## Abstract

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. An important application area of operations research is the design of structures, products or systems where both technical and business aspects must be considered. One expanding design domain is the design of computer or communications networks. While cost is a prime consideration, reliability is equally important. A common reliability measure is all-terminal reliability, the probability that all nodes (computers or terminals) on the network an communicate with all others. Exact calculation of all-terminal reliability is an NP-hard problem, precluding its use during optimal network topology design, where this calculation must be made thousands or millions of times. This paper presents a novel computationally practical method for estimating all-terminal network reliability. Is shown how a neural network can be used to estimate all-terminal network reliability by using the network topology, the link reliabilities and an upperbound on all-terminal network reliability as inputs. The neural network is trained and validated on a very minute fraction of possible network topologies, and once trained, it can be used without restriction during network design for a topology of a fixed number of nodes. The trained neural network is extremely fast computationally and can accommodate a variety of network design problems. The neural network approach, an upper bound approach and an exact backtracking calculation are compared for network design using simulated annealing for optimization and show that the neural network approach yields superior designs at manageable computational cost.

Original language | English (US) |
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Pages (from-to) | 849-868 |

Number of pages | 20 |

Journal | Computers and Operations Research |

Volume | 29 |

Issue number | 7 |

DOIs | |

State | Published - Jun 2002 |

## All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Modeling and Simulation
- Management Science and Operations Research