Routing and capacity assignment models and algorithms for the design of telecommunication networks

Abstract

We consider several routing and capacity assignment problems for the design of current and future fiber-optic telecommunication networks, specifically for interoffice transmission networks. We present formulations of the problems and algorithms for them which are based on the integer programming approaches. First, we consider the primary path selection and working capacity assignment problem (PWP) for the design of current synchronous transmission networks. Given an undirected physical network, a set of selected pairs of nodes, the traffic requirement for each selected pairs of nodes, and one or more types of link facilities with discrete capacity and cost structure, (PWP) is to determine a path from a given set of candidate primary paths for each pair of nodes and the number of each type of link facilities to be installed on each link such that all the traffic requirements can be routed on the selected paths simultaneously at minimum installation costs. We present an integer programming formulation of (PWP), and then derive valid inequalities which can be used to tighten the LP relaxation of the proposed integer programming formulation of (PWP). Especially, we develop a new cut generation scheme which can generate valid inequalities for a specific knapsack problem arising from the capacity constraint on a link. We also customize the known valid inequalities. Using these results, we develop a branch-and-cut algorithm to solve (PWP) to optimality. Computational results show that the proposed cut generation scheme significantly enhance the performance of the algorithm. Second, we consider an integer programming based optimization algorithm to solve the spare capacity assignment problem (SCAP) for the design of current synchronous transmission networks. Given predetermined working channels on each link of the network, the problem is to determine the spare capacity that should be added on each link to ensure rerouting of the traffic in case of a link failure. We ...