Optimizing Network Reliability via Best-First Search over Decision Diagrams

Communication networks are an essential infrastructure and must be designed carefully to ensure high reliability. Identifying a fully reliable design is, however, computationally very tough since it requires that a reliability evaluation, which is known to be #P-complete, be repeated an exponential number of times. Existing studies, therefore, attempt to avoid exact optimization to reduce the computational burden by applying heuristics. Due to the importance of communication networks and to better assess the accuracy of heuristic approaches, exact optimization remains a key goal. This paper proposes an exact method for two network design problems: reliability maximization under budget constraints and cost minimization with assurance of reliability. Our method employs a common idea to solve these problems, i.e., a best-first search algorithm that runs on decision diagrams. Our method employs just a single binary decision diagram (BDD) to compute the reliability for any solution and is also used as the basis of a novel heuristic function, called the cost-aware BDD heuristic function, as a search guide. Numerical experiments show that our method scales well; it successfully optimizes a network with 189 links. In addition, our method reveals the poor performance of existing heuristic approaches; a well-known existing heuristic method is shown to yield a solution that offers less than half the optimal reliability.