Interior Point Methods With Decomposition For Multicommodity Flow Problems

This paper introduces an approach by decomposition of an interior point method for solving multicommodity flow problems. First, we present this approach in the general framework of coupling constraints problems. Next, we propose to specialize the algorithm to the linear multicommodity network-fl- ow problems. We expose this specialization using the node-arc formulation. Then, we focus on the arc-path formulation and we propose decomposition method witch incorporates the interior point method into the Dantzig-Wolfe decomposition technique. The numerical results show the superiority of this last formulation. Finally, we report some numerical results obtained by testing these algorithms with data from the France-Telecom Paris district transmission network.