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The work presents a method that incrementally refines problem specifications written in the Essence abstract constraint specification language into concrete constraint models via a sequence of refinement rules. It addresses symmetry handling by breaking modelling symmetries automatically during refinement, reducing redundant search. A system called Conjure reproduces effective model kernels across 42 benchmark problems.",{"@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/conjure-automatic-generation-of-constraint-models-from-problem-specifications/505114/",{"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/conjure-automatic-generation-of-constraint-models-from-problem-specifications/505114.png","ImageObject",300,407,{"name":92,"@type":93},"lugxt","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-11","2026-10-04",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does Conjure aim to solve?","Question",{"text":112,"@type":113},"Conjure automates the generation of constraint models from problem specifications, reducing the expertise and time needed to create effective models for combinatorial problems.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the method generate constraint models?",{"text":117,"@type":113},"It incrementally refines an Essence abstract constraint specification into a concrete model by applying a selected refinement rule at each step, exploring multiple possible refinements.",{"name":119,"@type":110,"acceptedAnswer":120},"Why is symmetry handling important, and how is it addressed?",{"text":121,"@type":113},"Symmetries can cause redundant search. The approach automatically breaks modelling symmetries as they enter the model during refinement, avoiding an expensive post-formulation symmetry detection step.","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},505114,1791274639,{"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":29,"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},3985747862600,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","[eprints@whiterose.ac.uk](eprints@whiterose.ac.uk)[ ](eprints@whiterose.ac.uk)[https://eprints.whiterose.ac.uk](https://eprints.whiterose.ac.uk)  \nUniversities of Leeds, Sheffield and York  \nDeposited via The University of York.  \nWhite Rose Research Online URL for this paper:  \n[https://eprints.whiterose.ac.uk/id/eprint/188771/](https://eprints.whiterose.ac.uk/id/eprint/188771/)  \n[Version: Accepted Version](Version: Accepted Version)  \nArticle:  \nAkgün, Özgür, Frisch, Alan Mark, Gent, Ian Philip et al. (2022) Conjure: Automatic Generation of Constraint Models from Problem Specifications. Artificial Intelligence.  \n103751. ISSN: 0004-3702  \n[https://doi.org/10.1016/j.artint.2022.103751](https://doi.org/10.1016/j.artint.2022.103751)  \nReuse  \nItems deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item.  \nTakedown  \nIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by  \nemailing [eprints@whiterose.ac.uk](eprints@whiterose.ac.uk) including the URL of the record and the reason for the withdrawal request.  \nConjure: Automatic Generation of Constraint Models from  \nProblem Speci􀀌cations  \n¨Ozg¨ur Akg¨una , Alan M. Frischb , Ian P. Genta , Christopher Jeﬀersona , Ian Miguela , Peter  \nNightingaleb  \na School of Computer Science, University of St Andrews, St Andrews, Fife KY16 9SX, UK b Department of Computer Science, University of York, Deramore Lane, Heslington, York YO10 5GH, UK  \nAbstract  \nWhen solving a combinatorial problem, the formulation or model of the problem is critical to the eﬃciency of the solver. Automating the modelling process has long been of interest because of the expertise and time required to produce an eﬀective model of a given problem. We describe a method to automatically produce constraint models from a problem speciﬁcation written in the abstract constraint speciﬁcation language Essence. Our approach is to incrementally reﬁne the speciﬁcation into a concrete model by applying a chosen reﬁnement rule at each step. Any nontrivial speciﬁcation may be reﬁned in multiple ways, creating a space of models to choose from.  \nThe handling of symmetries is a particularly important aspect of automated modelling. Many combinatorial optimisation problems contain symmetry, which can lead to redundant search. Ifa partial assignment is shown to be invalid, we are wasting time if we ever consider a symmetric equivalent of it. A particularly important class of symmetries are those introduced by the constraint modelling process: modelling symmetries. We show how modelling symmetries may be broken automatically as they enter a model during reﬁnement, obviating the need for an expensive symmetry detection step following model formulation.  \nOur approach is implemented in a system called Conjure. We compare the models produced by Conjure to constraint models from the literature that are known to be eﬀective. Our empirical results conﬁrm that Conjure can reproduce successfully the kernels of the constraint models of 42 benchmark problems found in the literature.  \nKeywords:  \nConstraint modelling, Constraint programming, Combinatorial optimization, Constraint satisfaction problem  \n1. Introduction  \nEﬃcient decision-making is of central importance to a modern society. It is natural to represent and reason about decision-making problems in terms of constraints. For example, in scheduling a football league many constraints occur, such as: every team has to play every other, home and  \nEmail addresses: [ozgur.akgun@st-andrews.ac.uk](ozgur.akgun@st-andrews.ac.uk) (¨Ozg¨ur Akg¨un), alan .frisch@york .ac .uk (A","cbCaiqcDgNb1qEeh","https://ap.wps.com/l/cbCaiqcDgNb1qEeh","pdf",569062,49,"English","# Abstract\n# Keywords\n# 1. Introduction","[{\"question\":\"What problem does Conjure aim to solve?\",\"answer\":\"Conjure automates the generation of constraint models from problem specifications, reducing the expertise and time needed to create effective models for combinatorial problems.\"},{\"question\":\"How does the method generate constraint models?\",\"answer\":\"It incrementally refines an Essence abstract constraint specification into a concrete model by applying a selected refinement rule at each step, exploring multiple possible refinements.\"},{\"question\":\"Why is symmetry handling important, and how is it addressed?\",\"answer\":\"Symmetries can cause redundant search. The approach automatically breaks modelling symmetries as they enter the model during refinement, avoiding an expensive post-formulation symmetry detection step.\"}]","Conjure - Automatic Generation of Constraint Models from Problem Specifications | PDF",1791090502,123]