Dual Ascent in Column Generation for Multi-Commodity Network Flow problems
Enrico Bettiol  1@  , Mathieu Lacroix  1@  , Youcef Magnouche  2@  , Roberto Wolfler Calvo  1@  
1 : Laboratoire d'Informatique de Paris-Nord
Centre National de la Recherche Scientifique, Université Sorbonne Paris nord, Centre National de la Recherche Scientifique : UMR7030
2 : Huawei Technologies France [Boulogne-Billancour]
HUAWEI Technologies France

We present a reformulation-based dual ascent approach for the Multi-Commodity network Flow problem. More specifically, we consider the path-flow formulation of the linear relaxation of the problem and we solve it with a column generation. We apply a suitable reformulation to each restricted master problem of the column generation in such a way as to obtain a Lagrangian relaxation that can be decomposed into smaller and easier sub-problems and we apply a dual ascent step. This allows to efficiently obtain a good quality dual bound of the linear relaxation of the problem and we show comparisons with other approaches.


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