Efficient Optimization of Reliable Two-Node Connected Networks: A Biobjective Approach

T paper presents a biobjective genetic algorithm (GA) to design reliable two-node connected telecommunication networks. Because the exact calculation of the reliability of a network is NP-hard, network designers have been reluctant to use network reliability as a design criterion; however, it is clearly an important aspect. Herein, three methods of reliability assessment are developed: an exact reliability calculation method using factoring, an efficient Monte Carlo estimation procedure using the sequential construction technique and network reductions, and an upper bound for the all-terminal reliability of networks with arbitrary arc reliabilities. These three methods of reliability assessment are used collectively in a biobjective GA with specialized mutation operators that perturb solutions without disturbing two-node connectivity. Computational experiments show that the proposed approach is tractable and significantly improves upon the results found by single-objective heuristics.