Finding $K$ dissimilar paths using integer linear formulations

While finding a path between two nodes is the basis for several applications, the need for alternative paths also may have various motivations. For instance, this can be of interest for ensuring reliability in a telecommunications network, for reducing the consequences of possible accidents in the transportation of hazardous materials, or to decrease the risk of robberies in money distribution. Each of these applications has particular characteristics, but they all have the common purpose of searching for a set of paths which are as dissimilar as possible with respect to the nodes/arcs that compose them. In this work we present linear integer programming formulations for finding K dissimilar paths, with the main goal of preventing the overlap of arcs in the paths for a given integer K. The different formulations are tested for randomly generated general networks and for grid networks. The obtained results are compared in terms of the solutions’ dissimilarity and of the run time. Two of the new formulations are able to find 10 paths with better average and minimum dissimilarity values than an iterative approach in the literature, in less than 20 seconds, for random networks with 500 nodes and 5000 arcs.