Solving large-scale linear multicommodity flow problems with an active set strategy and proximal-analytic center cutting-plane method

Solving large-scale linear multicommodity flow problems with an active set strategy and proximal-analytic center cutting-plane method

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Article ID: iaor2008955
Country: United States
Volume: 54
Issue: 1
Start Page Number: 184
End Page Number: 197
Publication Date: Jan 2006
Journal: Operations Research
Authors: , ,
Keywords: programming: integer
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.

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