Management of Railroad Impedances for Shortest Path-based Routing

Abstract

The routing of traffic is a major logistical concern for transportation services. For railroads, routing has historically been handled by large, hard-coded tables. Norfolk Southern Railways developed a more sophisticated routing system that takes advantage of network flow theory. Their Algorithmic Blocking and Classification (ABC) system routes traffic commodities (waybills) according to shortest paths. The routing of multiple waybills is a form of the Multicommodity Flow Problem (MCFP).Since routes for commodities are often predetermined, the success of ABC relies on finding costs that make the desired routes shortest paths. The problem of finding costs to make a solution optimal is called inverse optimization. The procedure of finding an adequate set of costs for the ABC system is known as calibration and is a form of the Inverse Multicommodity Flow Problem (IMCFP).Calibration seeks a solution that makes all predetermined paths uniquely optimal with respect to the costs. The calibration problem (IMCFP) can be solved optimally using the simplex method. However, direct application of the simplex algorithm is not always advantageous, especially for large problems. We present formulations, a primal-dual solution algorithm, and a hot start basis-finding algorithm for deriving optimal solutions. In addition, we can use Lagrangian relaxation to find good heuristic solutions.