Enhanced Exact Approach for the Network Loading Problem

We investigate the Network Loading Problem (NLP) where a set of multicommodity demands (traffic) should be routed between pairs of nodes (customers). The problem consists of designing a network by installing capacities that allow simultaneous transmission of all the point-to-point demands with a minimum cost. In recent years, this challenging NP-hard problem has caught the interest of professionals and scientists, as it remains of crucial importance in telecommunications field. In order to solve the NLP to optimality, we use a path-based formulation to develop a tailored Benders decomposition scheme combined to a column generation approach for solving the master problem. Then, to accelerate the solution of the relaxed master program, we dynamically derive efficient cutset inequalities using a new max-cut-like integer programming model. To evaluate the efficacity of the proposed algorithms, computational results are reported using Benchmark instances from SNDLib.