Optimization models and algorithms for the design of ring networks

Abstract

In this thesis, we propose optimization models and algorithms for the design of telecommunication networks with ring topology. First, we consider the problem of designing a local network in a two-level telecommunication network. Given a cluster with one or two hubs, central offices (COs) and conduits which connect them, the problem is to find a set of unidirectional path switched rings (UPSRs) which covers all COs and hubs, and satisfies all the traffic demands at minimum cost. We decomposed the problem into master problem and subproblem and presented integer programming models of them. Since master problem formulation has exponentially many columns, we applied the column generation technique to solve the LP relaxation. Then we used a branch-and-bound algorithm to obtain an integer solution. For the optimization of subproblem that generates profitable columns of the master problem formulation, a class of strong valid inequalities was derived and a branch-and-cut algorithm was applied. Computational results on problem instances of practical size show that our algorithm yields optimal or near optimal solutions to the problem in a short time. Second, we consider the traffic grooming problem for the design of SONET/ WDM (Synchronous Optical NETwork/Wavelength Division Multiplexing) ring networks, which is also referred to as the stacked ring design problem. Given a physical network with ring topology and a set of traffic demands between pairs of nodes, we are to obtain a stack of rings with the objective of minimizing the number of ADMs installed at the nodes. This problem arises when a single ring capacity is not large enough to accommodate all the given demands. We consider all types of SONET ring architectures: UPSR, two-fiber bidirectional line switched ring (BLSR/2), and BLSR/4. As a solution method, an efficient algorithm based on the branch-and-price approach has been reported in the literature for the problem in which only UPSR was considered. In this st...