An Augmented Lagrangian Algorithm for Large Scale Multicommodity Routing

Larsson, Torbjörn; Yuan, Di

doi:10.1023/b:coap.0000008652.29295.eb

Cited by 30 publications

(46 citation statements)

References 51 publications

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“…In [2], P. Chardaire and A. Lisser claim that in real transmission networks the number of saturated arcs is usually no more than 10 percent of the total number of arcs. T. Larsson and Di Yuan in [11] make the same observation on their test problems. McBride and Mamer report the same in [14].…”

Section: Introductionmentioning

confidence: 68%

“…The arc costs, commodities, and demands are generated in a way similar to that of planar networks. These two sets of problems are solved in [11]. The data can be downloaded from http://www.di.unipi.…”

Section: Test Problemsmentioning

confidence: 99%

“…The problems Sioux-Falls, Winnipeg, Barcelona are solved in [11]; there the demands of Winnipeg and Barcelona are divided, as in [11], by 2.7 and 3 respectively, to make those problems feasible. The last three problems, Chicago-sketch, Chicago-region and Philadelphia can be downloaded from http://www.bgu.ac.il/~bargera/tntp/.…”

Section: Test Problemsmentioning

confidence: 99%

“…A. Fragioni and G. Gallo [7] implement a bundle type approach. In a recent contribution, Larsson and Yuang [11] apply an augmented Lagrangian algorithm that combines Lagrangian relaxation and nonlinear penalty technique. They introduce nonlinear penalty in order to improve the dual convergence and obtain convergence to a primal solution.…”

Section: Introductionmentioning

confidence: 99%

“…As in [11], we focus on problems with many commodities, each one having one origin and one destination node. The subproblems are simple shortest path problems, possibly very numerous.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM

Babonneau

Merle²,

Vial

2006

Operations Research

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In this paper, we propose to solve the linear multicommodity flow problem using a partial Lagrangian relaxation. The relaxation is restricted to the set of arcs that are likely to be saturated at the optimum. This set is itself approximated by an active set strategy. The partial Lagrangian dual is solved with Proximal-ACCPM, a variant of the analytic center cutting plane method. The new approach makes it possible to solve huge problems when few arcs are saturated at the optimum, as it appears to be the case in many practical problems.Acknowledgments.

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Section: Introductionmentioning

confidence: 68%

Section: Test Problemsmentioning

confidence: 99%

Section: Test Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…As in [11], we focus on problems with many commodities, each one having one origin and one destination node. The subproblems are simple shortest path problems, possibly very numerous.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM

Babonneau

Merle²,

Vial

2006

Operations Research

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Multicommodity Flows

Vaidyanathan¹,

Ahuja²

2011

Wiley Encyclopedia of Operations Research and Management Science

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The multicommodity flow problem is a generalization of the minimum cost network flow problem. In this problem, several commodities governed by their own network flow constraints share the same underlying network. Given the supplies and demands of the different commodities, the shared capacity of each arc in the network, and cost of flow of each commodity on each arc, the objective is to determine the flow that minimizes the total cost. The multicommodity flow problem has been extensively applied to solve problems in areas such as transportation, telecommunications, and scheduling. In this article, we introduce the multicommodity flow problem, outline some of its applications, and describe efficient methods to solve the problem.

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Decomposition techniques for the minimum toll revenue problem

2004

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The objective of the minimum toll revenue (MINREV) problem is to find tolls that simultaneously cause users to use the transportation network efficiently and minimize the total toll revenues that must be collected. This article investigates the Dantzig-Wolfe (DW) decomposition as an approach for solving the MINREV problem and establishes its relationships with a cutting plane algorithm and other proposed approaches. The article also identifies the variant of DW decomposition most suitable for implementation. Numerical experiments with real transportation networks suggest that DW decomposition is robust and should be used when the problems are too large for standard linear programming software. Although transportation planning is the application emphasized in this article, it should be noted that the MIN-REV problem also has applications in telecommunication network design and control.

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An Augmented Lagrangian Algorithm for Large Scale Multicommodity Routing

Cited by 30 publications

References 51 publications

Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM

Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM

Multicommodity Flows

Decomposition techniques for the minimum toll revenue problem

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