The capacitated arc routing problem. A heuristic algorithm

Abstract

In this paper we consider the Capacitated Arc Routing Problem, in which a fleet of K vehicles, all of them based on a specific vertex (the depot) and with a known capacity Q, must service a subset of the edges of the graph, with minimum total cost and such that the load assigned to each vehicle does not exceed its capacity. A heuristic algorithm for this problem is proposed consisting of: the selection of K centers, the construction of K connected graphs with associated loads not exceeding the vehicle capacities, the resolution of a General Assignment Problem, if necessary, to get a complete assignment of edges to vehicles and finally the construction of the routes by solving heuristically a Rural Postman Problem for each vehicle. Computational results on graphs up to 50 vertices and 97 edges are included. On average, the feasible solution is within 6,4% of the best known lower bound.