data, whereas the CNN model is best known for its dominating performances on Euclidean data structures like text [38,39], image [40][41][42], and videos [4344]. In [37], because the network topology is encoded as the pixel image derived from the adjacency matrix, the "local" structures are learned for nodes and links with consecutive indices, rather for nodes and links that are actually near each other in the topology. If the nodes are reindexed, the input features can change dramatically.…”

“…Without an appropriate node indexing strategy in place, the high-level feature extracted by the convolution filters lacks rationality. Besides, the CNN model in [37] assumes homogeneity for the network link reliability, which is an unrealistic simplification of many real-world systems and makes it unsuitable for certain applications.…”

Guest Editorial of Special Issue “Advanced Deep Learning Methods in Risk and Reliability Engineering”

“…Davila-Frias et al 7 aimed to solve the problem of all-terminal network reliability estimation and proposed using convolutional neural networks. The unique contribution of the proposed method is to capture the topology of a network according to its adjacency matrix, link reliability, and topological attributes.…”