The k-Color Shortest Path Problem

This paper proposes a mathematical model and an exact algorithm for a novel problem, the k-Color Shortest Path Problem. This problem is defined on a edge-colored weighted graph, and its aim is to find a shortest path that uses at most k different edge-colors. The main support and motivation for this problem arise in the field of transmission networks design, where two crucial matters, reliability and cost, can be addressed using both colors and arc distances in the solution of a constrained shortest path problem. In this work, we describe a first mathematical formulation of the problem of interest and present an exact solution approach based on a branch and bound technique.