Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Structural and Multidisciplinary Optimization
Erschienen in: Structural and Multidisciplinary Optimization 3/2015

01.09.2015 | RESEARCH PAPER

Benchmarking optimization solvers for structural topology optimization

verfasst von: Susana Rojas-Labanda, Mathias Stolpe

Erschienen in: Structural and Multidisciplinary Optimization | Ausgabe 3/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving SAND formulations consumes more computational time than solving the corresponding nested formulations.
Vorheriger Artikel Analytical sensitivity in topology optimization for elastoplastic composites
Nächster Artikel Weight and mechanical performance optimization of blended composite wing panels using lamination parameters

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Fußnoten
1
There are implementations of these methods which do allow equality constraints see e.g. (Zhang et al. 1996; Wang et al. 2011). However, to the best of our knowledge there are no numerical results suggesting that these methods can be used to solve SAND formulation of topology optimization problems.
 
2
MMA and GCMMA are considered as first-order methods. IPOPT, SNOPT and FMINCON are considered as second-order methods even though for certain problem formulations, limited memory BFGS (Broyden-Fletcher-Goldfarb-Shanno) is used to approximate the Hessian of the Lagrangian.
 
3
A design, which is deemed incorrect by the optimality conditions, can indeed be a capable design and visually describe the correct topology. However, we experience that tight optimality conditions lead to better objective function values.
 
Literatur
Amestoy PR, Duff IS, L’Excellent JY (2000) Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput Methods Appl Mech Eng 184(24):501–520MATHCrossRef
Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidiscip Optim 43(1):1–16MATHCrossRef
Arora JS, Wang Q (2005) Review of formulations for structural and mechanical system optimization. Struct Multidiscip Optim 30(4):251–272MATHMathSciNetCrossRef
Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1:192–202CrossRef
Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654CrossRef
Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer
Benson HY, Shanno DF, Vanderbei RJ (2002) A comparative study of large-scale nonlinear optimization algorithms. Tech. rep., Operations Research and Financial Engineering, Princeton University, ORFE-01-04
Bondarenko AS, Bortz DM, Moré JJ (1999) COPS: Large-scale nonlinearly constrained optimization problems. Tech. rep., Mathematics and Computer Science Division, Argonne National Laboratory, Technical Memorandum ANL/MCS-TM-237
Bongartz I, Conn AR, Gould N, Toint PL (1995) CUTE: Constrained and unconstrained testing environment. ACM Trans Math Softw 21(1):123–160MATHCrossRef
Borrvall T, Petersson J (2001) Large-scale topology optimization in 3D using parallel computing. Comput Methods Appl Mech Eng 190(46–47):6201–6229MATHMathSciNetCrossRef
Bruggi M, Duysinx P (2012) Topology optimization for minimum weight with compliance and stress constraints. Struct Multidiscip Optim 46(3):369–384MATHMathSciNetCrossRef
Bruns TE (2005) A reevaluation of the SIMP method with filtering and an alternative formulation for solid void topology optimization. Struct Multidiscip Optim 30(6):428–436MathSciNetCrossRef
Burger M., Stainko R. (2006) Phase-field relaxation of topology optimization with local stress constraints. SIAM J Control Optim 45(4):1447–1466MATHMathSciNetCrossRef
Byrd RH, Nocedal J, Waltz RA (2006) KNITRO : an integrated package for nonlinear optimization. In: Large scale nonlinear optimization, vol 83, pp 35–59
Conn AR, Gould NIM, Toint PL (1992) Lancelot: a FORTRAN package for large-scale nonlinear optimization (Release A), Springer-Verlag New York, Inc., Secaucus
Deepak SR, Dinesh M, Sahu DK, Ananthasuresh GK (2009) A comparative study of the formulations and benchmark problems for the topology optimization of compliant mechanisms. J Mech Robot 1(1)
Evgrafov A, Rupp CJ, Maute K, Dunn ML (2008) Large-scale parallel topology optimization using a dual-primal substructuring solver. Struct Multidiscip Optim 36(4):329–345MATHMathSciNetCrossRef
Fleury C (1989) CONLIN: an efficient dual optimizer based on convex approximation concepts. Struct Optim 1(2):81–89CrossRef
Gill PE, Murray W, Saunders MA (2005) SNOPT: an SQP algorithm for large -scale constrained optimization. SIAM J Optim 47(4):99–131MATHMathSciNetCrossRef
Gould NIM, Orban D, Toint PL (2003) CUTEr and SifDec: a constrained and unconstrained testing environment, revisited. ACM Trans Math Softw 29(4):373–394MATHMathSciNetCrossRef
Haber RB, Jog CS, Bendsøe MP (1996) A new approach to variable-topology shape design using a constraint on perimeter. Struct Optim 11(1–2):1–12CrossRef
Herskovits J (1998) A feasible directions interior-point technique for nonlinear optimization. J Optim Theory Appl 99(1):121–146MATHMathSciNetCrossRef
Hvejsel CF, Lund E (2011) Material interpolation schemes for unified topology and multi material optimization. Struct Multidiscip Optim 43(6):811–825MATHCrossRef
Koch T, Achterberg T, Andersen E, Bastert O, Berthold T, Bixby RE, Danna E, Gamrath G, Gleixner AM, Heinz S, Lodi A, Mittelmann H, Ralphs T, Salvagnin D, Steffy DE, Wolter K (2011) MIPLIB 2010. Math Program Comput 3(2):103–163MathSciNetCrossRef
Kočvara M, Stingl M (2003) PENNON: A code for convex nonlinear and semidefinite programming. Optimization Methods and Software 18(3):317–333MATHMathSciNetCrossRef
Lau G.K., Du H., Lim MK (2001) Use of functional specifications as objective functions in topological optimization of compliant mechanism. Comput Methods Appl Mech Eng 190(34):4421–4433CrossRef
Leyffer S., Mahajan A. (2010) Software for Nonlinearly Constrained Optimization. Tech. rep., Mathematics and Computer Science Division, Argonne National Laboratory, Technical Report ANS/MCS-P1768-0610
Luenberger DG, Ye Y (2008) Linear and nonlinear programming. Springer
Mathworks I (2013) Optimization toolbox user’s guide R 2013 b
Murtagh BA, Saunders MA (1998) MINOS 5.5 User’s Guide. Tech. rep., Stanford University Systems Optimization Laboratory, Department of Operations Research, Technical report SOL 83–20R
Nocedal J, Wächter R, Waltz RA (2009) Adaptive barrier update strategies for nonlinear interior methods. SIAM J Optim 19(4):1674–1693MATHCrossRef
Rietz A (2001) Sufficiency of a finite exponent in SIMP (power law) methods. Struct Multidiscip Optim 21(2):159–163CrossRef
Rozvany GIN, Zhou M (1991) The COC algorithm, part I: cross-section optimization or sizing. Comput Methods Appl Mech Eng 89(13):281–308CrossRef
Saxena A., Ananthasuresh GK (2001) Topology synthesis of compliant mechanisms for nonlinear force-deflection and curved path specifications. J Mech Des 123(1):33–42CrossRef
Sigmund O (1997) On the design of compliant mechanisms using topology optimization. J Struct Mech 25(4):492–526
Sigmund O (2009) Manufacturing tolerant topology optimization. Acta Mech Sinica 25:227–239MATHCrossRef
Stolpe M, Svanberg K (2001) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidiscip Optim 22(2):116–124CrossRef
Svanberg K (1987) The method of moving asymptotes a new method for structural optimization. Int J Numer Methods Eng 24(2):359–373MATHMathSciNetCrossRef
Svanberg K (2002) A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM J Optim 12(2):555–573MATHMathSciNetCrossRef
Vanderbei RJ (2006) LOQO user’s manual. Version 4.05. Tech. rep., Operations Research and Financial Engineering Princeton University
Wächter A, Biegler LT (2006) On the implementation of an interior point filter line-search algorithm for large-scale nonlinear programming. Math Program 106(1):25–57MATHMathSciNetCrossRef
Wang F, Lazarov BS, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767–784MATHCrossRef
Wang H, Ni Q, Liu H (2011) A new method of moving asymptotes for large-scale linearly equality-constrained minimization. Acta Mathematicae Applicatae Sinica, English Series 27(2):317–328MATHMathSciNetCrossRef
Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1–2):227–246MATHCrossRef
Wang S, Sturler E, Paulino GH (2007) Large scale topology optimization using preconditioned Krylov subspace methods with recycling. Int J Numer Methods Eng 69:2441–2468MATHCrossRef
Zhang WH, Fleury C, Duysinx P, Nguyen VH, Laschet I (1996) A generalized method of moving asymptotes (GMMA) including equality constraints. Struct Optim 12(2–3):143–146CrossRef
Zhou M, Rozvany GIN (1991) The COC algorithm, part II: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89(1–3):309–336CrossRef
Zillober C (1993) A globally convergent version of the method of moving asymptotes. Structural Optimization 6(3):166–174CrossRef
Metadaten
Titel
Benchmarking optimization solvers for structural topology optimization
verfasst von
Susana Rojas-Labanda
Mathias Stolpe
Publikationsdatum
01.09.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Structural and Multidisciplinary Optimization / Ausgabe 3/2015
Print ISSN: 1615-147X
Elektronische ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-015-1250-z

Weitere Artikel der Ausgabe 3/2015

Structural and Multidisciplinary Optimization 3/2015 Zur Ausgabe

RESEARCH PAPER

Analytical sensitivity in topology optimization for elastoplastic composites

RESEARCH PAPER

Optimization of structures with unrestricted dynamic shakedown constraints

INDUSTRIAL APPLICATION

Torque control strategy and optimization for fuel consumption and emission reduction in parallel hybrid electric vehicles

RESEARCH PAPER

On the layout of a least weight multiple span structure with uniform load

REVIEW ARTICLE

Topology and shape optimization methods using evolutionary algorithms: a review

RESEARCH PAPER

New optimization method for steered fiber composites using the level set method

Premium Partner

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen. 

    Zur Marktübersicht
    Bildnachweise