VNS with Path Relinking for the Profitable Close-Enough Arc Routing Problem

Arc Routing Problems typically deal with traversing a set of connecting edges or arcs in a network at the minimum possible cost. In this paper, we target the close enough model in which clients can be served from relatively close arcs, addressing some practical situations, such as inventory management or automated meter reading. We propose a heuristic to maximize the sum of profits of the clients served (penalized with the distance traveled). Our solving procedure, based on the VNS methodology, incorporates efficient search strategies to obtain high-quality solutions in short computational times, as required in practical applications. We study its improvement by coupling the method with Path Relinking as a post-processing. Our experimentation over a benchmark of previously reported instances shows the good performance of the heuristics as compared with a previous GRASP.