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Adv Eng Softw 31:385–389\nGould N, Orban D, Toint PL (2004) GALAHAD, a library of thread-safe Fortran 90 packages for large-scale nonlinear optimization. ACM Trans Math Softw 29:353–372\nGould N, Orban D, Toint P (2005) Numerical methods for large-scale nonlinear optimization. Acta Numerica 14:299–361\nGroenwold AA, Etman LFP (2008) Sequential approximate optimization using dual subproblems based on incomplete series expansions. Struct Multidisc Optim 36:547–570\nGroenwold AA, Etman LFP (2010a) On the conditional acceptance of iterates in SAO algorithms based on convex separable approximations. Struct Multidisc Optim 42:165–178\nGroenwold AA, Etman LFP (2010b) A quadratic approximation for structural topology optimization. Int J Numer Methods Eng 82:505–524\nGroenwold AA, Etman LFP, Snyman JA, Rooda JE (2007) Incomplete series expansion for function approximation. 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Report NASA-CR 2552, NASA\nStarnes Jr JH, Haftka RT (1979) Preliminary design of composite wings for buckling, stress and displacement constraints. J Aircr 16:564–570\nSvanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24:359–373\nSvanberg K (1993) Some second order methods for structural optimization. In: Rozvany G (ed) Optimization of Large Structural Systems, NATA ASI series, vol 231, Kluwer Academic Publishers, pp 567–578\nSvanberg K (2002) A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J Optim 12:555–573\nvan Keulen F, Haftka RT, Kim NH (2005) Review of options for structural design sensitivity analysis. part 1: linear systems. Comput Methods Appl Mech Engrg 194:3213–3243\nVanderplaats G (1993) Thirty years of modern structural optimization. Adv Eng Softw 16:81–88\nVanderplaats GN (1984) Numerical optimization techniques for engineering design. McGraw-Hill, New York\nVanderplaats GN (2004) Very large scale continuous and discrete variable optimization. In: Proc. 10th AIAA\u002FISSMO multidisciplinary analysis and optimization conference, Albany, New York, aIAA-2004-4458\nXu S, Grandhi RV (1998) Effective two-point function approximation for design optimization. AIAA J 36:2269–2275\nZhang WH, Fleury C (1997) A modification of convex approximation methods for structural optimization. Comput Struct 64:89–95\nZhu C, Byrd RH, Lu P, Nocedal J (1994) L-bfgs-b: Fortran subroutines for large scale bound constrained optimization. Tech. Rep. Report NAM-11, Northwestern University, EECS Department\nZillober C (1993) A globally convergent version of the method of moving asymptotes. Struct Optim 6:166–174\nZillober C (2001) A combined convex approximation - interior point approach for large scale nonlinear programming. Optim Eng 2:51–73\nZillober C (2002) SCPIP - an efficient software tool for the solution of structural optimization problems. Struct Multidisc Optim 24:362–371\nZillober C, Schittkowski K, Moritzen K (2004) Very large scale optimization by sequential convex programming. Optim Methods Softw 19:103–120",{"EN":712},"Optimization algorithms based on convex separable approximations for optimal structural design often use reciprocal-like approximations in a dual setting; CONLIN and the method of moving asymptotes (MMA) are well-known examples of such sequential convex programming (SCP) algorithms. We have previously demonstrated that replacement of these nonlinear (reciprocal) approximations by their own second order Taylor series expansion provides a powerful new algorithmic option within the SCP class of algorithms. This note shows that the quadratic treatment of the original nonlinear approximations also enables the restatement of the SCP as a series of Lagrange-Newton QP subproblems. This results in a diagonal trust-region SQP type of algorithm, in which the second order diagonal terms are estimated from the nonlinear (reciprocal) intervening variables, rather than from historic information using an exact or a quasi-Newton Hessian approach. The QP formulation seems particularly attractive for problems with far more constraints than variables (when pure dual methods are at a disadvantage), or when both the number of design variables and the number of (active) constraints is very large.",{"EN":714},"First-order sequential convex programming using approximate diagonal QP subproblems",{"VOID":716},"10.1007\u002Fs00158-011-0739-3","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs00158-011-0739-3",[719,736,748],{"id":720,"sortIndex":23,"researcher":22,"roles":721,"affiliations":722,"properties":733},"f3c9fcd4-ca16-44e5-9af0-304ead98cb3f",[280],[723],{"id":22,"sortIndex":23,"affiliation":724,"properties":22},{"id":725,"createTime":726,"updateTime":727,"relativeEntities":728,"slug":729,"properties":730,"entityType":75,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"0e78e239-e0c0-4a8f-aa76-2684459432fb","2024-04-06T14:58:04.253+00:00","2025-01-06T22:52:56.644+00:00",[],"Department-of-Mechanical-Engineering-Eindhoven-University-of-Technology-Eindhoven-The-Netherlands",{"title":731},{"VI":732},"Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands",{"title":734},{"VI":735},"L. F. P. Etman",{"id":737,"sortIndex":297,"researcher":22,"roles":738,"affiliations":739,"properties":745},"d5d278de-a39c-4638-9fc2-d76154cdfd35",[280],[740],{"id":22,"sortIndex":23,"affiliation":741,"properties":22},{"id":725,"createTime":726,"updateTime":727,"relativeEntities":742,"slug":729,"properties":743,"entityType":75,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},[],{"title":744},{"VI":732},{"title":746},{"VI":747},"J. E. 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Groenwold",{"url":717,"publisher":764,"properties":793},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":765,"slug":10,"properties":766,"entityType":20,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"subjectFields":771,"manageAffiliations":772,"indexDatabases":773,"url":22,"thumbnailPath":22,"statistic":788,"gsStatistic":22,"type":258,"analyzePriority":22},[],{"issn":767,"eissn":768,"title":769,"url":770},{"VOID":13},{"VOID":15},{"EN":17},{"VOID":19},[],[],[774,781],{"id":111,"indexDatabase":775,"url":124,"indexYears":125,"academicFieldIds":780,"indexDatabaseRanking":132},{"id":113,"createTime":114,"updateTime":115,"relativeEntities":776,"label":777,"description":778,"key":121,"publicationTags":779,"standard":22},[],{"EN":118,"VI":118},{"EN":118,"VI":120},[123],[127,128,129,130,131],{"id":90,"indexDatabase":782,"url":105,"indexYears":22,"academicFieldIds":787,"indexDatabaseRanking":22},{"id":92,"createTime":93,"updateTime":94,"relativeEntities":783,"label":784,"description":785,"key":101,"publicationTags":786,"standard":22},[],{"EN":97,"VI":97},{"VI":99,"EN":100},[103,104],[107,108,109],{"impactFactor":23,"impactFactorByYear":789,"i10Index":146,"i10IndexLast5Year":147,"totalPublication":148,"totalPublicationByYear":790,"totalCitation":184,"totalCitationByYear":791,"totalCitationPerPublication":220,"totalCitationPerPublicationByYear":792,"hindexLast5Year":257,"hindex":257},{"2012":135,"2013":136,"2014":137,"2015":138,"2016":139,"2017":140,"2018":141,"2019":142,"2020":143,"2021":144,"2022":136,"2023":145},{"1989":150,"1990":151,"1991":152,"1992":153,"1993":154,"1994":155,"1995":156,"1996":157,"1997":158,"1998":159,"1999":160,"2000":161,"2001":162,"2002":163,"2003":164,"2004":165,"2005":163,"2006":166,"2007":167,"2008":168,"2009":169,"2010":170,"2011":171,"2012":172,"2013":173,"2014":174,"2015":165,"2016":175,"2017":176,"2018":177,"2019":178,"2020":179,"2021":180,"2022":181,"2023":182,"2024":183},{"1990":186,"1991":187,"1992":188,"1993":189,"1994":190,"1995":191,"1996":192,"1997":193,"1998":194,"1999":195,"2000":196,"2001":197,"2002":198,"2003":159,"2004":199,"2005":200,"2006":201,"2007":202,"2008":203,"2009":204,"2010":205,"2011":206,"2012":207,"2013":208,"2014":209,"2015":210,"2016":211,"2017":212,"2018":213,"2019":214,"2020":215,"2021":216,"2022":217,"2023":218,"2024":219},{"1990":222,"1991":223,"1992":224,"1993":225,"1994":226,"1995":227,"1996":228,"1997":229,"1998":230,"1999":231,"2000":232,"2001":233,"2002":234,"2003":235,"2004":236,"2005":237,"2006":238,"2007":239,"2008":240,"2009":241,"2010":242,"2011":243,"2012":244,"2013":245,"2014":246,"2015":247,"2016":248,"2017":249,"2018":250,"2019":251,"2020":252,"2021":253,"2022":254,"2023":255,"2024":256},{"volume":794,"pages":796},{"VOID":795},"45",{"VOID":797},"479-488","2011-11-29",2011,{"id":801,"createTime":802,"updateTime":803,"relativeEntities":804,"slug":805,"properties":806,"entityType":274,"verifyStatus":377,"verifyTime":803,"verifyNote":379,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":817,"fullTextUrl":22,"authors":818,"publicationType":323,"publisherRelationship":896,"citationCount":22,"citationInfo":22,"publishDate":926,"publishYear":927,"citationAnalyzeStatus":21,"lastCitationAnalyze":22,"indexDatabases":22,"openAccess":22,"references":22,"isForceReanalyzing":361},"e52f280c-2158-4c09-b117-4d9139c17c01","2024-04-06T19:06:23.117+00:00","2025-02-19T23:57:42.102+00:00",[],"A-deep-reinforcement-learning-optimization-framework-for-supercritical-airfoil-aerodynamic-shape-design",{"references":807,"keywords":809,"abstract":811,"title":813,"doi":815},{"VOID":808},"Crouch JD, Garbaruk A, Magidov D, Travin A (2009) Origin of transonic buffet on aerofoils. 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JSME Int J A-Solid M 43(2):124–129. https:\u002F\u002Fdoi.org\u002F10.1299\u002Fjsmea.43.124\nQian J, Yi J, Cheng Y, Liu J, Zhou Q (2020) A sequential constraint updating approach for Kriging surrogate model-assisted engineering optimization design problem. Eng Comput 36:993–1009. https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs00366-019-00745-w\nRabault J, Kuchta M, Jensen A, Réglade U, Cerardi N (2019) Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control. J Fluid Mech 865:281–302. https:\u002F\u002Fdoi.org\u002F10.1017\u002Fjfm.2019.62\nRaul V, Leifsson L (2021) Surrogate-based aerodynamic shape optimization for delaying airfoil dynamic stall using Kriging regression and infill criteria. 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J Aircr 32(4):901–903. https:\u002F\u002Fdoi.org\u002F10.2514\u002F3.46815\nTao J, Sun G (2019) Application of deep learning based multi-fidelity surrogate model to robust aerodynamic design optimization. Aerosp Sci Technol 92:722–737. https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.ast.2019.07.002\nTian X, Li J (2020) Robust aerodynamic shape optimization using a novel multi-objective evolutionary algorithm coupled with surrogate model. Struct Multidisc Optim 62:1969–1987. https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs00158-020-02589-1\nViquerat J, Rabault J, Kuhnle A, Ghraieb H, Larcher A, Hachem E (2021) Direct shape optimization through deep reinforcement learning. J Comput Phys 428:110080. https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.jcp.2020.110080\nWang J, He C, Li R, Chen H, Zhai C, Zhang M (2021) Flow field prediction of supercritical airfoils via variational autoencoder based deep learning framework. Phys Fluids 33:086108. https:\u002F\u002Fdoi.org\u002F10.1063\u002F5.0053979\nWang J, Xie H, Zhang M, Xu H (2023) Physics-assisted reduced-order modeling for identifying dominant features of transonic buffet. Phys Fluids 35:066124. https:\u002F\u002Fdoi.org\u002F10.1063\u002F5.0152127\nXie H, Wang J, Zhang M (2023) Parametric generative schemes with geometric constraints for encoding and synthesizing airfoils. arXiv:2205.02458. https:\u002F\u002Fdoi.org\u002F10.48550\u002FarXiv.2205.02458\nXu Z, Saleh JH, Yang V (2019) Optimization of supercritical airfoil design with buffet effect. AIAA J 57:4343–4353. https:\u002F\u002Fdoi.org\u002F10.2514\u002F1.j057573s\nYilmaz E, German B (2017) A convolutional neural network approach to training predictors for airfoil performance. 18th AIAA\u002FISSMO MA&O conference 3660. https:\u002F\u002Fdoi.org\u002F10.2514\u002F6.2017-3660\nYonekura K, Hattori H (2019) Framework for design optimization using deep reinforcement learning. Struct Multidisc Optim 60:1709–1713. https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs00158-019-02276-w",{"EN":810},"",{"EN":812},"In the context of traditional aerodynamic shape optimization design methods, the necessity to re-execute the complete optimization process when the initial shape changes poses significant challenges in engineering applications. These challenges encompass problems like data wastage and restricted ability for experience learning. We propose a policy learning-based optimization method that can automatically learn optimization experience through interactions with the environment. This optimization framework is based on deep reinforcement learning and consists of the policy learning process and the policy execution process. The action network, trained during the policy learning process, serves as a black box model of optimization experience and can directly and efficiently participate in guiding the actual optimization process. The optimization framework is validated through two-dimensional Rosenbrock function optimization, demonstrating its exceptional performance in achieving high-precision optimal solutions. Then, the effectiveness of this optimization method is demonstrated in the multi-point optimization design of supercritical airfoils, which aims to improve the buffet onset lift within predefined design constraints while maintaining the cruise lift-drag ratio. With the datum-coupled state format, the optimization experience can be tailored to the optimization requirements of different initial states during the learning process, leading to an optimization success rate in the optimization space that can exceed 90%.",{"EN":814},"A deep reinforcement learning optimization framework for supercritical airfoil aerodynamic shape design",{"VOID":816},"10.1007\u002Fs00158-024-03755-5","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs00158-024-03755-5",[819,834,851,868,884],{"id":820,"sortIndex":219,"researcher":22,"roles":821,"affiliations":822,"properties":831},"bbd12001-318b-4882-bf56-aac8ee31f9a2",[280],[823],{"id":22,"sortIndex":23,"affiliation":824,"properties":22},{"id":825,"createTime":826,"updateTime":826,"relativeEntities":827,"slug":22,"properties":828,"entityType":75,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"32c86676-c023-4624-a363-218ed4eeec55","2024-02-12T10:31:57.538+00:00",[],{"title":829},{"VI":830},"Shanghai Aircraft Design and Research Institute, Shanghai, China",{"title":832},{"VI":833},"Miao Zhang",{"id":835,"sortIndex":297,"researcher":22,"roles":836,"affiliations":837,"properties":848},"66338609-5fc5-47ee-b243-da92b4a9a102",[280],[838],{"id":22,"sortIndex":23,"affiliation":839,"properties":22},{"id":840,"createTime":841,"updateTime":842,"relativeEntities":843,"slug":844,"properties":845,"entityType":75,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"06d23642-694c-4f21-a223-0317a022d273","2024-04-06T02:28:59.452+00:00","2025-06-11T19:52:46.807+00:00",[],"National-Key-Laboratory-of-Science-and-Technology-on-Aerodynamic-Design-and-Research-Northwestern-Polytechnical-University-Xi-an-China",{"title":846},{"VI":847},"National Key Laboratory of Science and Technology on Aerodynamic Design and Research, Northwestern Polytechnical University, Xi’an, China",{"title":849},{"VI":850},"Di Sun",{"id":852,"sortIndex":413,"researcher":22,"roles":853,"affiliations":854,"properties":865},"71fe2617-39fb-46f3-a40e-89964e5e7908",[280],[855],{"id":22,"sortIndex":23,"affiliation":856,"properties":22},{"id":857,"createTime":858,"updateTime":859,"relativeEntities":860,"slug":861,"properties":862,"entityType":75,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"syncStatus":21,"languages":22,"translateLanguages":22,"viewCount":23},"1ee2ed71-615c-4b88-b39d-c7b3f834768f","2023-12-13T12:19:15.041+00:00","2024-08-31T23:36:41.012+00:00",[],"Xi-an-Aeronautics-Computing-Technique-Research-Institute-AVIC-Xi-an-China",{"title":863},{"VI":864},"Xi’an Aeronautics Computing Technique Research Institute, AVIC, Xi’an, China",{"title":866},{"VI":867},"Li 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AIAA\u002FASME\u002FASCE\u002FAHS\u002FASC 29th Structures, Structural Dynamics and Materials Conf. (held in Williamsburg, VA), Part 1, pp. 572–581\nBrown, R.T.; Nachlas, J.A. 1981: Structural optimization of laminated conical shells. In: Marshall, I.H. (ed.)Composite structures, pp. 144–157. Amsterdam: Elsevier\nDraper, N.R.; Smith, H. 1981:Applied regression analysis (2nd ed.). New York: John Wiley & Sons\nFadel, G.M.; Riley, M.F.; Barthelemy, J.M. 1990: Two point exponential approximation method for structural optimization.Struct. Optim. 2, 117–124\nFleury, C. 1989: First and second order convex approximation strategies in structural optimization.Struct. Optim. 1, 3–10\nFleury, C. 1989: CONLIN: An efficient dual optimizer based on convex approximation concepts.Struct. Optim. 1, 81–89\nFleury, C.; Braibant, V. 1986: Structural optimization: a new dual method using mixed variables.Int. J. Num. Meth. 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(submitted)\nSchmit, L.A.; Farshi, B. 1974: Some approximation concepts for structural synthesis.AIAA J. 12, 692–699\nSchmit, L.A.; Fleury, C. 1980: Structural synthesis by combining approximation concepts and dual methods.AIAA J. 18, 1252–1260\nSchoofs, A.J.G. 1987:Experimental design and structural optimization. Doctoral Dissertation, Technical University of Eindhoven\nSvanberg, K. 1987: The method of moving asymptotes — a new method for structural optimization.Int. J. Num. Meth. Eng. 24, 359–373\nToropov, V.V. 1989: Simulation approach to structural optimization.Struct. Optim. 1, 37–46\nVanderplaats, G.N. 1979: Efficient algorithm for numerical airfoil optimization.AIAA J. Aircaft 16, 842–847\nVanderplaats, G.N. 1989: Effective use of numerical optimization in structural design.Finite Elements in Analysis and Design 6, 97–112",{"EN":1331},"A unified approach to various problems of structural optimization, based on approximation concepts, is presented. 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