Study on Multi-stage and Multi-Objective Hierarchical Virtual Optimization Algorithm for Nonlinear Workflow

Study on Multi-stage and Multi-Objective Hierarchical Virtual Optimization Algorithm for Nonlinear Workflow | 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 Study on Multi-stage and Multi-Objective Hierarchical Virtual Optimization Algorithm for Nonlinear Workflow zhiyong LUO, Chunqiao Ge, Haixin Yu, Jinwei Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8571510/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract Nonlinear workflow scheduling in intelligent manufacturing systems is often constrained by complex task–resource dependencies, multi-objective conflicts, and inconsistencies between production planning and real execution. To address these challenges, this study proposes a virtual multi-stage nonlinear workflow model (VGD) and develops a hierarchical multi-objective scheduling algorithm (VGDP). In the VGD model, process tasks and manufacturing resources are abstracted into virtual nodes, enabling nonlinear process chains to be transformed into linearized multi-stage structures by introducing detection nodes that capture intermediate quality and cost requirements. Building on this model, the VGDP algorithm performs reverse-stage optimization to compute local feasible solutions within each stage, followed by forward Pareto-guided integration to construct the global non-dominated scheduling path.A real-world sheet-metal workshop is used to validate the proposed method. Comparative experiments against two widely adopted multi-objective evolutionary algorithms, NSGA-II and MOEA/D, demonstrate that the VGDP algorithm achieves higher-quality schedules while maintaining stable computational performance. In particular, VGDP improves production quality by approximately 0.3% compared with NSGA-II and 11.7% compared with MOEA/D under the same cost and time constraints. Moreover, the multi-stage virtualization mechanism effectively reduces the complexity of nonlinear workflows and enhances optimization stability as system scale increases.Overall, the proposed VGD/VGDP framework provides an effective and scalable approach to nonlinear multi-objective scheduling, offering strong applicability to advanced manufacturing environments that require high customization and dynamic process adaptability. Optimized scheduling Multi-stage Workflow Pareto Multilayer virtual Production quality Full Text Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 13 Jan, 2026 Reviewers invited by journal 13 Jan, 2026 Editor assigned by journal 13 Jan, 2026 First submitted to journal 10 Jan, 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-8571510","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":574019009,"identity":"906a2ea4-db85-43ec-b034-653fe4eac697","order_by":0,"name":"zhiyong 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To address these challenges, this study proposes a virtual multi-stage nonlinear workflow model (VGD) and develops a hierarchical multi-objective scheduling algorithm (VGDP). In the VGD model, process tasks and manufacturing resources are abstracted into virtual nodes, enabling nonlinear process chains to be transformed into linearized multi-stage structures by introducing detection nodes that capture intermediate quality and cost requirements. Building on this model, the VGDP algorithm performs reverse-stage optimization to compute local feasible solutions within each stage, followed by forward Pareto-guided integration to construct the global non-dominated scheduling path.A real-world sheet-metal workshop is used to validate the proposed method. Comparative experiments against two widely adopted multi-objective evolutionary algorithms, NSGA-II and MOEA/D, demonstrate that the VGDP algorithm achieves higher-quality schedules while maintaining stable computational performance. 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