The multi-layered network design problem

Knippel, Arnaud; Lardeux, Benoit

doi:10.1016/j.ejor.2006.07.046

Cited by 22 publications

(20 citation statements)

References 17 publications

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“…We conducted a thorough computational study on a large set of instances. For the bi-layer network design problem, our branch-and-cut algorithm outperforms the cutting plane algorithm of Knippel and Lardeux (2007) by a factor of 10 in average.…”

Section: Benders Decomposition For Telecommunications Network Designmentioning

confidence: 99%

“…Gabrel et al (1999) introduce a constraint generation procedure based on a Benders decomposition for capacitated network design problems. Knippel and Lardeux (2007) and Ge ard et al (2007) extend this work to multi-layered networks and multi-period time scheduling, respectively. In Knippel et al (2003), the authors improve these methods using the knapsack-like structure of the master problem to facilitate its resolution.…”

Section: Multi-layer Network Designmentioning

confidence: 99%

“…Our branch-and-cut algorithm solves the Benders decomposition of the problem more than 10 times faster on average than the cutting planes from Knippel and Lardeux (2007).…”

Section: Multi-layer Network Designmentioning

confidence: 99%

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Models and algorithms for network design problems

Poss¹

2011

4OR-Q J Oper Res

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Section: Benders Decomposition For Telecommunications Network Designmentioning

confidence: 99%

Section: Multi-layer Network Designmentioning

confidence: 99%

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Models and algorithms for network design problems

Poss¹

2011

4OR-Q J Oper Res

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“…Metric inequalities allow us to eliminate flow variables at the cost of obtaining a non compact formulation, which requires the use of a cutting-plane approach. Metric inequalities have already been used in the literature, both for single-layer problems (see for example [7], [2]) and for two-layer problems (see for example [6], [17]) without survivability requirements. They have also been used when survivability issues must be taken into account (see for example [30], [29] and references therein).…”

Section: The Flow Formulationmentioning

confidence: 99%

“…In [18] a problem with survivability requirements and node hardware installation issues is addressed: the problem is solved by branch-and-cut using single-layer cuts. In [6] a model based on metric inequalities without survivability requirements, based on [17], is used to solve a variant of the problem belonging to the class that in this paper is called implicit lightpaths case (see Section 2). In [4] a Lagrangean approach is proposed.…”

Section: Introductionmentioning

confidence: 99%

Solving survivable two-layer network design problems by metric inequalities

Mattia

2010

Comput Optim Appl

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We address the problem of designing a multi-layer network with survivability requirements. We are given a two-layer network: the lower layer represents the potential physical connections that can be activated, the upper layer is made of logical connections that can be set up using physical links. We are given origin-destination demands (commodities) to be routed at the upper layer. We are also given a set of failure scenarios and, for every scenarios, an associated subset of commodities. The goal is to install minimum cost integer capacities on the links of both layers in order to ensure that the commodities can be routed simultaneously on the network. In addition, in every failure scenario the routing of the associated commodities must be guaranteed. We consider two variants of the problem and develop a branch-and-cut scheme based on the capacity formulation. Computational results on instances derived from the SNDLib for single node failure scenarios are discussed.keywords: optical network design, branch-and-cut

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Benders decomposition approach for the robust network design problem with flow bifurcations

Lee

2012

Networks

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We consider a network design problem in which flow bifurcations are allowed. The demand data are assumed to be uncertain, and the uncertainties of demands are expressed by an uncertainty set. The goal is to install facilities on the edges at minimum cost. The solution should be able to deliver any of the demand requirements defined in the uncertainty set. We propose an exact solution algorithm based on a decomposition approach in which the problem is decomposed into two distinct problems: (1) designing edge capacities; and (2) checking the feasibility of the designed edge capacities with respect to the uncertain demand requirements. The algorithm is a special case of the Benders decomposition method. We show that the robust version of the Benders subproblem can be formulated as a linear program whose size is polynomially bounded. We also propose a simultaneous cut generation scheme to accelerate convergence of the Benders decomposition algorithm. Computational results on real-life telecommunication problems are reported, and these demonstrate that robust solutions with very small penalties in the objective values can be obtained.

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The multi-layered network design problem

Cited by 22 publications

References 17 publications

Models and algorithms for network design problems

Models and algorithms for network design problems

Solving survivable two-layer network design problems by metric inequalities

Benders decomposition approach for the robust network design problem with flow bifurcations

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