Superior Inferior Optimization: A New Metaphor-free Metaheuristic Algorithm and Its Implementation to Solve Standard and Practical Problems

Superior Inferior Optimization: A New Metaphor-free Metaheuristic Algorithm and Its Implementation to Solve Standard and Practical Problems | 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 Superior Inferior Optimization: A New Metaphor-free Metaheuristic Algorithm and Its Implementation to Solve Standard and Practical Problems Purba Daru Kusuma, Budhi Irawan, Andrew Brian Osmond This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9049791/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract This paper introduces a new metaphor-free metaheuristic algorithm called superior-inferior optimization (SIO). The fundamental concept of SIO comes from exploiting the most and least prominent members within swarm to create the median member. Then, it uses the most prominent and median members as guidance for six possible motions during iteration. SIO effectiveness is measured through experiment that use three cases including a set of 23 functions, two economic load dispatch problems (ELDP), and one balance delivery problem (BDP) which is a derivative of pickup and delivery problem (PDP). In this experiment, five new metaheuristic algorithms are chosen as competitors. The result shows that SIO is competitive in all cases. Besides, the experiment shows that the disparity among algorithms is narrow in both ELDP and BDP where the gap in ELDP is narrower than in BDP. The existence of constraints creates difficulty in creating significant advantage in solving these two practical problems. Source code of SIO can be accessed or available through the following link https://drive.google.com/drive/folders/1MBNkFWxdjGrYV_QDPcXstjntCIRU2mMN?usp=sharing Optimization metaheuristic economic load dispatch problem pickup delivery problem balance delivery problem. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Reviews received at journal 01 May, 2026 Reviewers agreed at journal 23 Apr, 2026 Reviews received at journal 24 Mar, 2026 Reviewers agreed at journal 20 Mar, 2026 Reviewers agreed at journal 16 Mar, 2026 Reviewers invited by journal 15 Mar, 2026 Editor assigned by journal 06 Mar, 2026 Submission checks completed at journal 06 Mar, 2026 First submitted to journal 06 Mar, 2026 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-9049791","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":606910464,"identity":"0aa4af98-81a1-4dea-a617-c426d828bf11","order_by":0,"name":"Purba Daru Kusuma","email":"data:image/png;base64,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","orcid":"","institution":"Telkom University","correspondingAuthor":true,"prefix":"","firstName":"Purba","middleName":"Daru","lastName":"Kusuma","suffix":""},{"id":606910465,"identity":"9ae5a068-4da1-407e-b932-95a4ef2634de","order_by":1,"name":"Budhi Irawan","email":"","orcid":"","institution":"Telkom University","correspondingAuthor":false,"prefix":"","firstName":"Budhi","middleName":"","lastName":"Irawan","suffix":""},{"id":606910466,"identity":"9da9556a-28f8-4fd8-b157-7271d47c03cd","order_by":2,"name":"Andrew Brian Osmond","email":"","orcid":"","institution":"Telkom University","correspondingAuthor":false,"prefix":"","firstName":"Andrew","middleName":"Brian","lastName":"Osmond","suffix":""}],"badges":[],"createdAt":"2026-03-06 11:08:33","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9049791/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9049791/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104797430,"identity":"009c8632-9258-431f-8c7b-7c99d0109417","added_by":"auto","created_at":"2026-03-17 09:55:19","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":604495,"visible":true,"origin":"","legend":"","description":"","filename":"springerevolintelsuperiorinferior.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9049791/v1_covered_0c6846a9-097c-4c3c-a8f9-0ad91bec5c49.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Superior Inferior Optimization: A New Metaphor-free Metaheuristic Algorithm and Its Implementation to Solve Standard and Practical Problems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"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":"evolutionary-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"evin","sideBox":"Learn more about [Evolutionary Intelligence](http://link.springer.com/journal/12065)","snPcode":"12065","submissionUrl":"https://submission.nature.com/new-submission/12065/3","title":"Evolutionary Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Optimization, metaheuristic, economic load dispatch problem, pickup delivery problem, balance delivery problem.","lastPublishedDoi":"10.21203/rs.3.rs-9049791/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9049791/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper introduces a new metaphor-free metaheuristic algorithm called superior-inferior optimization (SIO). The fundamental concept of SIO comes from exploiting the most and least prominent members within swarm to create the median member. Then, it uses the most prominent and median members as guidance for six possible motions during iteration. SIO effectiveness is measured through experiment that use three cases including a set of 23 functions, two economic load dispatch problems (ELDP), and one balance delivery problem (BDP) which is a derivative of pickup and delivery problem (PDP). In this experiment, five new metaheuristic algorithms are chosen as competitors. The result shows that SIO is competitive in all cases. Besides, the experiment shows that the disparity among algorithms is narrow in both ELDP and BDP where the gap in ELDP is narrower than in BDP. The existence of constraints creates difficulty in creating significant advantage in solving these two practical problems. Source code of SIO can be accessed or available through the following link \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://drive.google.com/drive/folders/1MBNkFWxdjGrYV_QDPcXstjntCIRU2mMN?usp=sharing\u003c/span\u003e\u003cspan address=\"https://drive.google.com/drive/folders/1MBNkFWxdjGrYV_QDPcXstjntCIRU2mMN?usp=sharing\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e","manuscriptTitle":"Superior Inferior Optimization: A New Metaphor-free Metaheuristic Algorithm and Its Implementation to Solve Standard and Practical Problems","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-17 09:53:17","doi":"10.21203/rs.3.rs-9049791/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"editorInvitedReview","content":"","date":"2026-05-01T13:05:40+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"38948719656851081300345035789301005478","date":"2026-04-23T13:15:45+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2026-03-24T13:17:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"293787253397696209086818047548750029299","date":"2026-03-20T06:48:45+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"235851773521849297663979847242328138320","date":"2026-03-16T06:24:05+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-16T03:48:45+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-07T04:54:40+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-07T04:54:06+00:00","index":"","fulltext":""},{"type":"submitted","content":"Evolutionary Intelligence","date":"2026-03-06T10:55:38+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"evolutionary-intelligence","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"evin","sideBox":"Learn more about [Evolutionary Intelligence](http://link.springer.com/journal/12065)","snPcode":"12065","submissionUrl":"https://submission.nature.com/new-submission/12065/3","title":"Evolutionary Intelligence","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"bd7b4761-2a2c-42b6-ba5d-5c46e12db63a","owner":[],"postedDate":"March 17th, 2026","published":true,"recentEditorialEvents":[{"type":"editorInvitedReview","content":"","date":"2026-05-01T13:05:40+00:00","index":27,"fulltext":""}],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-17T09:53:17+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-17 09:53:17","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9049791","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9049791","identity":"rs-9049791","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}