Estimation of all-terminal network reliability using an artificial neural network

The exact calculation of all-terminal network reliability is an NP-hard problem, with computational effort growing exponentially with the number of nodes and links in the network. During optimal network design, a huge number of candidate topologies are typically examined with each requiring a network reliability calculation. Because of the impracticality of calculating all-terminal network reliability for networks of moderate to large size, Monte Carlo simulation methods to estimate network reliability and upper and lower bounds to bound reliability have been used as alternatives. This paper puts forth another alternative to the estimation of all-terminal network reliability -- that of artificial neural network (ANN) predictive models. Neural networks are constructed, trained and validated using the network topologies, the link reliabilities, and a network reliability upperbound as inputs and the exact network reliability as the target. A hierarchical approach is used: a general neural network screens all network topologies for reliability followed by a specialized neural network for highly reliable network designs. Both networks with identical link reliability and networks with varying link reliability are studied. Results, using a grouped cross-validation approach, show that the ANN approach yields more precise estimates than the upperbound, especially in the worst cases. Using the reliability estimation methods of the ANN, the upperbound and backtracking, optimal network design by simulated annealing is considered. Results show that the ANN regularly produces superior network designs at a reasonable computational cost.