Benders, metric and cutset inequalities for multicommodity capacitated network design

Costa, Alysson M.; Cordeau, Jean‐François; Gendron, Bernard

doi:10.1007/s10589-007-9122-0

Cited by 58 publications

(59 citation statements)

References 19 publications

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“…For these reasons, we rely instead on the multi-commodity capacitated fixed charge network design (MCND) problem introduced by [1], [2], [3] which deals with the simultaneous optimization of capacity installation cost and traffic flow routing cost. In this problem, a fixed cost is incurred for opening a link and a linear routing cost is paid for sending traffic flow over an edge (or arc).…”

Section: Introductionmentioning

confidence: 99%

Lagrangian relaxation for the time-dependent combined network design and routing problem

Papadimitriou¹,

Fortz

Gorgone

2015

2015 IEEE International Conference on Communications (ICC)

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Abstract-In communication networks, the routing decision process (distributed and online) remains decoupled from the network design process, i.e., resource installation and allocation planning process (centralized and offline). To reconcile both processes, we ambition to design a distributed optimization technique aware of distributed nature of the routing process by decomposing the optimization problem along same dimensions as (distributed) routing decision process. For this purpose, we generalize the capacitated multi-commodity capacitated fixed charge network design (MCND) class of problems by including different types of fixed costs (installation and maintenance costs) and variable costs (routing costs) but also variable traffic demands over multiple periods. However, conventional integer programming methods can typically solve only small to medium size instances. As an alternative, we propose a Lagrangian approach for computing a lower bound by relaxing the flow conservation constraints such that the Lagrangian subproblem itself decomposes by node. Though this approach yields one subproblem per network node, solving the Lagrangian dual by means of the bundle method remains a complex computational tasks. However, the approach is more robust than any LP solvers and it always returns some solutions. Instead, we proved that CPLEX, which uses the Dual Simplex algorithm, is not able to provide a solution for large instances.

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Section: Introductionmentioning

confidence: 99%

Lagrangian relaxation for the time-dependent combined network design and routing problem

Papadimitriou¹,

Fortz

Gorgone

2015

2015 IEEE International Conference on Communications (ICC)

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“…See for example [10], [32], [4], [8], [27], [14] and references therein. The graph in Figure 1(a) is an instance of the RNL problem with splittable flows on a directed graph with asymmetric demands.…”

Section: Introductionmentioning

confidence: 99%

The robust network loading problem with dynamic routing

Mattia

2012

Comput Optim Appl

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The Robust Network Loading Problem (RNL) can be stated as follows. Given a graph and a set of traffic matrices, install minimum cost integer capacities on the edges such that all the matrices can be routed non simultaneously on the network. The routing scheme is said to be dynamic if we can choose a (possibly) different routing for every matrix, it is called static if the routing must be the same for all the matrices. The flows are unsplittable if each point-to-point demand (commodity) must use a single path, they are splittable if the flow for every commodity can be splitted along several paths. In this paper we present the first exact approach for solving the RNL problem with splittable flows and dynamic routing under polyhedral uncertainty for the demands. A branch-and-cut algorithm based on the capacity formulation of the problem defined by metric inequalities is developed, and polyhedral results are given. The separation problem is formulated as a bilevel programming problem and a corresponding single level problem is derived. Computational results are presented.keywords: network design, robustness, branch-and-cut 1

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“…Base cutset inequalities are necessary for a capacity vector to be feasible, but it is well-known that they are not sufficient in general [CCG09]. By applying Chvátal-Gomory (CG) rounding to base cutset inequalities (cf.…”

Section: Cutset Inequalitiesmentioning

confidence: 99%

Chance-Constrained Optimization of Reliable Fixed Broadband Wireless Networks

Claßen

Koster

Coudert³

et al. 2014

INFORMS Journal on Computing

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In this paper, we extend our former investigation on conceiving reliable fixed point-topoint wireless networks under outage probability constraints [CCKN11b; CCKN11a]. We consider the problem of determining the minimum cost bandwidth assignment of a network, while guaranteeing a reliability level of the solution. If the optimal bandwidth assignment and routing of traffic demands are accomplished, the reliability criterion requires that network flows remain feasible with high probability, regarding that the performance of microwave links is prone to variations due to external factors, e.g., weather. We introduce a chance-constrained programming approach to tackle this problem and we present reformulations to standard Integer Linear Programming (ILP) models, including a budget constrained formulation. To improve the solving performance, we propose new valid inequalities and a primal heuristic. Computational results present a performance analysis of the valid inequalities and the heuristic. Further, the outperformance of the novel model compared to more traditional approaches is documented.

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Benders, metric and cutset inequalities for multicommodity capacitated network design

Abstract: Multicommodity capacitated network design, Benders decomposition, Metric inequalities, Cutset inequalities,

Cited by 58 publications

References 19 publications

Lagrangian relaxation for the time-dependent combined network design and routing problem

Lagrangian relaxation for the time-dependent combined network design and routing problem

The robust network loading problem with dynamic routing

Chance-Constrained Optimization of Reliable Fixed Broadband Wireless Networks

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