On the design of complex networks through a Branch-and-price algorithm

In this paper, we present a Branch-and-price algorithm for solving the Optimal Topology Design Problem of complex networks, based on a tightened deterministic formulation for the problem. The algorithm, which incorporates a delayed column generation approach within a Branch-and-bound framework, was proven to work well, being capable of finding optimal topologies within very low computational times, for networks with up to 60 nodes and different budget ranges. The algorithm allowed us to conclude that, by modifying the budget size values in our optimization model, different network features are found in optimal solutions. Accordingly, the budget size plays a similar role played by the probability of addition or rewiring arcs in randomized procedures for generating network topologies.