  Bundle methods are often used to solve dual problems that arise from
Lagrangian relaxations of large scale optimization problems. An example of such
problems is the train timetabling problem. This paper focuses on solving a dual
problem that arises from Lagrangian relaxation of a train timetabling
optimization program. The dual problem is solved using bundle methods. We
formulate and compare the performances of two different bundle methods: the
aggregate method, which is a standard method, and a new, disaggregate, method
which is proposed here. The two methods were tested on realistic train
timetabling scenarios from the Iron Ore railway line. The numerical results
show that the new disaggregate approach generally yields faster convergence
than the standard aggregate approach.
