Lagrangian relaxation and enumeration for solving constrained shortest-path problems

Recently published research indicates that a vertex-labeling algorithm based on dynamic-programming concepts is the most efficient procedure available for solving constrained shortest-path problems (CSPPs), i.e., shortest-path problems with one or more side constraints on the total "weight" of the optimal path. However, we investigate an alternative procedure that Lagrangianises the side constraints, optimises the resulting Lagrangian function and then closes any duality gap through enumeration of near-shortest paths. These paths are measured with respect to Lagrangian-modified edge lengths, and "near-shortest" implies -optimal, with equal to the duality gap. Our recently developed procedure for enumerating nearshortest-paths leads to an algorithm for CSPP that, empirically, proves to be an order of magnitude faster than the most recent vertex-labeling algorithm.

• Type: Journal
• Year: 2008
• Where: NETWORKS
• Authors: W. Matthew Carlyle, Johannes O. Royset, R. Kevin Wood
• Keywords: Computer Networks, Duality Gap, NETWORKS 2008, Shortest-path Problems, Vertex-labeling Algorithm