The Set Orienteering Problem

In this paper, we study the Set Orienteering Problem which is a generalization of the Orienteering Problem where customers are grouped in clusters and a profit is associated with each cluster. The profit of a cluster is collected only if at least one customer from the cluster is visited. A single vehicle is available to collect the profit and the objective is to find the vehicle route that maximizes the profit collected and such that the route duration does not exceed a given threshold. We propose a mathematical formulation of the problem and a matheuristic algorithm. Computational tests are made on instances derived from benchmark instances for the Generalized Traveling Salesman Problem with up 1084 vertices. Results show that the matheuristic produces robust and high-quality solutions in a short computing time.