Enhancing Column Generation by a Machine-Learning-Based Pricing Heuristic for Graph Coloring
This addresses the computational bottleneck in large-scale optimization for researchers and practitioners, though it is incremental as it builds on existing CG methods with a novel heuristic.
The paper tackles the bottleneck of solving NP-hard pricing problems in Column Generation by proposing a Machine-Learning-based Pricing Heuristic (MLPH) that predicts optimal solutions to guide efficient column generation, empirically showing significant enhancement over six state-of-the-art methods in graph coloring.
Column Generation (CG) is an effective method for solving large-scale optimization problems. CG starts by solving a sub-problem with a subset of columns (i.e., variables) and gradually includes new columns that can improve the solution of the current subproblem. The new columns are generated as needed by repeatedly solving a pricing problem, which is often NP-hard and is a bottleneck of the CG approach. To tackle this, we propose a Machine-Learning-based Pricing Heuristic (MLPH)that can generate many high-quality columns efficiently. In each iteration of CG, our MLPH leverages an ML model to predict the optimal solution of the pricing problem, which is then used to guide a sampling method to efficiently generate multiple high-quality columns. Using the graph coloring problem, we empirically show that MLPH significantly enhancesCG as compared to six state-of-the-art methods, and the improvement in CG can lead to substantially better performance of the branch-and-price exact method.