Evolutionary algorithms for periodic arc routing problems

The capacitated arc routing problem (CARP) involves the routing of vehicles to treat a set of arcs in a network. In many applications, the trips must be planned over a multiperiod horizon, giving a new problem called periodic CARP (PCARP). The paper describes several versions encountered in practice and suggests a simple classification, enabling the definition of a very general PCARP. For instance, the demand for each arc treatment may depend on the period or on the date of the previous visit. The proposed solution method is a memetic algorithm based on a sophisticated crossover, able to simultaneously change tactical (planning) decisions, such as the treatment days of each arc, and operational (scheduling) decisions, such as the trips performed for each day. Two versions are appraised on two sets of PCARP instances derived from standard CARP files. The results show significant savings compared to one insertion heuristic and a more elaborate two-phase method.