On generating Pareto optimal set in bi-objective reliable network topology design

This paper considers an NP-hard network topology design (NTD) problem called NTD-CB/R. A key challenge when solving the bi-objective optimisation problem is to simultaneously minimise cost while maximising bandwidth. This paper aims to generate the best set of non-dominated feasible topologies, known as the Pareto Optimal Set (POS). It formally defines a dynamic programming (DP) formulation for NTD-CB/R. Then, it proposes two alternative Lagrange relaxations to compute a weight for each link. The paper proposes a DP approach, called DPCB/R-LP, to generate POS with maximum weight. Extensive simulations on hundreds of networks that contain up to 299 paths show that DPCB/R-LP can generate 70.4% of the optimal POS while using only up to 984 paths and 27.06 CPU seconds. Overall-Pareto-spread (OR), DPCB/R-LP produces 94.4% of POS with OS = 1, measured against the optimal POS. Finally, all generated POS's with largest bcr, significantly higher than 88% obtained by existing methods.