[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125982-en":3,"doc-seo-125982-105":31,"detail-sidebar-cat-0-en-105":93},{"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":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},125982,687207024478,"Liam","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Machine Learning-Enhanced Ant Colony Optimization for Column Generation","Column generation addresses optimization problems with many variables by repeatedly solving a restricted master problem and generating new columns. A key bottleneck is that column generation often requires repeatedly solving difficult pricing subproblems. MLACO proposes using machine learning to predict optimal pricing solutions from problem features and statistics, then injecting this prediction into an ant colony optimization sampling process to obtain multiple high-quality columns. Experiments on bin packing with conflicts show clear CG performance gains versus state-of-the-art methods, and incorporating MLACO into Branch-and-Price reduces solution time.","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)  \narXiv :2407 .01546v1 [ cs .NE] 23 Apr 2024  \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)  \nPermission to make digital or hard copies of part or all ofthis work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the owner/author(s) .  \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","cbCainqwnyQ34QxJ","https://ap.wps.com/l/cbCainqwnyQ34QxJ","pdf",748854,5,1,9,"English","en",105,"# Abstract\n# Introduction\n## Column Generation and Pricing Bottleneck\n## Proposed MLACO Method\n## Advantages Over Existing Approaches","[{\"question\":\"What problem does column generation solve, and how does it work?\",\"answer\":\"Column generation solves large linear programs with many variables by iteratively solving a restricted master problem and using dual information to generate new columns. The process continues until no column with negative reduced cost can be found.\"},{\"question\":\"Why is pricing a bottleneck in column generation?\",\"answer\":\"Pricing requires solving a typically NP-hard subproblem to find columns with negative reduced costs. Repeating this step many times can significantly slow down the overall CG procedure.\"},{\"question\":\"How does MLACO integrate machine learning with ant colony optimization?\",\"answer\":\"MLACO trains a machine learning model to map problem features and statistics to optimal pricing solutions. During column generation, the ML prediction is incorporated into the ant colony optimization probabilistic model to sample diverse, high-quality columns.\"}]","Machine Learning-Enhanced Ant Colony Optimization for Column Generation | PDF",1785902372,23,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":88,"head_meta":90,"extra_data":92,"updated_unix":29},"machine-learning-enhanced-ant-colony-optimization-for-column-generation-125982","",{"@graph":37,"@context":87},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/document/research-report/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/document/machine-learning-enhanced-ant-colony-optimization-for-column-generation-125982/125982/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-23","2026-08-05",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83],{"name":74,"@type":75,"acceptedAnswer":76},"What problem does column generation solve, and how does it work?","Question",{"text":77,"@type":78},"Column generation solves large linear programs with many variables by iteratively solving a restricted master problem and using dual information to generate new columns. The process continues until no column with negative reduced cost can be found.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"Why is pricing a bottleneck in column generation?",{"text":82,"@type":78},"Pricing requires solving a typically NP-hard subproblem to find columns with negative reduced costs. Repeating this step many times can significantly slow down the overall CG procedure.",{"name":84,"@type":75,"acceptedAnswer":85},"How does MLACO integrate machine learning with ant colony optimization?",{"text":86,"@type":78},"MLACO trains a machine learning model to map problem features and statistics to optimal pricing solutions. During column generation, the ML prediction is incorporated into the ant colony optimization probabilistic model to sample diverse, high-quality columns.","https://schema.org",{"og:url":53,"og:type":89,"og:title":13,"og:site_name":60,"og:description":14},"article",{"robots":91,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":94},[95,99,103,107,111,116,121,124,128,131,135],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":96,"show_sort_weight":97,"slug":98},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":100,"show_sort_weight":101,"slug":102},"Literature",80,"literature",{"id":54,"doc_module":4,"doc_module_name":47,"category_name":104,"show_sort_weight":105,"slug":106},"Exam",70,"exam",{"id":20,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":109,"slug":110},"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":47,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":22,"doc_module":4,"doc_module_name":47,"category_name":125,"show_sort_weight":126,"slug":127},"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":47,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":47,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":47,"category_name":137,"show_sort_weight":20,"slug":138},19,"General","general"]