A Relax-and-Fix Decomposition Strategy Based on Adjacent Nodes Applied to the Periodic Capacitated Arc Routing Problem (PCARP)

Periodic Capacitated Arc Routing Problem (PCARP) is a combinatorial problem of hard resolution and due to its intrinsic intractability, researchers have concentrated on designing heuristic methods to obtain good quality solutions. In this work, the aim is to use the Relax-and-Fix heuristic (R and F) as a method of resolution of PCARP. The R and F heuristic consists of decomposing the original model in smaller submodels that are probably easier to be solved. Some factors that contribute to the success of the heuristics are applied decompositions. In this work we introduce a new form of decomposition which is not found in the literature yet as far as we know called Relax-and-Fix Adjacent Nodes (R and F-AN). This new strategy considers the characteristics of the PCARP and the decomposition of the model occurs by exploring in adjacencies in the associated graph. The efficiency of this new approach is evaluated on a set of 23 instances in the literature. Results have shown a reduction of 45% in the number of infeasible problems, when it is compared with other classic strategies of R and F heuristic decomposition. The R and F-AN has obtained 6 new better quality solutions than those already known, being 4 times faster in mean than the attempt of the resolution of the PCARP in the exact form.