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Robust Network Design: Formulations, Valid Inequalities, and Computations

Arie M.C.A. Koster(koster***at***math2.rwth-aachen.de)
Manuel Kutschka(kutschka***at***math2.rwth-aachen.de)
Christian Raack(raack***at***zib.de)

Abstract: Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this paper we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of Bertsimas and Sim (2004). We present three different mathematical formulations for this problem, provide valid inequalities, study the computational implications, and evaluate the realized robustness. To enhance the performance of the mixed-integer programming solver we derive robust cutset inequalities generalizing their deterministic counterparts. Instead of a single cutset inequality for every network cut, we derive multiple valid inequalities by exploiting the extra variables available in the robust formulations. We show that these inequalities define facets under certain conditions and that they completely describe a projection of the robust cutset polyhedron if the cutset consists of a single edge. For realistic networks and live traffic measurements we compare the formulations and report on the speed up by the valid inequalities. We study the “price of robustness” and evaluate the approach by analyzing the real network load. The results show that the robust optimization approach has the potential to support network planners better than present methods.

Keywords: network design, robust optimization, traffic demand uncertainty, cutset inequalities, integer linear programming

Category 1: Robust Optimization

Category 2: Combinatorial Optimization (Polyhedra )

Category 3: Integer Programming (Cutting Plane Approaches )

Citation: submitted to Networks

Download: [PDF]

Entry Submitted: 09/20/2011
Entry Accepted: 09/20/2011
Entry Last Modified: 09/20/2011

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