Sur l'accélération de la convergence de la génération de colonnes

Nora Touati (1) , Lucas Létocart (1) , Anass Nagih (2)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LITA - Laboratoire d'Informatique Théorique et Appliquée

The use of the method of column generation was intensified during the last decades, in particular for the resolution of huge discrete problems in order to obtain a lagrangian bound. It is also integrated in a branch and bound method (branch-and-price) where it is used for the computation of the evaluation function at each node of the research tree. The efficiency of this method is very related to the resolution of the subproblems and to the quality of the columns generated at each iteration. Like iterative methods, it suffers from the long tail effect, particularly when it is used to solve degenerated problems. The scheme of column generation offers several possibilities for improvements. We present in this report some of these possibilities suggested in the literature, which are based on varied principles according to whether one operates on the primal or dual plan, or that acceleration relates to the resolution of the master problem, the subproblem or the whole process, or his hybridization with other resolution methods. At the end of this report, we focus our study on reoptimization techniques, which prove to be promising for the acceleration of column generation, particularly when the total time of resolution is dominated by that of the subproblems.

Mots clés: Génération de colonnes; stabilisation; réoptimisation

Domaines: Combinatoire [math.CO]

Nora Touati, Lucas Létocart, Anass Nagih. Sur l'accélération de la convergence de la génération de colonnes. 2006. ⟨hal-00145748⟩