A traffic grooming problem of SONET-WDM rings

In this paper, we present a traffic grooming problem of the SONET-WDM ring. The objective is to minimize the total cost of optical add-drop multiplexers (OADMs) and inter-ring hub equipment, while satisfying intra-ring and inter-ring capacities. We develop integer programming (IP) formulations for the problem and devise some reformulations for enhancing the mathematical representation of the proposed IP model. By investigating the polyhedral structure of the problem, we develop some valid inequalities that provide a tight lower bound for the problem. Dealing with the inherent computational complexity of the problem, we also devise an effective tabu search procedure for finding a feasible solution of good quality within reasonable computation time. Computational results are provided to demonstrate the relative strength of the proposed formulations, and to reveal the efficacy of the lower and upper bound procedures for solving the problem.