{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/enhancing-column-generation-by-a-machine","title":"Enhancing Column Generation by a Machine-Learning-Based Pricing Heuristic for Graph Coloring","arxiv_id":"2112.04906","date":"2021-12-08","proceeding":null,"authors":["Yunzhuang Shen","Yuan Sun","XiaoDong Li","Andrew Eberhard","Andreas Ernst"],"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.","url_abs":"https://arxiv.org/abs/2112.04906v3","url_pdf":"https://arxiv.org/pdf/2112.04906v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"enhancing-column-generation-by-a-machine","repo_url":"https://github.com/joey-shen/mlph","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}