Mathematical Programming Algorithms for Two-Path Routing Problems with Reliability Considerations

Most traditional routing problems assume perfect operability of all arcs and nodes. However, when independent arc failure probabilities exist, a secondary objective must be present to retain some measure of expected functionality, introducing nonlinear, nonconvex constraints. We examine the Robust Two-Path Problem, which seeks to establish two paths between a source and destination node wherein at least one path must remain fully operable with some threshold probability. We consider the case where both paths must be arc-disjoint and the case where arcs can be shared between the paths. We begin by proving the NP-hardness of these problems, and then examine various strategies for solving the resulting nonlinear integer program, including pruning, coefficient tightening, lifting, and branch-and-bound partitioning schemes. We discuss the advantages and disadvantages of these methods, and conclude with computational results. Subject Classifications: Programming, Integer: Nonlinear. Network...

• Type: Journal
• Year: 2008
• Where: INFORMS
• Authors: April K. Andreas, J. Cole Smith
• Keywords: Independent Arc Failure, INFORMS 2008, Most Traditional Routing, Robust Two-Path Problem