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

Authors:
F. Babonneau;O. du Merle;J. -P. Vial
Affiliations:
Logilab, HEC, Universit de Genve, 40 Bd du Pont dArve, CH-1211 Geneva, Switzerland;Air France, Operations Research Department, 1 Avenue du Marchal Devaux, 91550 Paray-Vieille-Poste, France;Logilab, HEC, Universit de Genve, 40 Bd du Pont dArve, CH-1211 Geneva, Switzerland
Venue:
Operations Research
Year:
2006

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Abstract

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 appears to be the case in many practical problems.