A note on the primal-dual column generation method for combinatorial optimization

In this paper, we address the primal-dual column generation technique, which relies on well-centred suboptimal solutions of the restricted master problems. We summarize new theoretical developments and present computational results for two classical combinatorial optimization problems, in which this technique has not been tested before. The results show that the primal-dual column generation technique usually leads to substantial reductions in the number of iterations and CPU time when compared to two other well-established approaches: the classical column generation technique and the analytic centre cutting plane method.