José André de Moura Brito

Column Generation in Integer Linear Programming

We present an exact method for integer linear programming problems that combines branch and bound with column generation at each node of the search tree. For the case of models involving binary column vectors only, we propose the use of so-called geometrical cuts to be added to the subproblem in order to eliminate previously generated columns. This scheme could be applied to general integer problems without specific structure. We report computational results on a successful application of this approach to a telecommunications network planning problem.

Column Generation Method for Network Design

This work deals with the Two-architecture Network Problem, which consists in satisfying growing traffic demand by superimposing rings on an existing meshed network. The goal of this work is to solve the proposed mathematical model via column generation techniques. Firstly a complete model is proposed, then it is simplified to become more manageable. A branch-and-price approach is presented with all its problem-dependent issues. The numerical experience reported consists of two cases, one of 7 nodes and 11 edges, the other with 10 nodes and 36 edges, both drawn from real European telecommunications networks.