Improved bounds for large scale capacitated arc routing problem

The Capacitated Arc Routing Problem (CARP) stands among the hardest combinatorial problems to solve or to find high quality solutions. This becomes even more true when dealing with large instances. This paper investigates methods to improve on lower and upper bounds of instances on graphs with over two hundred vertices and three hundred edges, dimensions that, today, can be considered of large scale. On the lower bound side, we propose to explore the speed of a dual ascent heuristic to generate capacity cuts. These cuts are next improved with a new exact separation enchained to the linear program resolution that follows the dual heuristic. On the upper bound, we apply a modified Iterated Local Search procedure to Capacitated Vehicle Routing Problem (CVRP) instances obtained through a transformation from the CARP original instances. Computational experiments were carried out on the set of large instances from Brandão and Eglese and also on the regular size set. The experiments on the latter allows evaluating the quality of the proposed lower bounds, while the ones on the former presents improved lower and upper bounds to all the set of larger instances.