Connectivity Upgrade Models for Survivable Network Design

Abstract

Disruptions in infrastructure networks to transport material, energy, and information can have serious economic, and even catastrophic, consequences. Since these networks require enormous investments, network service providers emphasize both survivability and cost effectiveness in their topological design decisions. This paper addresses the survivable network design problem, a core model incorporating the cost and redundancy trade-offs facing network planners. Using a novel connectivity upgrade strategy, we develop several families of inequalities to strengthen a multicommodity flow-based formulation for the problem, and show that some of these inequalities are facet defining. By increasing the linear programming lower bound, the valid inequalities not only lead to better performance guarantees for heuristic solutions, but also accelerate exact and approximate solution methods. We also consider a heuristic strategy that sequentially rounds the fractional values, starting with the linear programming solution to our strong model. Extensive computational tests confirm that the valid inequalities, added via a cutting plane algorithm, and the heuristic procedure are very effective, and their performance is robust to changes in the network dimensions and connectivity structure. Our solution approach generates tight lower and upper bounds with average gaps that are less than 1.2% for various problem sizes and connectivity requirements.

Hierarchical Survivable Network Design Problems

“…Constraints (2) ensure that each node is either a hub or it is assigned to another hub. Constraints (3) are capacity constraints that limit the number of nodes assigned to a hub by q.…”

“…Fortz and Labbé [5] and Fortz et al [6,7,8] study the design of networks with bounded rings. Magnanti and Raghavan [14] and Balakrishnan et al [2] consider different variants of two-edge connected networks. Soriano et al [18] and Caserta et al [4] treat the design of survivable telecommunications networks based on ring structures.…”

Survivability in Hierarchical Telecommunications Networks Under Dual Homing

“…The studies by Mahjoub and Pesneau (2008), Stoer (1992), and Vandenbussche and Nemhauser (2005) also relate to the current work because they consider twoedge-connected survivable designs, though only in a single layer. Magnanti and Raghavan (2005) and Balakrishnan et al (2009) focused on single-level survivable network design problems with connectivity requirements that generalize our two-edgeconnectivity requirement in the backbone layer. Labbé et al (2004) performed a facial study of the ring/star network design problems and provided an efficient branch-and-cut algorithm.…”

Genetic Algorithm for the Topological Design of Survivable Optical Transport Networks

“…The survivable topological design problem has attracted the attention of many researchers [2,[6][7][8][9][10]. A survey on ILP models, decomposition methods, and heuristics for the topological design of survivable networks can be found in [2,6].…”

“…A survey on ILP models, decomposition methods, and heuristics for the topological design of survivable networks can be found in [2,6]. In [8][9][10] ILP models and heuristics are analyzed to minimize the total number of links. Optimization methods to minimize the CAPEX of an optical WDM network can be found in [11][12][13][14].…”