The Optimist: Towards Fully AutomatedGraph Theory Research

The Optimist: Towards Fully AutomatedGraph Theory Research | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article The Optimist: Towards Fully AutomatedGraph Theory Research Randy Davila This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5450820/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper introduces the Optimist, an autonomous system developed to advanceautomated conjecture generation in graph theory. Leveraging mixed-integer pro-gramming (MIP) and heuristic methods, the Optimist generates conjectures thatboth rediscover established theorems and propose novel inequalities. Througha combination of memory-based computation and agent-like adaptability, theOptimist iteratively refines its conjectures by integrating new data, enabling afeedback process with minimal human (or machine) intervention. Initial exper-iments reveal the Optimist’s potential to uncover foundational results in graphtheory, as well as to produce conjectures of interest for future exploration. Thiswork also outlines the Optimist’s evolving integration with a counterpart agent,the Pessimist (a human or machine agent), to establish a dueling system thatwill drive fully automated graph theory research. Automated conjecturing automated reasoning graph theory TxGraffiti Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5450820","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":378466353,"identity":"e400926d-4ad4-4d7d-afc6-9e3cf8e94dfe","order_by":0,"name":"Randy Davila","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAn0lEQVRIiWNgGAWjYHACwwcfGCTALAlitRgbziBVi5kwD5RFnBbz2Ye3MdvusZDnZ2A+eJuHsAYGBplzaWWPc55JGM5sYEu2JkqLBA+PuXHOAYkEgwM8ZtLEajGTtgBqsT/A/40ELQwgWxh42IjVwlZs2HNAwnDGYTZjyznEaWHe+ODHgTp5/vbmhzfeEKMFAZhJUz4KRsEoGAWjAB8AAIPsJZ9YUQoDAAAAAElFTkSuQmCC","orcid":"","institution":"Rice University","correspondingAuthor":true,"prefix":"","firstName":"Randy","middleName":"","lastName":"Davila","suffix":""}],"badges":[],"createdAt":"2024-11-14 04:38:16","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5450820/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5450820/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":86576809,"identity":"84e84015-a132-48fe-a15c-1c722dbc0dd0","added_by":"auto","created_at":"2025-07-12 17:31:46","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":719745,"visible":true,"origin":"","legend":"","description":"","filename":"Optimist2024.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5450820/v1_covered_4685f6d4-192c-4586-b129-df34009c3392.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"The Optimist: Towards Fully AutomatedGraph Theory Research","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Automated conjecturing, automated reasoning, graph theory, TxGraffiti","lastPublishedDoi":"10.21203/rs.3.rs-5450820/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5450820/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"This paper introduces the Optimist, an autonomous system developed to advanceautomated conjecture generation in graph theory. 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