A branch and cut algorithm for hub location problems with by Labbe M.

By Labbe M.

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The formulation given to CPLEX is the aggregated multicommodity flow formulation QHL3 with the additional constraints xij ≤ xjj for all (i, j ) ∈ A. The variables whose values are fixed to 0 or 1 during the preprocessing are removed from this formulation. We report the duality gap, the number of nodes in the branch and cut tree and the CPU time in Table 8. The duality gap is computed using the best upper bound found by any of the two methods. When the program stops because of the time limit or lack of memory then we report the final duality gap computed using the best upper bound of the corresponding method.

2462, Springer, Berlin, 2002 pp. 256–269 22. : Faces for a Linear Inequality in 0-1 Variables. Math. Program. 8, 165–178 (1975) 23. D. Thesis, Universit´e Libre de Bruxelles, 2002. be/ 24. : An Annotated Bibliography in Communication Network Design and Routing. In: Optimization Models and Methods for Communication Network Design and Routing. D.

The results did not change significantly. Based on this result and some preliminary tests, we decided to use Algorithm 3 during the preprocessing and to separate the cover inequalities on linear knapsacks for the remaining test instances as they have bigger sizes than the problems we solved up to now. We also adapted the separation of projection inequalities so that we only consider the commodities with nonzero traffic demands. In Table 11, we report the results for problems with 22 nodes. There is one problem that is not solved to optimality as we ran out of memory.

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