Heuristics for the bi-objective path dissimilarity problem

In this paper the Path Dissimilarity Problem is considered. The problem has been previously studied in several contexts, the most popular motivated by the need of selecting routes for transportation of hazardous materials. The aim of this paper is to formally introduce the problem as a bi-objective optimization problem, in which a single solution consists of a set of p different paths, and two conflicting objectives arise, on one side the average length of the paths that must be kept low, and on the other side the dissimilarity among the paths in the set, that should be kept high. Previous methods are reviewed and adapted to our bi-objective problem, in this way we are able to compare the methods using the standard measures in multi-objective optimization. A new GRASP procedure is proposed and tested among the revised methods, and we show that it is able of creating better approximations of the efficient frontiers than existing methods.