New upper bounds for the multi-depot capacitated arc routing problem

The multi-depot capacitated arc routing problem (MD-CARP) generalises the well-known capacitated arc routing problem (CARP) by extending the single depot to a multi-depot network. The CARP consists of designing a set of vehicle trips, so that each vehicle starts and ends at the single depot. The MD-CARP involves the assignment of edges, which have to be served, to depots and the determination of vehicle trips for each depot. The first proposed work is based on ant colony optimisation (ACO) combined with an insertion heuristic: the ACO is used to optimise the order of insertion of the edges and the heuristic is devoted to inserting each edge in the solution. The second one is a memetic algorithm based on a special crossover. The computational results on benchmark instances show the satisfactory quality of the proposed methods and the superiority of the memetic algorithm compared to the ACO method.