{"paper":{"title":"Bayesian Algorithm for Collaborative Optimization with Application to Aircraft Design","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A Bayesian algorithm for collaborative optimization uses Gaussian process surrogates to reduce black-box evaluations while achieving better designs in multidisciplinary problems.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mohamed Ali Belhafnaoui, Youssef Diouane","submitted_at":"2026-05-06T21:53:00Z","abstract_excerpt":"Collaborative Optimization (CO) is a multidisciplinary design optimization (MDO) framework that decomposes large-scale engineering problems into parallel, independently solvable subsystems coordinated by a system-level optimizer. Its practical utility is limited by the high frequency of expensive black-box disciplinary evaluations arising from the bi-level consistency constraints. This paper introduces BACO, a Bayesian Algorithm for Collaborative Optimization, which replaces the direct black-box calls at both levels with Gaussian process (GP) surrogates and acquisition function maximization. A"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"On the Scalable MDO problem, BACO consistently achieves lower objective values and drives both constraint violation and interdisciplinary discrepancy to near-zero within the evaluation budget, outperforming all three CO variants across all tested DoE sizes. On the CRM wing problem, BACO identifies a feasible solution within 886 of 1000 allocated evaluations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The Gaussian process surrogates accurately capture the black-box disciplinary responses and feasibility regions sufficiently well that the acquisition-function-driven points remain informative and the predicted discrepancy constraints enforce true consistency.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"BACO replaces direct black-box calls in collaborative optimization with Gaussian process surrogates at both subsystem and system levels, achieving lower objectives and near-zero constraint violations on MDO benchmarks and a CRM wing problem within limited evaluations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A Bayesian algorithm for collaborative optimization uses Gaussian process surrogates to reduce black-box evaluations while achieving better designs in multidisciplinary problems.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a9c41ed0073e04ccee9a280a69f3d0d838eeac2ef01ac8a53a57a3042e741c58"},"source":{"id":"2605.05474","kind":"arxiv","version":1},"verdict":{"id":"e411448a-e90e-473a-b0cf-f6d476e70003","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T15:59:35.027159Z","strongest_claim":"On the Scalable MDO problem, BACO consistently achieves lower objective values and drives both constraint violation and interdisciplinary discrepancy to near-zero within the evaluation budget, outperforming all three CO variants across all tested DoE sizes. On the CRM wing problem, BACO identifies a feasible solution within 886 of 1000 allocated evaluations.","one_line_summary":"BACO replaces direct black-box calls in collaborative optimization with Gaussian process surrogates at both subsystem and system levels, achieving lower objectives and near-zero constraint violations on MDO benchmarks and a CRM wing problem within limited evaluations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The Gaussian process surrogates accurately capture the black-box disciplinary responses and feasibility regions sufficiently well that the acquisition-function-driven points remain informative and the predicted discrepancy constraints enforce true consistency.","pith_extraction_headline":"A Bayesian algorithm for collaborative optimization uses Gaussian process surrogates to reduce black-box evaluations while achieving better designs in multidisciplinary problems."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.05474/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T09:40:59.421635Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T20:31:19.623699Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T13:31:15.987288Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"458acbdb77fa7929c6f8af91751d9bc61e401c66c68ec4b0e96d5fc387166640"},"references":{"count":42,"sample":[{"doi":"10.2514/1.j051895","year":2013,"title":"Multidisciplinary Design Optimization: A Survey of Architectures","work_id":"4c07829a-4acd-495e-a9c5-9c37242a2f8f","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1996,"title":"Collaborative Optimization: An Architecture for Large-Scale Distributed Design","work_id":"750c3000-0f72-4763-b230-0afa1e458a3e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1995,"title":"Development and Application of the Collaborative Optimization Architecture in a Multidisci- plinary Design Environment","work_id":"47fcc023-0145-4470-8828-ea623e2382f9","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.2514/2.1646","year":2002,"title":"Analytical and Computational Aspects of Collaborative Optimization for Multidisci- plinary Design","work_id":"507e35c8-4024-40dd-af47-1b5391913119","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.2514/6.2008-","year":2008,"title":"Enhanced Collaborative Optimization: Application to an Analytic Test Problem and Aircraft Design","work_id":"9841927e-b522-4083-b7e5-04e1fa5af53f","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":42,"snapshot_sha256":"07e5974379a399a716376002d3c4c7b6e541711eb59fd595242fd4026171faa9","internal_anchors":1},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}