This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree.
In this article we study capacitated network design problems. We unify and extend polyhedral results for directed, bidirected and undirected link capacity models. Based on valid inequalities for a network cut we show that regardless of the link capacity model, facets of the polyhedra associated with such a cut translate to facets of the original network design polyhedra if the two subgraphs defined by the network cut are (strongly) connected. Our investigation of the facial structure of the cutset polyhedra allows to complement existing polyhedral results for the three variants by presenting facet-defining flow-cutset inequalities in a unifying way. In addition, we present a new class of facet-defining inequalities, showing as well that flow-cutset inequalities alone do not suffice to give a complete description for single-commodity, single-module cutset polyhedra in the bidirected and undirected case – in contrast to a known result for the directed case. The practical importance of the theoretical investigations is highlighted in an extensive computational study on 27 instances from the Survivable Network Design Library (SNDlib).
We estimate potential energy savings in IP-over-WDM networks achieved by switching off router line cards in low-demand hours. We compare three approaches to react on dynamics in the IP traffic over time, FUFL,
DUFL and DUDL. They provide different levels of freedom in adjusting the routing of lightpaths in the WDM layer and the routing of demands in the IP layer. Using MILP models based on realistic network topologies and node architectures as well as realistic demands, power, and cost values, we show that already a simple monitoring of the lightpath utilization in order to deactivate empty line cards (FUFL) brings substantial
benefits. The most significant savings, however, are achieved by rerouting traffic in the IP layer (DUFL), which allows emptying and deactivating lightpaths together with the corresponding line cards. A
sophisticated reoptimization of the virtual topologies and the routing in the optical domain for every demand scenario (DUDL) yields nearly no additional profits in the considered networks.
Given a general mixed integer program (MIP), we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity flow formulations. We
identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of SCIP and CPLEX. We make use of the complemented mixed integer rounding framework (cMIR) but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speeds-up the computation for a large set of MIPs coming from network design problems
by a factor of two on average.
Affinely-Adjustable Robust Counterparts provide tractable alternatives to (two-stage) robust programs with arbitrary recourse. We apply them to robust network design with polyhedral demand uncertainty, introducing the affine routing principle. We compare the affine routing to the well-studied static and dynamic routing schemes for robust network design. All three schemes are embedded into the general framework of two-stage network design with recourse. It is shown that affine routing can be seen as a generalization of the widely used static routing still being tractable and providing cheaper solutions. We investigate properties on the demand polytope under which affine routings reduce to static routings and also develop conditions on the uncertainty set leading to dynamic routings being affine. We show however that affine routings suffer from the drawback that (even totally) dominated demand vectors are not necessarily supported by affine solutions. Uncertainty sets have to be designed accordingly. Finally, we present computational results on networks from SNDlib. We conclude that for these instances the optimal solutions based on affine routings tend to be as cheap as optimal network designs for dynamic routings. In this respect the affine routing principle can be used to approximate the cost for two-stage solutions with free recourse which are hard to compute.
In this paper, we study the influence of technology, traffic properties and price trends on optimized
design of a reference IP-over-WDM network with rich underlying fiber topology. In each network node,
we investigate the optimal degree of traffic switching in an optical (lambda) domain versus an electrical
(packet) domain, also known as measure of \emph{node transparency}. This measure is studied in connection to changes in
traffic volume,
demand affinity, optical circuit speeds and equipment cost. By applying variable design constraints,
we assess the relative roles of the two distinct equipment groups, IP routers and optical
cross-connects, with respect to resulting changes in cost-sensitive network architectures
We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost
installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation that takes many practical side constraints into account, including node hardware, several bitrates, and survivability against single physical node or link failures. This model is solved using a branch-and-cut approach with problem-specific preprocessing and cutting planes based on either of the two layers. On several realistic two-layer planning scenarios, we show that these cutting planes are still useful in the multi-layer context,
helping to increase the dual bound and to reduce the optimality gaps.
In this paper, we present a model-based optimization approach for the design of multi-layer networks. The proposed framework is based on a series of increasingly abstract models – from a general technical system model to a problem specific mathematical model – which are used in a planning cycle to optimize the multi-layer networks. In a case study we show how central design questions for an IP-over-WDM network architecture can be answered
using this approach. Based on reference networks from the German research project EIBONE, we investigate the influence of various planning parameters on the total design cost. This includes a comparison of point-to-point vs. transparent optical layer architectures, different traffic distributions, and the use of PoS vs. Ethernet interfaces.
In this paper we study a certain cardinality constrained packing integer program which is motivated by the problem of dimensioning a cut in a two-layer network. We prove NP-hardness and consider the facial structure of the corresponding polytope. We provide a complete description for the smallest nontrivial case and develop two general classes of facet-defining inequalities. This approach extends the
notion of the well known cutset inequalities to two network layers.
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 [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.