Robust network design: Formulations, valid inequalities, and computations

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 [21]. 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.

Single-commodity robust network design problem: Complexity, instances and heuristic solutions

“…Bertsimas and Sim [7] introduced Γ-robustness as a general model for robustification. Exact approaches that apply this type of robustness to multicommodity network design are presented in [19].…”

Future research directions in design of reliable communication systems

“…The so-called Γ -Robust Network Design Problem has been studied in detail in a series of papers by Koster et al, i.e., in [88][89][90]. The following description has been merely taken from Koster and Kutschka [87].…”

“…Therefore, it would be fairer to compare with Γ = ∞, i.e., the case where the network is designed ford k +d k instead ofd k . Figure 9 shows the results for four test instances and different values of Γ (see [90] for more details). For Γ = 5 about 10 % of the cost can be saved for all considered network instances.…”

“…In some cases it may be beneficial to avoid these extra variables by separating the exponentially-sized set of constraints resulting from a straightforward linearization (see Fischetti and Monaci [48]) or to project the polyhedron to a subspace of the original variables (see the work of Claßen et al [28]). In addition, the derivation of additional valid inequalities can be considered (see Koster et al [90]). …”

A comparison of routing sets for robust network design

“…The polytope introduced by Bertsimas and Sim [13], used for robust network design problems in [6,23,24,20,26], satisfies the assumption of (b) when the number of deviations allowed is integer. We present examples in Section 4 showing that it is not possible, in general, to order opt(F 2 ), opt(F V ) and opt(F aff ).…”