A Cutting Plane Approach to Solve the Railway Traveling Salesman Problem

We consider the Railway Traveling Salesman Problem. We show that this problem can be reduced to a variant of the generalized traveling salesman problem, defined on an undirected graph G = (V, E) with the nodes partitioned into clusters, which consists in finding a minimum cost cycle spanning a subset of nodes with the property that exactly two nodes are chosen from each cluster. We describe an exact exponential time algorithm for the problem, as well we present two mixed integer programming models of the problem. Based on one of this models proposed, we present an efficient solution procedure based on a cutting plane algorithm. Extensive computational results for instances taken from the railroad company of the Netherlands Nederlandse Spoorwegen and involving graphs with up to 2182 nodes and 38650 edges are reported.