Branch-and-bound algorithm for an arc routing problem

The Open Capacitated Arc Routing Problem (OCARP) is an NP-hard combinatorial optimization problem where, given an undirected graph, the objective is to find a minimum cost set of tours that services a subset of edges with positive demand under capacity constraints. This problem is related to the Capacitated Arc Routing Problem (CARP) but differs from it since OCARP does not consider a depot, and tours are not constrained to form cycles. Three lower bounds are proposed to the OCARP, one of them uses a subgradient method to solve a Lagrangian relaxation. These lower bounds are integrated within a branch-and-bound framework to conceive the first OCARP exact algorithm. The branch-and-bound algorithm is started with high-quality upper bounds obtained with a sucessful GRASP with evolutionary path-relinking, originally developed to solve the CARP. Computational tests compared the proposed branchand-bound with a commercial state-of-the-art ILP solver. The results show that the branch-andbound outperformed CPLEX in both overall average deviation from lower bounds and number of best lower bounds.