A Path Relinking approach for the Team Orienteering Problem

This paper introduces a Path Relinking metaheuristic approach for solving the Team Orienteering Problem (TOP), a particular routing problem in which a score is earned for visiting a location. The objective is to maximise the sum of the scores, while not exceeding a time budget T-max for travelling to the selected locations. In the case of the simple Orienteering Problem (OP), a single route connecting all selected locations should be followed; in TOP m routes are required and the length of each route is restricted to T-max. A fast and a slow variant of the approach are tested using a large set of test instances from the literature; they are compared to other state-of-the-art approaches. The fast variant achieves an average gap of 0.39% to the best known solutions in 5.0s of calculation time, while the slow variant achieves a 0.04% gap within 272.8s. Moreover, next to achieving most of the best known solutions for many testproblems, the slow variant improved the best known results in five instances. (C) 2009 Elsevier Ltd. All rights reserved.