A Branch-Cut-and-Price Algorithm for the Capacitated Arc Routing Problem

Arc routing problems are among the most challenging combinatorial optimization problems. We tackle the Capacitated Arc Routing Problem where demands are spread over a subset of the edges of a given graph, called the required edge set. Costs for traversing edges, demands on the required ones and the capacity of the available identical vehicles at a vertex depot are given. Routes that collect all the demands at minimum cost are sought. In this work, we devise a Branch-Cut-and-Price algorithm for the Capacitated Arc Routing problem using a column generation which generates non-elementary routes (usually called q-routes) and exact separation of odd edge cutset and capacity cuts. Computational experiments report one new optimal and twelve new lower bounds.