[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125274-en":3,"doc-seo-125274-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125274,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Machine Learning-Enhanced Ant Colony Optimization for Column Generation","Column generation (CG) addresses optimization problems with a large number of variables by iteratively solving a restricted master problem and generating new columns using dual information. A major bottleneck is the repeated solution of pricing subproblems, which are often NP-hard. The proposed MLACO method trains a machine learning model to predict optimal pricing solutions and then injects the predictions into the ACO sampling process to produce multiple high-quality columns. Experiments on bin packing with conflicts show improved CG performance and faster solution times within Branch-and-Price.","Machine Learning-Enhanced Ant Colony Optimization for  \nColumn Generation  \nHongjie Xu  \nSchool of Computing Technologies, RMIT University Melbourne, Australia [s3880497@student.rmit.edu.au](s3880497@student.rmit.edu.au)  \nYunzhuang Shen  \nUniversity of Technology Sydney Sydney, Australia [yunzhuang.shen@uts.edu.au](yunzhuang.shen@uts.edu.au)  \nYuan Sun  \nLa Trobe Business School, La Trobe University Melbourne, Australia [yuan.sun@latrobe.edu.au](yuan.sun@latrobe.edu.au)  \nABSTRACT  \nColumn generation (CG) is a powerful technique for solving optimization problems that involve a large number of variables or columns. This technique begins by solving a smaller problem with a subset of columns and gradually generates additional columns as needed. However, the generation of columns often requires solving difficult subproblems repeatedly, which can be a bottleneck for CG. To address this challenge, we propose a novel method called machine learning enhanced ant colony optimization (MLACO), to efficiently generate multiple high-quality columns from a subproblem. Specifically, we train a ML model to predict the optimal solution of a subproblem, and then integrate this ML prediction into the probabilistic model ofACO to sample multiple high-quality columns. Our experimental results on the bin packing problem with conflicts show that the MLACO method significantly improves the performance of CG compared to several state-of-the-art methods. Furthermore, when our method is incorporated into a Branch-andPrice method, it leads to a significant reduction in solution time.  \nCCS CONCEPTS  \n• Applied computing → Operations research; • Computing methodologies → Machine learning.  \nKEYWORDS  \nAnt colony optimization, machine learning, column generation, combinatorial optimization  \nACM Reference Format:  \nHongjie Xu, Yunzhuang Shen, Yuan Sun, and Xiaodong Li. 2024. Machine Learning-Enhanced Ant Colony Optimization for Column Generation. In Genetic and Evolutionary Computation Conference (GECCO’24), July 14– 18, 2024, Melbourne, VIC, Australia. ACM, New York, NY, USA, 9 pages. [https://doi.org/10.1145/3638529.3654043](https://doi.org/10.1145/3638529.3654043)  \nThis work is licensed under a Creative Commons Attribution International 4.0 License.  \nGECCO’24, July 14–18, 2024, Melbourne, VIC, Australia © 2024 Copyright held by the owner/author(s) .  \nACM ISBN 979-8-4007-0494-9/24/07 .  \n[https://doi.org/10.1145/3638529.3654043](https://doi.org/10.1145/3638529.3654043)  \nXiaodong Li  \nSchool of Computing Technologies, RMIT University Melbourne, Australia [xiaodong.li@rmit.edu.au](xiaodong.li@rmit.edu.au)  \n1 INTRODUCTION  \nColumn generation (CG) is a powerful method for solving linear programs (LP) that have a large number of variables (or columns) [17] . It is commonly used to obtain tight LP bounds to accelerate the process of the branch-and-bound method in combinatorial optimization [1] . CG is especially beneficial for tackling optimization problems that have a decomposable structure, such as vehicle routing, bin packing, and graph coloring problems.  \nCG solves a large-scale LP in iterative steps, starting from the LP containing a subset of columns, i.e., the restricted master problem (RMP) . In an iteration, CG solves the current RMP and uses its dual solution to generate new columns that can improve the current RMP. Such columns should have negative reduced costs, and finding them typically involves solving an NP-hard subproblem called pricing problem. At optimality, no column with negative reduced costs can be further generated, and existing columns with nonzero values form an optimal solution to the original large-scale LP.  \nRepeatedly solving pricing problems is often a bottleneck in CG [17], and researchers have devised different approaches to tackle this issue, including exact methods, heuristics, and metaheuristics. It is widely recognized that the performance of CG is heavily influenced by both the quality and quantity of generated colu","cbCain2gXr81SbKS","https://ap.wps.com/l/cbCain2gXr81SbKS","pdf",274143,1,9,"English","en",105,"# Introduction\n## Column generation and pricing bottleneck\n## MLACO: hybrid machine learning and ACO for column generation","[{\"question\":\"What problem does column generation (CG) address?\",\"answer\":\"CG solves linear programs with a large number of variables (columns) by iteratively refining bounds using a restricted master problem and generated columns.\"},{\"question\":\"Why is the pricing problem a bottleneck in CG?\",\"answer\":\"Finding columns with negative reduced costs typically requires solving an NP-hard pricing subproblem repeatedly.\"},{\"question\":\"How does MLACO improve CG performance?\",\"answer\":\"MLACO trains a machine learning model to predict optimal solutions for pricing instances and incorporates these predictions into the ant colony optimization (ACO) probabilistic model to sample multiple high-quality columns, reducing solution time in Branch-and-Price.\"}]","Machine Learning-Enhanced Ant Colony Optimization for Column Generation | 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problem does column generation (CG) address?","Question",{"text":75,"@type":76},"CG solves linear programs with a large number of variables (columns) by iteratively refining bounds using a restricted master problem and generated columns.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why is the pricing problem a bottleneck in CG?",{"text":80,"@type":76},"Finding columns with negative reduced costs typically requires solving an NP-hard pricing subproblem repeatedly.",{"name":82,"@type":73,"acceptedAnswer":83},"How does MLACO improve CG performance?",{"text":84,"@type":76},"MLACO trains a machine learning model to predict optimal solutions for pricing instances and incorporates these predictions into the ant colony optimization (ACO) probabilistic model to sample multiple high-quality columns, reducing solution time in 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