{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T05:10:41Z","timestamp":1778821841580,"version":"3.51.4"},"reference-count":42,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,8,1]],"date-time":"2026-08-01T00:00:00Z","timestamp":1785542400000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computer-Aided Design"],"published-print":{"date-parts":[[2026,8]]},"DOI":"10.1016\/j.cad.2026.104084","type":"journal-article","created":{"date-parts":[[2026,4,27]],"date-time":"2026-04-27T23:36:05Z","timestamp":1777332965000},"page":"104084","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A unified optimization framework for parametric modelers with mixed explicit and black-box constraints"],"prefix":"10.1016","volume":"197","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-8631-4165","authenticated-orcid":false,"given":"Elhocine","family":"Mansouri","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3641-3707","authenticated-orcid":false,"given":"Kamal Eddine","family":"Melkemi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1256-9080","authenticated-orcid":false,"given":"Dominique","family":"Michelucci","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4888-8267","authenticated-orcid":false,"given":"Bilal","family":"Mokhtari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"issue":"4","key":"10.1016\/j.cad.2026.104084_b1","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/0010-4485(82)90292-5","article-title":"Modification of geometric models through variational geometry","volume":"14","author":"Light","year":"1982","journal-title":"Computer-Aided Design"},{"key":"10.1016\/j.cad.2026.104084_b2","doi-asserted-by":"crossref","DOI":"10.1016\/j.cad.2022.103465","article-title":"Variational direct modeling: A framework towards integration of parametric modeling and direct modeling in CAD","volume":"157","author":"Zou","year":"2023","journal-title":"Comput-Aided Des"},{"key":"10.1016\/j.cad.2026.104084_b3","series-title":"Simulation-driven design by optimization","author":"Rao","year":"2007"},{"issue":"5","key":"10.1016\/j.cad.2026.104084_b4","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1137\/0916069","article-title":"A limited memory algorithm for bound constrained optimization","volume":"16","author":"Byrd","year":"1995","journal-title":"SIAM J Sci Comput"},{"key":"10.1016\/j.cad.2026.104084_b5","series-title":"Code_Aster \u2013 Analysis of structures and thermomechanics for studies and research","author":"EDF R&D","year":"2024"},{"key":"10.1016\/j.cad.2026.104084_b6","series-title":"OpenFOAM \u2013 The open source CFD toolbox","author":"OpenFOAM Foundation","year":"2024"},{"key":"10.1016\/j.cad.2026.104084_b7","series-title":"FreeCAD \u2013 Your own 3D parametric modeler","author":"FreeCAD Project","year":"2025"},{"key":"10.1016\/j.cad.2026.104084_b8","series-title":"Blender \u2013 Free and open source 3D creation software","author":"Blender Foundation","year":"2025"},{"key":"10.1016\/j.cad.2026.104084_b9","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.mechmachtheory.2015.04.003","article-title":"Computing mobility condition using groebner basis","volume":"91","author":"Rameau","year":"2015","journal-title":"Mech Mach Theory"},{"issue":"2","key":"10.1016\/j.cad.2026.104084_b10","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/s10472-018-9599-5","article-title":"Towards a better integration of modelers and black box constraint solvers within the product design process","volume":"85","author":"Pernot","year":"2019","journal-title":"Ann Math Artif Intell"},{"key":"10.1016\/j.cad.2026.104084_b11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cad.2016.02.002","article-title":"Variational geometric modeling with black box constraints and DAGs","volume":"75","author":"Gouaty","year":"2016","journal-title":"Comput-Aided Des"},{"issue":"4","key":"10.1016\/j.cad.2026.104084_b12","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1093\/comjnl\/7.4.308","article-title":"A simplex method for function minimization","volume":"7","author":"Nelder","year":"1965","journal-title":"Comput J"},{"issue":"1","key":"10.1016\/j.cad.2026.104084_b13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1137\/S1052623493250780","article-title":"On the convergence of pattern search algorithms","volume":"7","author":"Torczon","year":"1997","journal-title":"SIAM J Optim"},{"key":"10.1016\/j.cad.2026.104084_b14","series-title":"Genetic Algorithms in Search, Optimization and Machine Learning","author":"Goldberg","year":"1989"},{"issue":"3","key":"10.1016\/j.cad.2026.104084_b15","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1007\/s10898-012-9951-y","article-title":"Derivative-free optimization: a review of algorithms and comparison of software implementations","volume":"56","author":"Rios","year":"2013","journal-title":"J Global Optim"},{"issue":"3\u20134","key":"10.1016\/j.cad.2026.104084_b16","first-page":"393","article-title":"An introduction to the adjoint approach to design","volume":"65","author":"Giles","year":"2001","journal-title":"Flow, Turbul Combust"},{"key":"10.1016\/j.cad.2026.104084_b17","doi-asserted-by":"crossref","DOI":"10.1016\/j.paerosci.2019.05.002","article-title":"Effective adjoint approaches for computational fluid dynamics","volume":"110","author":"Kenway","year":"2019","journal-title":"Prog Aerosp Sci"},{"key":"10.1016\/j.cad.2026.104084_b18","series-title":"Evaluating derivatives: Principles and techniques of algorithmic differentiation","author":"Griewank","year":"2008"},{"key":"10.1016\/j.cad.2026.104084_b19","series-title":"Engineering design via surrogate modelling: a practical guide","author":"Forrester","year":"2008"},{"issue":"3","key":"10.1016\/j.cad.2026.104084_b20","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1109\/TEVC.2018.2869001","article-title":"Data-driven evolutionary optimization: An overview and case studies","volume":"23","author":"Jin","year":"2019","journal-title":"IEEE Trans Evol Comput"},{"issue":"3","key":"10.1016\/j.cad.2026.104084_b21","doi-asserted-by":"crossref","first-page":"550","DOI":"10.1137\/16M1082469","article-title":"Survey of multifidelity methods in uncertainty propagation, inference, and optimization","volume":"60","author":"Peherstorfer","year":"2018","journal-title":"SIAM Rev"},{"key":"10.1016\/j.cad.2026.104084_b22","series-title":"Numerical optimization","author":"Nocedal","year":"2006"},{"key":"10.1016\/j.cad.2026.104084_b23","series-title":"Constrained optimization and Lagrange multiplier methods","author":"Bertsekas","year":"1996"},{"issue":"151","key":"10.1016\/j.cad.2026.104084_b24","doi-asserted-by":"crossref","first-page":"773","DOI":"10.1090\/S0025-5718-1980-0572855-7","article-title":"Updating quasi-Newton matrices with limited storage","volume":"35","author":"Nocedal","year":"1980","journal-title":"Math Comp"},{"issue":"1\u20133","key":"10.1016\/j.cad.2026.104084_b25","doi-asserted-by":"crossref","first-page":"503","DOI":"10.1007\/BF01589116","article-title":"On the limited memory BFGS method for large scale optimization","volume":"45","author":"Liu","year":"1989","journal-title":"Math Program"},{"key":"10.1016\/j.cad.2026.104084_b26","volume":"vol. 11","author":"Haftka","year":"1992"},{"issue":"3","key":"10.1016\/j.cad.2026.104084_b27","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1561\/2400000003","article-title":"Proximal algorithms","volume":"1","author":"Parikh","year":"2014","journal-title":"Found Trends Optim"},{"issue":"3","key":"10.1016\/j.cad.2026.104084_b28","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1038\/s41592-019-0686-2","article-title":"SciPy 1.0: fundamental algorithms for scientific computing in Python","volume":"17","author":"Virtanen","year":"2020","journal-title":"Nature Methods"},{"key":"10.1016\/j.cad.2026.104084_b29","series-title":"Iterative methods for optimization","author":"Kelley","year":"1999"},{"key":"10.1016\/j.cad.2026.104084_b30","series-title":"Accelerating practical engineering design optimization with computational graph transformations","author":"Sharpe","year":"2024"},{"key":"10.1016\/j.cad.2026.104084_b31","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.compstruc.2015.05.004","article-title":"Application of structural topology optimisation to perforated steel beams","volume":"158","author":"Tsavdaridis","year":"2015","journal-title":"Comput Struct"},{"issue":"3","key":"10.1016\/j.cad.2026.104084_b32","doi-asserted-by":"crossref","first-page":"1021","DOI":"10.1115\/1.3438995","article-title":"Optimal design of a class of welded structures using geometric programming","volume":"98","author":"Ragsdell","year":"1976","journal-title":"J Eng Ind"},{"key":"10.1016\/j.cad.2026.104084_b33","article-title":"Particle swarm algorithms to solve engineering problems: A comparison of performance","volume":"2013","author":"Tomassetti","year":"2013","journal-title":"J Eng"},{"issue":"3","key":"10.1016\/j.cad.2026.104084_b34","first-page":"319","article-title":"Solving engineering optimization problems with the simple constrained particle swarm optimizer","volume":"32","author":"Cagnina","year":"2008","journal-title":"Informatica"},{"issue":"11","key":"10.1016\/j.cad.2026.104084_b35","doi-asserted-by":"crossref","first-page":"3316","DOI":"10.1016\/j.cnsns.2010.01.009","article-title":"Two improved harmony search algorithms for solving engineering optimization problems","volume":"15","author":"Jaberipour","year":"2010","journal-title":"Commun Nonlinear Sci Numer Simul"},{"issue":"5","key":"10.1016\/j.cad.2026.104084_b36","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1090\/S0002-9904-1958-10224-4","article-title":"Outline of an algorithm for integer solutions to linear programs","volume":"64","author":"Gomory","year":"1958","journal-title":"Bull Am Math Soc"},{"issue":"3","key":"10.1016\/j.cad.2026.104084_b37","doi-asserted-by":"crossref","first-page":"497","DOI":"10.2307\/1910129","article-title":"An automatic method for solving discrete programming problems","volume":"28","author":"Land","year":"1960","journal-title":"Econometrica"},{"key":"10.1016\/j.cad.2026.104084_b38","series-title":"Integer and combinatorial optimization","author":"Nemhauser","year":"1988"},{"key":"10.1016\/j.cad.2026.104084_b39","doi-asserted-by":"crossref","DOI":"10.1155\/2013\/419043","article-title":"Design optimization of a speed reducer using deterministic techniques","volume":"2013","author":"Lin","year":"2013","journal-title":"Math Probl Eng"},{"issue":"3","key":"10.1016\/j.cad.2026.104084_b40","doi-asserted-by":"crossref","first-page":"332","DOI":"10.1109\/9.119632","article-title":"Multivariate stochastic approximation using a simultaneous perturbation gradient approximation","volume":"37","author":"Spall","year":"1992","journal-title":"IEEE Trans Autom Control"},{"key":"10.1016\/j.cad.2026.104084_b41","series-title":"JAX: composable transformations of Python+NumPy programs","author":"Bradbury","year":"2018"},{"key":"10.1016\/j.cad.2026.104084_b42","unstructured":"CGAL, Computational Geometry Algorithms Library. https:\/\/www.cgal.org."}],"container-title":["Computer-Aided Design"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010448526000540?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0010448526000540?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T04:24:41Z","timestamp":1778819081000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0010448526000540"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8]]},"references-count":42,"alternative-id":["S0010448526000540"],"URL":"https:\/\/doi.org\/10.1016\/j.cad.2026.104084","relation":{},"ISSN":["0010-4485"],"issn-type":[{"value":"0010-4485","type":"print"}],"subject":[],"published":{"date-parts":[[2026,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A unified optimization framework for parametric modelers with mixed explicit and black-box constraints","name":"articletitle","label":"Article Title"},{"value":"Computer-Aided Design","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cad.2026.104084","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"104084"}}