[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-504941-105":59,"doc-detail-504941-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","learning-sat-encodings-for-constraint-satisfaction-problems-phd-thesis","Learning SAT Encodings for Constraint Satisfaction Problems - PhD Thesis","","Constraint programming addresses complex real-world problems, translating high-level constraint models into SAT instances to leverage efficient Boolean solvers. This thesis investigates how to select strong SAT encodings for pseudo-Boolean and linear integer constraints, where encoding choice can drastically change solving time. It applies and evaluates machine learning techniques across an empirical pipeline in three stages, improving performance over defaults, unseen classes, and general algorithm configuration tools.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/learning-sat-encodings-for-constraint-satisfaction-problems-phd-thesis/504941/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/learning-sat-encodings-for-constraint-satisfaction-problems-phd-thesis/504941.png","ImageObject",300,407,{"name":92,"@type":93},"EvelynWrites","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-22","2026-10-04",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why does choosing a SAT encoding matter for CSPs?","Question",{"text":112,"@type":113},"Different SAT encodings for the same constraint type can lead to dramatically different solving times, so the encoding choice strongly affects performance.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What constraint types does the thesis focus on?",{"text":117,"@type":113},"It investigates selecting SAT encodings for pseudoBoolean and linear integer constraints within constraint satisfaction settings.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the proposed machine learning approach select encodings?",{"text":121,"@type":113},"It evaluates a three-phase pipeline: selecting per constraint type using generic instance features, adding specialised constraint-focused features, and finally learning to select encodings for individual constraints.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},504941,1791273990,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":39,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145},687212989558,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Learning SAT Encodings for Constraint Satisfaction Problems  \nFelix Ulrich-Oltean  \nPhD  \nUniversity of York  \nComputer Science  \nSeptember 2023  \nAbstract  \nConstraint programming addresses many interesting and challenging problems in our world, including recent applications to contexts as diverse as allocating refugee relief funds, short-term mine planning and hardware circuit design.  \nUsers define their problems in high-level modelling languages which include descriptive global constraints. One of the most effective ways to solve constraint satisfaction problems (CSPs) is by translating them into instances of the Boolean Satisfiability Problem (SAT). For some global constraints in CSPs there exist many algorithms which encode the constraint into SAT; choosing an appropriate SAT encoding can alter the ultimate solving time dramatically.  \nWe investigate the problem of selecting the best SAT encoding for pseudoBoolean and linear integer constraints. Many machine learning techniques are explored, applied and evaluated to aid this selection. The result is a significant improvement in performance compared to the default choice and to the single best choice from a training set. The approach is successful even for previously unseen problem classes and it greatly outperforms a sophisticated general algorithm selection and configuration tool.  \nThis work provides a thorough empirical study and detailed analysis of each stage in the machine learning process as applied to choosing SAT encodings. It does this in three phases: firstly by using generic CSP instance features to select an encoding per constraint type for each instance, then by introducing new features which focus on the constraint types in question, and finally by learning to select encodings for individual constraints.  \nWe find that even generic instance features can produce good predictions, but that the specialised features introduced give more robust performance especially when predicting for unseen problem classes. Training to predict per constraint shows potential and leads to better performance for some problem classes, but per-instance selection is still competitive across the corpus of problems as a whole.  \nContents  \nAuthor Declaration vii  \nAcknowledgements viii  \nList of Figures x  \nList of Tables xii  \nList of Code Listings xiv  \nGlossary xv  \n1 Introduction: Solving Problems by Searching for Truth 1  \n1.1 Constraint Programming ............................... 2  \n1.2 Motivation ....................................... 5  \n1.3 Thesis and Research Questions .......................... 6  \n1.4 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7  \n1.5 Summary of Contributions ............................. 9  \n1.6 Style and Conventions ................................ 10  \n2 Background: Constraint problems and Boolean SAT 11  \n2.1 Constraint Satisfaction and Optimisation ..................... 12  \n2.1.1 Formal Definition of CSP . . . . . . . . . . . . . . . . . . . . . . . . . . 12  \n2.1.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  \n2.1.3 Solving CS Ps ................................. 14  \n2.1.4 Describing CSPs: Constraint Modelling .................. 15  \n2.1.5 Competitions ................................. 17  \n2.2 The Boolean Satisfiability Problem ........................ 19  \n2.2.1 Definitions .................................. 19  \n2.2.2 SAT Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20  \n2.2.3 SAT Encodings ................................ 23  \n2.3 Encoding Linear Integer Constraints to SAT .................... 25  \n2.3.1 Expressing Linear Integer Constraints as Pseudo-Boolean ...... 25  \n2.3.2 Pseudo-Boolean Constraints with At-Most-One Partitions ...... 26  \n2.3.3 Performance of SAT Encodings ....................... 28  \n2.4 Constraint Reformulation and Solving with Savile Row ............ 29  \n2.5 Summary ...................................","cbCain7p02ubB23L","https://ap.wps.com/l/cbCain7p02ubB23L","pdf",2435222,170,"English","# Contents\n## 1 Introduction: Solving Problems by Searching for Truth\n## 2 Background: Constraint problems and Boolean SAT\n## 3 Background: Machine Learning, Portfolios and Constraints\n## 4 Selecting Encodings using Generic Features\n## 5 Learning Using Specialised Constraint Features","[{\"question\":\"Why does choosing a SAT encoding matter for CSPs?\",\"answer\":\"Different SAT encodings for the same constraint type can lead to dramatically different solving times, so the encoding choice strongly affects performance.\"},{\"question\":\"What constraint types does the thesis focus on?\",\"answer\":\"It investigates selecting SAT encodings for pseudoBoolean and linear integer constraints within constraint satisfaction settings.\"},{\"question\":\"How does the proposed machine learning approach select encodings?\",\"answer\":\"It evaluates a three-phase pipeline: selecting per constraint type using generic instance features, adding specialised constraint-focused features, and finally learning to select encodings for individual constraints.\"}]","Learning SAT Encodings for Constraint Satisfaction Problems - PhD Thesis | PDF",1791080410,428]