Section: New Results

Aggregation techniques to reduce the size of column generation models

We proposed an aggregation method to reduce the size of column generation (CG) models for a class of set-covering problems in which the feasible subsets depend on a resource constraint. The aggregation relies on a correlation between the resource consumption of the elements and the corresponding optimal dual values. The aggregated model obtained allows to find good quality lower bounds more rapidly than the original CG algorithm. The speedup is due to less primal and dual variables in the master, and to an aggregated pricing sub-problem. To guarantee optimaly, we designed an algorithm that iteratively refines the aggregation until the CG optimum is reached. Computational results prove the usefulness of our methods.