Deep Neural Networks for All-Terminal Network Reliability Estimation

All-terminal network reliability is a crucial feature as it provides a holistic measure for critical infrastructures such as transportation, computer, and communication networks. Fast and accurate network reliability estimation can help to prevent mishaps. Exact all-terminal calculation is an NP-hard and computationally expensive problem, which has led to the development of approximate methods based on artificial neural networks (ANNs). Although there have been some research studies on all-terminal reliability estimation using ANNs, there have not been yet many works that apply deep learning algorithms for all-terminal network reliability. This study presents a preliminary development of all-terminal network reliability estimation based on deep neural networks (DNNs), a state-of-the-art deep learning technique. To use DNNs for all-terminal network reliability estimation, an appropriate architecture of DNN needs to be developed. Different architectures are investigated by exploring parameters such as the number of hidden layers and the dropping probability parameter of a dropout layer to prevent overfitting. Hyperbolic tangent activation function limits the output to the range [0,1]. In addition, the network topology information needs to be preprocessed for the DNN to be able to process it and predict the network reliability. Graphs are used to represent the networks. Furthermore, to turn graphs into a computationally digestible format, advanced graph embedding methods (GEM) are employed. Different embedding methods and architectures are investigated together by training them with the network reliability as target. A dataset of 6000 Erdős-Rényi random graphs was generated to this end. The best input-architecture configuration is selected based on the root mean squared error (RMSE) using cross-validation. The best DNN proposed here, based on the RMSE (0.01), outperforms a previous traditional ANN approach. There is also a significant computation time reduction achieved by using the proposed DNN, which does not require the reliability upper bound as an additional input as employed in previous studies based on ANN.