Enhancing Column Generation by a Machine-Learning-Based Pricing Heuristic for Graph Coloring

• URL: http://arxiv.org/abs/2112.04906v1
• Date: Wed, 8 Dec 2021 03:58:25 GMT
• Title: Enhancing Column Generation by a Machine-Learning-Based Pricing Heuristic for Graph Coloring
• Authors: Yunzhuang Shen, Yuan Sun, Xiaodong Li, Andrew Eberhard, Andreas Ernst
• Abstract summary: Column Generation (CG) is an effective method for solving large-scale optimization problems. We propose a Machine-Learning Pricing Heuristic that can generate many high-quality columns efficiently.
• Score: 5.278929511653199
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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