Accelerating Column Generation Algorithm Using Machine-Learning-Based Column Elimination

The column generation (CG) algorithm is widely used in large-scale optimization problems. However, a large amount of columns in the restricted master problem (RMP) makes the computing process very time-consuming. This paper proposes a machine learning based column elimination strategy to accelerate the CG algorithm. Our approach represents the RMP by a bipartite graph and applies a learned Graph Neural Network model to predict redundant columns to be eliminated from the RMP, so as to reduce the time cost of solving the RMP and iterations required for convergence. Our approach is tested on cutting stock problem instances. Compared with the vanilla CG algorithm, the iterations and time required for convergence are reduced by up to 31 % and 48%, respectively. Furthermore, our approach shows great generalization to cutting stock problem instances of different sizes.