A discrete optimization model for joint communication network design and facility engineering

Abstract

Optimal network design and facility engineering constructs network topologies that minimize total network cost while selecting facility types, allocating capacity, and routing traffic to accommodate demand and performance requirements. Such problems are characterized by large dimensionality even when relatively small networks are considered. This paper describes a data network design model based on a Mixed Integer/Linear Programming (MILP) formulation that does not, as do most other approaches, separate link capacity and facility selection from routing and topological design but fully integrates these processes in order to capture the very important couplings that exist between them. The performance constraints are incorporated into the model in such a way that they are linear but lead to the same grade of service as nonlinear average network delay constraints. Even the basic single-facility network design problem is NP-complete, and no exact solution can be obtained for large-scale networks. The multifacility problem adds even more computational complexity. We present a fast link reduction algorithm that efficiently designs single-facility or multifacility networks and yields robust local extrema. This algorithm is based on a special-purpose greedy drop procedure. In the absence of capacity allocation constraints, the capacity and flow assignment problem is solved optimally and efficiently as part of the overall design process. Numerical results are provided to demonstrate the computational efficiency of the algorithm. A dual relaxation procedure for the computation of a lower bound on network cost is also suggested. In addition, the properties of optimal multifacility, networks are discussed by comparing single-facility and multifacility assignment policies under various network traffic scenarios.