Abstract: Given its wide spectrum of applications, the classical problem of all-terminal network reliability evaluation remains a highly relevant problem in network design. The associated optimization problem-to find a network with the best possible reliability under multiple constraints-presents an even more complex challenge, which has been addressed in the scientific literature but usually under strong assumptions over failures probabilities and/or the network topology. In this work, we propose a novel reliability optimization framework for network design with failures probabilities that are independent but not necessarily identical. We leverage the linear-time evaluation procedure for network reliability in the series-parallel graphs of Satyanarayana and Wood (1985) to formulate the reliability optimization problem as a mixed-integer nonlinear optimization problem. To solve this nonconvex problem, we use classical convex envelopes of bilinear functions, introduce custom cutting planes, and propose a new family of convex envelopes for expressions that appear in the evaluation of network reliability. Furthermore, we exploit the refinements produced by spatial branch-and-bound to locally strengthen our convex relaxations. Our experiments show that, using our framework, one can efficiently obtain optimal solutions in challenging instances of this problem.

Abstract: Availability, defined as the fraction of time a network service is operative, is a key network service parameter. Dedicated protection increases availability but also the cost. Shared protection instead decreases the cost, but also the availability. In this article, we formulate and solve an integer linear programming (ILP) model for the problem of minimizing the backup resources required by a shared-protected static optical network whilst guaranteeing an availability target per connection. The main research challenge is dealing with the nonlinear expression for the availability constraint. Taking the working/backup routes and the availability requirements as input data, the ILP model identifies the set of connections sharing backup resources in any given network link. We also propose a greedy heuristic to solve large instances in much shorter time than the ILP model with low levels of relative error (2.49% average error in the instances studied) and modify the ILP model to evaluate the impact of wavelength conversion. Results show that considering availability requirements can lead up to 56.4% higher backup resource requirements than not considering them at all, highlighting the importance of availability requirements in budget estimation. (C) 2016 Wiley Periodicals, Inc.