A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints

SUMMARY We present a method for finding solutions of large‐scale binary programming problems where the calculation of derivatives is very expensive. We then apply this method to a topology optimization problem of weight minimization subject to compliance and buckling constraints. We derive an analyt...

Full description

Saved in:

Bibliographic Details
Published in:	International journal for numerical methods in engineering Vol. 92; no. 12; pp. 1026 - 1043
Main Authors:	Browne, P. A., Budd, C., Gould, N. I. M., Kim, H. A., Scott, J. A.
Format:	Journal Article
Language:	English
Published:	Chichester Blackwell Publishing Ltd 21.12.2012 Wiley Wiley Subscription Services, Inc
Subjects:	binary programming Buckling eigenvalue Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis. Scientific computation Physics Sciences and techniques of general use Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics structural optimization topology optimization Geometrical shape High performance Stiffness matrix Constraint structural optimization Minimization Topology Distributed computing Modeling Weight Constrained optimization Finite element method Zero one programming binary programming Eigenvalue problem topology optimization Buckling eigenvalue Structural analysis
ISSN:	0029-5981, 1097-0207
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Abstract	SUMMARY We present a method for finding solutions of large‐scale binary programming problems where the calculation of derivatives is very expensive. We then apply this method to a topology optimization problem of weight minimization subject to compliance and buckling constraints. We derive an analytic expression for the derivative of the stress stiffness matrix with respect to the density of an element in the finite‐element setting. Results are presented for a number of two‐dimensional test problems.Copyright © 2012 John Wiley & Sons, Ltd.
AbstractList	SUMMARY We present a method for finding solutions of large-scale binary programming problems where the calculation of derivatives is very expensive. We then apply this method to a topology optimization problem of weight minimization subject to compliance and buckling constraints. We derive an analytic expression for the derivative of the stress stiffness matrix with respect to the density of an element in the finite-element setting. Results are presented for a number of two-dimensional test problems.Copyright © 2012 John Wiley & Sons, Ltd. [PUBLICATION ABSTRACT] We present a method for finding solutions of large‐scale binary programming problems where the calculation of derivatives is very expensive. We then apply this method to a topology optimization problem of weight minimization subject to compliance and buckling constraints. We derive an analytic expression for the derivative of the stress stiffness matrix with respect to the density of an element in the finite‐element setting. Results are presented for a number of two‐dimensional test problems.Copyright © 2012 John Wiley & Sons, Ltd. SUMMARY We present a method for finding solutions of large‐scale binary programming problems where the calculation of derivatives is very expensive. We then apply this method to a topology optimization problem of weight minimization subject to compliance and buckling constraints. We derive an analytic expression for the derivative of the stress stiffness matrix with respect to the density of an element in the finite‐element setting. Results are presented for a number of two‐dimensional test problems.Copyright © 2012 John Wiley & Sons, Ltd.
Author	Budd, C. Kim, H. A. Browne, P. A. Gould, N. I. M. Scott, J. A.
Author_xml	– sequence: 1 givenname: P. A. surname: Browne fullname: Browne, P. A. email: P. A. Browne, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, U.K., P.A.Browne@bath.ac.uk organization: Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK – sequence: 2 givenname: C. surname: Budd fullname: Budd, C. organization: Department of Mathematical Sciences, University of Bath, BA2 7AY, Bath, UK – sequence: 3 givenname: N. I. M. surname: Gould fullname: Gould, N. I. M. organization: Numerical Analysis Group, STFC Rutherford Appleton Laboratory, OX11 0QX, Oxfordshire, UK – sequence: 4 givenname: H. A. surname: Kim fullname: Kim, H. A. organization: Department of Mechanical Engineering, University of Bath, BA2 7AY, Bath, UK – sequence: 5 givenname: J. A. surname: Scott fullname: Scott, J. A. organization: Numerical Analysis Group, STFC Rutherford Appleton Laboratory, OX11 0QX, Oxfordshire, UK
BackLink	http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=26636567$$DView record in Pascal Francis
BookMark	eNp1kdFKHDEUhkOx0NUKfYRAKfSisyaTncnkUkStoBaqZS_DmUyyRmeSaZLVbl_A1zbj2kJLC0kO5P_OH07-XbTjvNMIvaNkTgkpD9yg5wtW81doRongBSkJ30GzLImiEg19g3ZjvCWE0oqwGXo8xAZiwoNON77DxgfcWgdhg8fgVwGGwboVXsfpNDbEVPjQ6YDztveQ7L2On_CDTTcYxrG3Kl95h5PPa_S9X22wH5Md7M-t8Ey2a3XXT4bKu5gCWJfiW_TaQB_1_kvdQ99Ojq-PPhfnX07Pjg7PC8VqyouSc1gANG1VCSMUaGYWhghKlGKmrQmj1HQtEUBMB7ThDUDbMMGh7DToTrE99H7rm8f7vtYxyVu_Di4_KSkrqWiqelFl6sMLBVFBbwI4ZaMcgx3y18iyrlld1Txz8y2ngo8xaCOVTc-TTmP1khI5hSJzKHIKJTd8_Kvhl-c_0GKLPtheb_7LycuL4z95G5P-8ZuHcCezyiu5vDyVy-WJ-HpVXcgr9gQHgLCh
CODEN	IJNMBH
CitedBy_id	crossref_primary_10_1016_j_compstruct_2016_09_055 crossref_primary_10_1016_j_compscitech_2015_08_003 crossref_primary_10_1016_j_amc_2021_126032 crossref_primary_10_1080_0305215X_2021_1982930 crossref_primary_10_1177_1687814017715422 crossref_primary_10_1007_s00158_019_02396_3 crossref_primary_10_1007_s00366_023_01829_4 crossref_primary_10_1016_j_compstruc_2021_106685 crossref_primary_10_1016_j_istruc_2024_107533 crossref_primary_10_1007_s00158_016_1511_5 crossref_primary_10_1007_s10338_019_00088_5 crossref_primary_10_1016_j_istruc_2023_105220 crossref_primary_10_1007_s00158_015_1286_0 crossref_primary_10_1007_s00158_021_03152_2 crossref_primary_10_1007_s10409_015_0531_5 crossref_primary_10_1007_s00158_016_1544_9
Cites_doi	10.1007/s00158‐006‐0074‐2 10.1007/s00158-009-0476-z 10.1002/1097-0207(20000830)48:12<1761::AID-NME963>3.0.CO;2-R 10.1080/10556780410001682844 10.1002/nme.700 10.1002/9780470689486 10.1007/s00158‐002‐0177‐3 10.1007/BF01743302 10.1007/s00158‐011‐0703‐2 10.1007/s10589‐007‐9138‐5 10.1002/nme.1620240207 10.1007/s10589‐007‐9152‐7 10.1145/512274.512284 10.1061/JSDEAG.0001952 10.1007/BF01743339 10.1007/s00158-010-0574-y 10.1002/nme.449 10.1137/090757216 10.1115/1.2912596 10.1007/s001580050130 10.1115/1.2912568 10.1080/03052158808940951
ContentType	Journal Article
Copyright	Copyright © 2012 John Wiley & Sons, Ltd. 2014 INIST-CNRS
Copyright_xml	– notice: Copyright © 2012 John Wiley & Sons, Ltd. – notice: 2014 INIST-CNRS
DBID	BSCLL AAYXX CITATION IQODW 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D
DOI	10.1002/nme.4367
DatabaseName	Istex CrossRef Pascal-Francis Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional
DatabaseTitle	CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional
DatabaseTitleList	Civil Engineering Abstracts CrossRef
DeliveryMethod	fulltext_linktorsrc
Discipline	Applied Sciences Engineering Mathematics Physics
EISSN	1097-0207
EndPage	1043
ExternalDocumentID	2932489051 26636567 10_1002_nme_4367 NME4367 ark_67375_WNG_WWF9RS5M_S
Genre	article
GrantInformation_xml	– fundername: EPSRC funderid: EP/E053351/1
GroupedDBID	-~X .3N .4S .DC .GA .Y3 05W 0R~ 10A 1L6 1OB 1OC 1ZS 33P 3SF 3WU 4.4 4ZD 50Y 50Z 51W 51X 52M 52N 52O 52P 52S 52T 52U 52W 52X 5GY 5VS 66C 702 7PT 8-0 8-1 8-3 8-4 8-5 8UM 930 A03 AAESR AAEVG AAHQN AAMMB AAMNL AANHP AANLZ AAONW AASGY AAXRX AAYCA AAZKR ABCQN ABCUV ABIJN ABJNI ACAHQ ACBWZ ACCZN ACGFS ACIWK ACPOU ACRPL ACXBN ACXQS ACYXJ ADBBV ADEOM ADIZJ ADKYN ADMGS ADNMO ADOZA ADXAS ADZMN AEFGJ AEIGN AEIMD AENEX AEUYR AEYWJ AFBPY AFFPM AFGKR AFWVQ AFZJQ AGQPQ AGXDD AGYGG AHBTC AIDQK AIDYY AITYG AIURR AJXKR ALAGY ALMA_UNASSIGNED_HOLDINGS ALUQN ALVPJ AMBMR AMYDB ARCSS ASPBG ATUGU AUFTA AVWKF AZBYB AZFZN AZVAB BAFTC BDRZF BFHJK BHBCM BMNLL BMXJE BNHUX BROTX BRXPI BSCLL BY8 CS3 D-E D-F DCZOG DPXWK DR2 DRFUL DRSTM DU5 EBS EJD F00 F01 F04 F5P FEDTE G-S G.N GNP GODZA H.T H.X HBH HF~ HGLYW HHY HVGLF HZ~ IX1 J0M JPC KQQ LATKE LAW LC2 LC3 LEEKS LH4 LITHE LOXES LP6 LP7 LUTES LW6 LYRES MEWTI MK4 MRFUL MRSTM MSFUL MSSTM MXFUL MXSTM N04 N05 NF~ O66 O9- OIG P2P P2W P2X P4D Q.N Q11 QB0 QRW R.K RNS ROL RX1 RYL SUPJJ TN5 TUS UB1 V2E W8V W99 WBKPD WIB WIH WIK WLBEL WOHZO WQJ WXSBR WYISQ XG1 XPP XV2 ZZTAW ~02 ~IA ~WT AAYXX CITATION O8X 31~ 6TJ ABDPE ABEML ACKIV ACSCC AGHNM AI. GBZZK IQODW M6O PALCI RIWAO SAMSI VH1 VOH ZY4 ~A~ 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D
ID	FETCH-LOGICAL-c3617-277a4aa8b559f9cae3f4f0910cc3fb60311fdb09a0fda1878aab8397a2deaedc3
IEDL.DBID	DRFUL
ISICitedReferencesCount	19
ISICitedReferencesURI	http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000311397600002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN	0029-5981
IngestDate	Fri Jul 25 12:33:47 EDT 2025 Mon Jul 21 09:16:23 EDT 2025 Sat Nov 29 06:43:46 EST 2025 Tue Nov 18 20:40:37 EST 2025 Sun Sep 21 06:12:27 EDT 2025 Sun Sep 21 06:15:49 EDT 2025
IsPeerReviewed	true
IsScholarly	true
Issue	12
Keywords	Geometrical shape High performance Stiffness matrix Constraint structural optimization Minimization Topology Distributed computing Modeling Weight Constrained optimization Finite element method Zero one programming binary programming Eigenvalue problem topology optimization Buckling eigenvalue Structural analysis
Language	English
License	http://onlinelibrary.wiley.com/termsAndConditions#vor CC BY 4.0
LinkModel	DirectLink
MergedId	FETCHMERGED-LOGICAL-c3617-277a4aa8b559f9cae3f4f0910cc3fb60311fdb09a0fda1878aab8397a2deaedc3
Notes	ark:/67375/WNG-WWF9RS5M-S ArticleID:NME4367 EPSRC - No. EP/E053351/1 istex:0A5059919A6DABA57C8B7295DBA5D5D13219E799 ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14
PQID	1321985645
PQPubID	996376
PageCount	18
ParticipantIDs	proquest_journals_1321985645 pascalfrancis_primary_26636567 crossref_citationtrail_10_1002_nme_4367 crossref_primary_10_1002_nme_4367 wiley_primary_10_1002_nme_4367_NME4367 istex_primary_ark_67375_WNG_WWF9RS5M_S
PublicationCentury	2000
PublicationDate	21 December 2012
PublicationDateYYYYMMDD	2012-12-21
PublicationDate_xml	– month: 12 year: 2012 text: 21 December 2012 day: 21
PublicationDecade	2010
PublicationPlace	Chichester
PublicationPlace_xml	– name: Chichester – name: Bognor Regis
PublicationTitle	International journal for numerical methods in engineering
PublicationTitleAlternate	Int. J. Numer. Meth. Engng
PublicationYear	2012
Publisher	Blackwell Publishing Ltd Wiley Wiley Subscription Services, Inc
Publisher_xml	– name: Blackwell Publishing Ltd – name: Wiley – name: Wiley Subscription Services, Inc
References	Stolpe M, Svanberg K.Modelling topology optimization problems as linear mixed 0 − − 1 programs. International Journal for Numerical Methods in Engineering June 2003; 57(5):723-739. DOI: 10.1002/nme.700. Available from: http://doi.wiley.com/10.1002/nme.700. Cook RD, Malkus DS, Plesha M.Concepts and Applications of Finite Element Analysis. John Wiley and Sons: London, UK, 1989. Salajegheh E, Vanderplaats G.Optimum design of trusses with discrete sizing and shape variables. Structural Optimization 1993; 6:79-85. Williams J.Algorithm 232: heapsort. Communications of the ACM 1964; 7(6):347-348. Beckers M.Dual methods for discrete structural optimization problems. International Journal for Numerical Methods in Engineering 2000; 48(12):1761-1784. Sandgren E.Nonlinear integer and discrete programming for topological decision making in engineering design. Journal of Mechanical Design 1990; 112(1):118-122. DOI: 10.1115/1.2912568. Available from: http://link.aip.org/link/?JMD/112/118/1 Hunt G, Thompson J.A General Theory of Elastic Stability. Wiley-Interscience: London, UK, 1973. Kočvara M.On the modelling and solving of the truss design problem with global stability constraints. Structural and Multidisciplinary Optimization April 2002; 23(3):189-203. DOI: 10.1007/s00158-002-0177-3. Available from: http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00158-002-0177-3 Rozvany GIN.Authors reply to a discussion by Gengdong Cheng and Xiaofeng Liu of the review article On symmetry and non-uniqueness in exact topology optimizationİ by George I. N. Rozvany (2011, Struct Multidisc Optim 43: 297317). Structural and Multidisciplinary Optimization September 2011; 44(5):719-721. DOI: 10.1007/s00158-011-0703-2. Available from: http://www.springerlink.com/index/10.1007/s00158-011-0703-2 Kočvara M, Stingl M.Solving nonconvex SDP problems of structural optimization with stability control. Optimization Methods and Software October 2004; 19(5):595-609. DOI: 10.1080/10556780410001682844. Available from: http://www.informaworld.com/openurl?genre=article&doi=10.1080/10556780410001682844&magic=crossref\|\|D404A21C5BB053405B1A640AFFD44AE3 Wolsey L.Integer programming, Wiley-Interscience series in discrete mathematics and optimization, Wiley: New York, USA, 1998. Available from: http://books.google.com/books?id=x7RvQgAACAAJ Pedersen N.Maximization of eigenvalues using topology optimization. Structural and Multidisciplinary Optimization 2000; 20(1):2-11. Neves MM, Sigmund O, Bendsøe MP.Topology optimization of periodic microstructures with a penalization of highly localized buckling modes. International Journal for Numerical Methods in Engineering June 2002; 54(6):809-834. DOI: 10.1002/nme.449. Available from: http://doi.wiley.com/10.1002/nme.449 Bendsøe MP, Sigmund O. Topology Optimization: Theory, Methods and Applications. Springer: Berlin, Germany, 2003. Achtziger W, Stolpe M.Truss topology optimization with discrete design variables-guaranteed global optimality and benchmark examples. Structural and Multidisciplinary Optimization December 2007; 34(1):1-20. DOI: 10.1007/s00158-006-0074-2. Available from: http://www.springerlink.com/index/10.1007/s00158-006-0074-2. Achtziger W, Stolpe M.Global optimization of truss topology with discrete bar areas-Part II: implementation and numerical results. Computational Optimization and Applications 2009; 44(2):315-341. DOI: 10.1007/s10589-007-9152-7. Huang X, Xie YM.Evolutionary Topology Optimization of Continuum Structures. John Wiley & Sons Ltd: Chichester, UK, 2010. Svanberg K.The method of moving asymptotes-a new method for structural optimization. International Journal For Numerical Methods in Engineering 1987; 24:359-373. Stolpe M, Bendsøe MP.Global optima for the Zhou-Rozvany problem. Structural and Multidisciplinary Optimization 2010; 43(2):151-164. Tenek LH, Hagiwara I.Eigenfrequency maximization of plates by optimization of topology using homogenization and mathematical programming. JSME International Journal Series C 1994; 37(4):667-677. Stolpe M.On some fundamental properties of structural topology optimization problems. Structural and Multidisciplinary Optimization 2010; 41(5):661-670. Hogg J, Reid J, Scott J.Design of a multicore sparse cholesky factorization using DAGs. SISC 2010; 32:3627-3649. Sandgren E.Nonlinear integer and discrete programming in mechanical design optimization. Journal of Mechanical Design 1990; 112(2):223-229. DOI: 10.1115/1.2912596. Available from: http://link.aip.org/link/?JMD/112/223/1. Farkas J, Szabo L.Optimum design of beams and frames of welded I-sections by means of backtrack programming. Acta Technica Academiae Scientiarum Hungaricae 1980; 91(1):121-135. Arora J, Huang M.Methods for optimization of nonlinear problems with discrete variables: a review. Structural Optimization 1994; 8:69-85. Toakley A,Optimum design using available sections. Journal of the Structural Division: proceedings of the American Society of Civil Engineers 1968; 94:1219-1241. Achtziger W, Stolpe M.Global optimization of truss topology with discrete bar areas-Part I: theory of relaxed problems. Computational Optimization and Applications November 2008; 40(2):247-280. DOI: 10.1007/s10589-007-9138-5. Available from: http://www.springerlink.com/index/10.1007/s10589-007-9138-5. John K, Ramakrishna C, Sharma K.Optimum design of trusses from available sections-use of sequential linear programming with branch and bound algorithm. Engineering Optimization 1988; 13(2):119-145. 2009; 44 2010; 32 2000; 48 2011 2010 1964; 7 2002; 54 2000; 20 1998 2003; 57 2009 1988; 13 1973 1980; 91 2003 2007; 34 2010; 41 1993; 6 1987; 24 1994; 8 2010; 43 2004; 19 2002; 23 2011; 44 1994; 37 1968; 94 1990; 112 2008; 40 1989 e_1_2_7_5_1 e_1_2_7_3_1 Tenek LH (e_1_2_7_21_1) 1994; 37 e_1_2_7_9_1 e_1_2_7_8_1 e_1_2_7_7_1 e_1_2_7_19_1 e_1_2_7_18_1 e_1_2_7_16_1 e_1_2_7_15_1 e_1_2_7_14_1 e_1_2_7_13_1 e_1_2_7_12_1 e_1_2_7_11_1 e_1_2_7_10_1 e_1_2_7_26_1 e_1_2_7_27_1 e_1_2_7_28_1 e_1_2_7_29_1 Toakley A (e_1_2_7_4_1) 1968; 94 Hunt G (e_1_2_7_24_1) 1973 Cook RD (e_1_2_7_25_1) 1989 Farkas J (e_1_2_7_6_1) 1980; 91 e_1_2_7_31_1 e_1_2_7_32_1 Bendsøe MP (e_1_2_7_17_1) 2003 e_1_2_7_23_1 e_1_2_7_22_1 e_1_2_7_20_1 Wolsey L (e_1_2_7_2_1) 1998 Williams J (e_1_2_7_30_1) 1964; 7
References_xml	– reference: Beckers M.Dual methods for discrete structural optimization problems. International Journal for Numerical Methods in Engineering 2000; 48(12):1761-1784. – reference: Neves MM, Sigmund O, Bendsøe MP.Topology optimization of periodic microstructures with a penalization of highly localized buckling modes. International Journal for Numerical Methods in Engineering June 2002; 54(6):809-834. DOI: 10.1002/nme.449. Available from: http://doi.wiley.com/10.1002/nme.449 – reference: Williams J.Algorithm 232: heapsort. Communications of the ACM 1964; 7(6):347-348. – reference: Arora J, Huang M.Methods for optimization of nonlinear problems with discrete variables: a review. Structural Optimization 1994; 8:69-85. – reference: Kočvara M.On the modelling and solving of the truss design problem with global stability constraints. Structural and Multidisciplinary Optimization April 2002; 23(3):189-203. DOI: 10.1007/s00158-002-0177-3. Available from: http://www.springerlink.com/openurl.asp?genre=article&id=doi:10.1007/s00158-002-0177-3 – reference: Wolsey L.Integer programming, Wiley-Interscience series in discrete mathematics and optimization, Wiley: New York, USA, 1998. Available from: http://books.google.com/books?id=x7RvQgAACAAJ – reference: Achtziger W, Stolpe M.Global optimization of truss topology with discrete bar areas-Part I: theory of relaxed problems. Computational Optimization and Applications November 2008; 40(2):247-280. DOI: 10.1007/s10589-007-9138-5. Available from: http://www.springerlink.com/index/10.1007/s10589-007-9138-5. – reference: Cook RD, Malkus DS, Plesha M.Concepts and Applications of Finite Element Analysis. John Wiley and Sons: London, UK, 1989. – reference: Achtziger W, Stolpe M.Global optimization of truss topology with discrete bar areas-Part II: implementation and numerical results. Computational Optimization and Applications 2009; 44(2):315-341. DOI: 10.1007/s10589-007-9152-7. – reference: Bendsøe MP, Sigmund O. Topology Optimization: Theory, Methods and Applications. Springer: Berlin, Germany, 2003. – reference: Tenek LH, Hagiwara I.Eigenfrequency maximization of plates by optimization of topology using homogenization and mathematical programming. JSME International Journal Series C 1994; 37(4):667-677. – reference: Sandgren E.Nonlinear integer and discrete programming for topological decision making in engineering design. Journal of Mechanical Design 1990; 112(1):118-122. DOI: 10.1115/1.2912568. Available from: http://link.aip.org/link/?JMD/112/118/1 – reference: Sandgren E.Nonlinear integer and discrete programming in mechanical design optimization. Journal of Mechanical Design 1990; 112(2):223-229. DOI: 10.1115/1.2912596. Available from: http://link.aip.org/link/?JMD/112/223/1. – reference: Hogg J, Reid J, Scott J.Design of a multicore sparse cholesky factorization using DAGs. SISC 2010; 32:3627-3649. – reference: Toakley A,Optimum design using available sections. Journal of the Structural Division: proceedings of the American Society of Civil Engineers 1968; 94:1219-1241. – reference: Farkas J, Szabo L.Optimum design of beams and frames of welded I-sections by means of backtrack programming. Acta Technica Academiae Scientiarum Hungaricae 1980; 91(1):121-135. – reference: Stolpe M, Svanberg K.Modelling topology optimization problems as linear mixed 0 − − 1 programs. International Journal for Numerical Methods in Engineering June 2003; 57(5):723-739. DOI: 10.1002/nme.700. Available from: http://doi.wiley.com/10.1002/nme.700. – reference: Achtziger W, Stolpe M.Truss topology optimization with discrete design variables-guaranteed global optimality and benchmark examples. Structural and Multidisciplinary Optimization December 2007; 34(1):1-20. DOI: 10.1007/s00158-006-0074-2. Available from: http://www.springerlink.com/index/10.1007/s00158-006-0074-2. – reference: Huang X, Xie YM.Evolutionary Topology Optimization of Continuum Structures. John Wiley & Sons Ltd: Chichester, UK, 2010. – reference: Svanberg K.The method of moving asymptotes-a new method for structural optimization. International Journal For Numerical Methods in Engineering 1987; 24:359-373. – reference: Kočvara M, Stingl M.Solving nonconvex SDP problems of structural optimization with stability control. Optimization Methods and Software October 2004; 19(5):595-609. DOI: 10.1080/10556780410001682844. Available from: http://www.informaworld.com/openurl?genre=article&doi=10.1080/10556780410001682844&magic=crossref\|\|D404A21C5BB053405B1A640AFFD44AE3 – reference: Salajegheh E, Vanderplaats G.Optimum design of trusses with discrete sizing and shape variables. Structural Optimization 1993; 6:79-85. – reference: Pedersen N.Maximization of eigenvalues using topology optimization. Structural and Multidisciplinary Optimization 2000; 20(1):2-11. – reference: John K, Ramakrishna C, Sharma K.Optimum design of trusses from available sections-use of sequential linear programming with branch and bound algorithm. Engineering Optimization 1988; 13(2):119-145. – reference: Rozvany GIN.Authors reply to a discussion by Gengdong Cheng and Xiaofeng Liu of the review article On symmetry and non-uniqueness in exact topology optimizationİ by George I. N. Rozvany (2011, Struct Multidisc Optim 43: 297317). Structural and Multidisciplinary Optimization September 2011; 44(5):719-721. DOI: 10.1007/s00158-011-0703-2. Available from: http://www.springerlink.com/index/10.1007/s00158-011-0703-2 – reference: Stolpe M.On some fundamental properties of structural topology optimization problems. Structural and Multidisciplinary Optimization 2010; 41(5):661-670. – reference: Hunt G, Thompson J.A General Theory of Elastic Stability. Wiley-Interscience: London, UK, 1973. – reference: Stolpe M, Bendsøe MP.Global optima for the Zhou-Rozvany problem. Structural and Multidisciplinary Optimization 2010; 43(2):151-164. – volume: 20 start-page: 2 issue: 1 year: 2000 end-page: 11 article-title: Maximization of eigenvalues using topology optimization publication-title: Structural and Multidisciplinary Optimization – year: 2011 – volume: 13 start-page: 119 issue: 2 year: 1988 end-page: 145 article-title: Optimum design of trusses from available sections—use of sequential linear programming with branch and bound algorithm publication-title: Engineering Optimization – volume: 6 start-page: 79 year: 1993 end-page: 85 article-title: Optimum design of trusses with discrete sizing and shape variables publication-title: Structural Optimization – volume: 44 start-page: 315 issue: 2 year: 2009 end-page: 341 article-title: Global optimization of truss topology with discrete bar areas—Part II: implementation and numerical results publication-title: Computational Optimization and Applications – volume: 91 start-page: 121 issue: 1 year: 1980 end-page: 135 article-title: Optimum design of beams and frames of welded I‐sections by means of backtrack programming publication-title: Acta Technica Academiae Scientiarum Hungaricae – volume: 8 start-page: 69 year: 1994 end-page: 85 article-title: Methods for optimization of nonlinear problems with discrete variables: a review publication-title: Structural Optimization – volume: 23 start-page: 189 issue: 3 year: 2002 end-page: 203 article-title: On the modelling and solving of the truss design problem with global stability constraints publication-title: Structural and Multidisciplinary Optimization – year: 1989 – year: 2003 – year: 1973 – volume: 41 start-page: 661 issue: 5 year: 2010 end-page: 670 article-title: On some fundamental properties of structural topology optimization problems publication-title: Structural and Multidisciplinary Optimization – volume: 32 start-page: 3627 year: 2010 end-page: 3649 article-title: Design of a multicore sparse cholesky factorization using DAGs publication-title: SISC – volume: 112 start-page: 118 issue: 1 year: 1990 end-page: 122 article-title: Nonlinear integer and discrete programming for topological decision making in engineering design publication-title: Journal of Mechanical Design – volume: 34 start-page: 1 issue: 1 year: 2007 end-page: 20 article-title: Truss topology optimization with discrete design variables—guaranteed global optimality and benchmark examples publication-title: Structural and Multidisciplinary Optimization – year: 1998 – year: 2010 – volume: 44 start-page: 719 issue: 5 year: 2011 end-page: 721 article-title: Authors reply to a discussion by Gengdong Cheng and Xiaofeng Liu of the review article On symmetry and non‐uniqueness in exact topology optimizationİ by George I. N. Rozvany (2011, Struct Multidisc Optim 43: 297317) publication-title: Structural and Multidisciplinary Optimization – volume: 43 start-page: 151 issue: 2 year: 2010 end-page: 164 article-title: Global optima for the Zhou–Rozvany problem publication-title: Structural and Multidisciplinary Optimization – volume: 24 start-page: 359 year: 1987 end-page: 373 article-title: The method of moving asymptotes—a new method for structural optimization publication-title: International Journal For Numerical Methods in Engineering – volume: 19 start-page: 595 issue: 5 year: 2004 end-page: 609 article-title: Solving nonconvex SDP problems of structural optimization with stability control publication-title: Optimization Methods and Software – volume: 54 start-page: 809 issue: 6 year: 2002 end-page: 834 article-title: Topology optimization of periodic microstructures with a penalization of highly localized buckling modes publication-title: International Journal for Numerical Methods in Engineering – volume: 57 start-page: 723 issue: 5 year: 2003 end-page: 739 article-title: Modelling topology optimization problems as linear mixed 0 − − 1 programs publication-title: International Journal for Numerical Methods in Engineering – volume: 7 start-page: 347 issue: 6 year: 1964 end-page: 348 article-title: Algorithm 232: heapsort publication-title: Communications of the ACM – volume: 112 start-page: 223 issue: 2 year: 1990 end-page: 229 article-title: Nonlinear integer and discrete programming in mechanical design optimization publication-title: Journal of Mechanical Design – start-page: 1 year: 2009 end-page: 10 – volume: 37 start-page: 667 issue: 4 year: 1994 end-page: 677 article-title: Eigenfrequency maximization of plates by optimization of topology using homogenization and mathematical programming publication-title: JSME International Journal Series C – volume: 94 start-page: 1219 year: 1968 end-page: 1241 article-title: Optimum design using available sections publication-title: Journal of the Structural Division: proceedings of the American Society of Civil Engineers – volume: 40 start-page: 247 issue: 2 year: 2008 end-page: 280 article-title: Global optimization of truss topology with discrete bar areas—Part I: theory of relaxed problems publication-title: Computational Optimization and Applications – volume: 48 start-page: 1761 issue: 12 year: 2000 end-page: 1784 article-title: Dual methods for discrete structural optimization problems publication-title: International Journal for Numerical Methods in Engineering – ident: e_1_2_7_13_1 doi: 10.1007/s00158‐006‐0074‐2 – ident: e_1_2_7_31_1 doi: 10.1007/s00158-009-0476-z – ident: e_1_2_7_20_1 – volume-title: Integer programming year: 1998 ident: e_1_2_7_2_1 – ident: e_1_2_7_11_1 doi: 10.1002/1097-0207(20000830)48:12<1761::AID-NME963>3.0.CO;2-R – ident: e_1_2_7_19_1 doi: 10.1080/10556780410001682844 – volume-title: Concepts and Applications of Finite Element Analysis year: 1989 ident: e_1_2_7_25_1 – volume-title: Topology Optimization: Theory, Methods and Applications year: 2003 ident: e_1_2_7_17_1 – ident: e_1_2_7_28_1 – ident: e_1_2_7_12_1 doi: 10.1002/nme.700 – ident: e_1_2_7_29_1 doi: 10.1002/9780470689486 – ident: e_1_2_7_18_1 doi: 10.1007/s00158‐002‐0177‐3 – ident: e_1_2_7_3_1 doi: 10.1007/BF01743302 – volume-title: A General Theory of Elastic Stability year: 1973 ident: e_1_2_7_24_1 – ident: e_1_2_7_32_1 doi: 10.1007/s00158‐011‐0703‐2 – ident: e_1_2_7_14_1 doi: 10.1007/s10589‐007‐9138‐5 – ident: e_1_2_7_16_1 doi: 10.1002/nme.1620240207 – volume: 37 start-page: 667 issue: 4 year: 1994 ident: e_1_2_7_21_1 article-title: Eigenfrequency maximization of plates by optimization of topology using homogenization and mathematical programming publication-title: JSME International Journal Series C – ident: e_1_2_7_15_1 doi: 10.1007/s10589‐007‐9152‐7 – volume: 7 start-page: 347 issue: 6 year: 1964 ident: e_1_2_7_30_1 article-title: Algorithm 232: heapsort publication-title: Communications of the ACM doi: 10.1145/512274.512284 – volume: 94 start-page: 1219 year: 1968 ident: e_1_2_7_4_1 article-title: Optimum design using available sections publication-title: Journal of the Structural Division: proceedings of the American Society of Civil Engineers doi: 10.1061/JSDEAG.0001952 – ident: e_1_2_7_10_1 doi: 10.1007/BF01743339 – ident: e_1_2_7_5_1 doi: 10.1007/s00158-010-0574-y – ident: e_1_2_7_23_1 doi: 10.1002/nme.449 – ident: e_1_2_7_27_1 doi: 10.1137/090757216 – ident: e_1_2_7_9_1 doi: 10.1115/1.2912596 – ident: e_1_2_7_22_1 doi: 10.1007/s001580050130 – volume: 91 start-page: 121 issue: 1 year: 1980 ident: e_1_2_7_6_1 article-title: Optimum design of beams and frames of welded I‐sections by means of backtrack programming publication-title: Acta Technica Academiae Scientiarum Hungaricae – ident: e_1_2_7_8_1 doi: 10.1115/1.2912568 – ident: e_1_2_7_26_1 – ident: e_1_2_7_7_1 doi: 10.1080/03052158808940951
SSID	ssj0011503
Score	2.162746
Snippet	SUMMARY We present a method for finding solutions of large‐scale binary programming problems where the calculation of derivatives is very expensive. We then... We present a method for finding solutions of large‐scale binary programming problems where the calculation of derivatives is very expensive. We then apply this... SUMMARY We present a method for finding solutions of large-scale binary programming problems where the calculation of derivatives is very expensive. We then...
SourceID	proquest pascalfrancis crossref wiley istex
SourceType	Aggregation Database Index Database Enrichment Source Publisher
StartPage	1026
SubjectTerms	binary programming Buckling eigenvalue Exact sciences and technology Fundamental areas of phenomenology (including applications) Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Numerical analysis. Scientific computation Physics Sciences and techniques of general use Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics structural optimization topology optimization
Title	A fast method for binary programming using first-order derivatives, with application to topology optimization with buckling constraints
URI	https://api.istex.fr/ark:/67375/WNG-WWF9RS5M-S/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fnme.4367 https://www.proquest.com/docview/1321985645
Volume	92
WOSCitedRecordID	wos000311397600002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
hasFullText	1
inHoldings	1
isFullTextHit
isPrint
journalDatabaseRights	– providerCode: PRVWIB databaseName: Wiley Online Library - Journals customDbUrl: eissn: 1097-0207 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0011503 issn: 0029-5981 databaseCode: DRFUL dateStart: 19960101 isFulltext: true titleUrlDefault: https://onlinelibrary.wiley.com providerName: Wiley-Blackwell
link	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1Bb9MwFLag5QAHBoOJwpiMhOBCWGI7xDlOsMJhrdDG6G6W7dhograoCRPcuO6238gv4T3HiVoJJCSkRFGkZ8d6fs_-Yj9_j5Cn0Ms6rRxLLHcyEU7kSSl8lnBmcuYLXVZho_3jUTGdyrOz8n2MqsSzMC0_RL_ghp4Rxmt0cG3q_TXS0Ll7Kfir4joZMjDbfECGb47Hp0f9HgJAHd4FeOSlzDrq2ZTtd2U3JqMh6vU7BkfqGvTj28QWG8hzHb-GCWi89T9Nv0NuR9hJD1o7uUuuucU22YoQlEYHr7fJrTV-Qnib9KSu9T1yeUC9rhvaJp2mgHapCad5aQzymkMhioH0n6g_B1T56-dVYPakcIckaheufkFx5Zeu7ZvTZglXSNXwgy5hBJvHo6GtpMHNZ6zSIpLFhBZNfZ-cjg8_vH6XxEwOYAIAkRJWFFpoLQ38v_jSase98IhUrOXeYKLrzFcmLXXqK53JQmptALkVmlVOu8ryHTJYLBfuAaHC5N5k0vrKZUisKEUmtPG5YKnnJbcj8rzrUmUjzTk27otqCZqZAu0r1P6IPOklv7bUHn-QeRasohfQq88YClfkajZ9q2azcXl8kk_UyYjsbZhNXwAAEAfMDDXtdnak4jBRq4zDhCGR0Ac-FCzmry1R08khPh_-q-AjchPAXchcw7JdMmhW39xjcsNeNOf1ai86y28o4x2N
linkProvider	Wiley-Blackwell
linkToHtml	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3di9QwEB_OW0F98PRUbvU8I4i-2Lu2SW2LT4feeuLuIvfh3ltI0kSOc3dlWw9989U3_0b_EmfSD3ZBQRBaSmGShslM8msy-Q3AE-xlFRY2Dgy3WSCsSIJcuCjgsU5il6q88BvtH4bpeJydneXv1-Blexam5ofoFtzIM_x4TQ5OC9J7S6yhU7sr-Iv0CvQEWhGad-_10eB02G0iINbhbYRHkmdRyz0bxntt2ZXZqEeK_UrRkapEBbk6s8UK9FwGsH4GGmz8V9tvwc0GeLL92lJuw5qdbcJGA0JZ4-LlJtxYYijEt1FH61regR_7zKmyYnXaaYZ4l2l_npc1YV5TLMQolP4jc-eIK399_-m5PRnePo3apS2fM1r7ZUs756ya4-WTNXxjcxzDps3h0FpS0_YzVWkIy1JKi6q8C6eDg5NXh0GTywGNAEFSEKepEkplGv9gXG6U5U44wirGcKcp1XXkCh3mKnSFirI0U0ojdktVXFhlC8PvwfpsPrNbwIROnI4y4wobEbViJiKhtEtEHDqec9OHZ22fStMQnVPjPsmaojmWqH1J2u_D407yc03u8QeZp94sOgG1uKBguDSRk_EbOZkM8qPjZCSP-7CzYjddAYRAHFEz1rTdGpJsBopSRhynjIwoffBD3mT-2hI5Hh3Q8_6_Cj6Ca4cno6Ecvh2_ewDXEer5PDZxtA3r1eKLfQhXzWV1Xi52Gs_5DSBnIX0
linkToPdf	http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3Pi9QwFH6sMyJ6cHVVHF3XCKIX6zZNals8Le5WxZmy7LrO3kKSJrLozCzTuujNqzf_Rv8SX9IfzICCILSUwksakpfka_LyfQCPsZVlWJoo0MykATc8DjJuacAiFUc2kVnpN9o_jJOiSE9Ps8MNeNmdhWn4IfoFN9cz_HjtOrg5L-3uCmvozDzn7EVyCYbcacgMYLh_lJ-M-00ExDqsi_CIs5R23LNhtNulXZuNhq5iv7roSFlhBdlG2WINeq4CWD8D5Zv_VfYbcL0FnmSv8ZSbsGHmW7DZglDSdvFqC66tMBTi26Snda1uwY89YmVVk0Z2miDeJcqf5yVtmNcMExEXSv-R2DPElb--__TcngRvL6N2YapnxK39kpWdc1Iv8PJiDd_IAsewWXs4tLFUbvvZZakdlnWSFnV1G07yg_ev3gStlgM6AYKkIEoSyaVMFf7B2ExLwyy3DqtozaxyUtfUlirMZGhLSdMklVIhdktkVBppSs3uwGC-mJu7QLiKraKptqWhjlox5ZRLZWMehZZlTI_gademQrdE565wn0VD0RwJrH3han8Ej3rL84bc4w82T7xb9AZy-ckFwyWxmBavxXSaZ0fH8UQcj2BnzW_6BAiBGKJmzGm7cyTRDhSVoAynjNRR-uCHvMv8tSSimBy4571_NXwIVw73czF-W7y7D1cR6XkZm4huw6BefjEP4LK-qM-q5U7bcX4Dfkgg-A
openUrl	ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=A+fast+method+for+binary+programming+using+first-order+derivatives%2C+with+application+to+topology+optimization+with+buckling+constraints&rft.jtitle=International+journal+for+numerical+methods+in+engineering&rft.au=BROWNE%2C+P.+A&rft.au=BUDD%2C+C&rft.au=GOULD%2C+N.+I.+M&rft.au=KIM%2C+H.+A&rft.date=2012-12-21&rft.pub=Wiley&rft.issn=0029-5981&rft.volume=92&rft.issue=12&rft.spage=1026&rft.epage=1043&rft_id=info:doi/10.1002%2Fnme.4367&rft.externalDBID=n%2Fa&rft.externalDocID=26636567
thumbnail_l	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0029-5981&client=summon
thumbnail_m	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0029-5981&client=summon
thumbnail_s	http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0029-5981&client=summon