Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization
This paper presents a new approach that automates the tuning process in topology optimization of parameters that are traditionally defined by the user. The new method draws inspiration from hyperparameter optimization in machine learning. A new design problem is formulated where the topology optimiz...
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| Published in | Structural and multidisciplinary optimization Vol. 67; no. 9; p. 157 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.09.2024
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1615-147X 1615-1488 1615-1488 |
| DOI | 10.1007/s00158-024-03850-7 |
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| Abstract | This paper presents a new approach that automates the tuning process in topology optimization of parameters that are traditionally defined by the user. The new method draws inspiration from hyperparameter optimization in machine learning. A new design problem is formulated where the topology optimization hyperparameters are defined as design variables and the problem is solved by surrogate optimization. The new design problem is nested, such that a topology optimization problem is solved as an inner problem. To encourage the identification of high-performing solutions while limiting the computational resource requirements, the outer objective function is defined as the original objective combined with penalization for intermediate densities and deviations from the prescribed material consumption. The contribution is demonstrated on density-based topology optimization with various hyperparameters and objectives, including compliance minimization, compliant mechanism design, and buckling load factor maximization. Consistent performance is observed across all tested examples. For a simple two hyperparameter case, the new framework is shown to reduce amount of times a topology optimization algorithm is executed by 90% without notably sacrificing the objective compared to a rigorous manual grid search. |
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| AbstractList | This paper presents a new approach that automates the tuning process in topology optimization of parameters that are traditionally defined by the user. The new method draws inspiration from hyperparameter optimization in machine learning. A new design problem is formulated where the topology optimization hyperparameters are defined as design variables and the problem is solved by surrogate optimization. The new design problem is nested, such that a topology optimization problem is solved as an inner problem. To encourage the identification of high-performing solutions while limiting the computational resource requirements, the outer objective function is defined as the original objective combined with penalization for intermediate densities and deviations from the prescribed material consumption. The contribution is demonstrated on density-based topology optimization with various hyperparameters and objectives, including compliance minimization, compliant mechanism design, and buckling load factor maximization. Consistent performance is observed across all tested examples. For a simple two hyperparameter case, the new framework is shown to reduce amount of times a topology optimization algorithm is executed by 90% without notably sacrificing the objective compared to a rigorous manual grid search. |
| ArticleNumber | 157 |
| Author | Ha, Dat Carstensen, Josephine |
| Author_xml | – sequence: 1 givenname: Dat orcidid: 0000-0002-7936-0759 surname: Ha fullname: Ha, Dat email: datha@mit.edu organization: Civil and Environmental Engineering, Massachusetts Institute of Technology – sequence: 2 givenname: Josephine surname: Carstensen fullname: Carstensen, Josephine organization: Civil and Environmental Engineering, Massachusetts Institute of Technology |
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| Keywords | Topology optimization Hyperparameter optimization Surrogate optimization Parameter tuning |
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In: Automated machine learning: methods, systems, challenges, pp 3–33 (2019) QueipoNVHaftkaRTShyyWGoelTVaidyanathanRTuckerPKSurrogate-based analysis and optimizationProg Aerosp Sci2005411128 XuSCaiYChengGVolume preserving nonlinear density filter based on heaviside functionsStruct Multidiscip Optim20104144955052601469 KuhnMJohnsonKApplied predictive modeling20131New YorkSpringer BorrvallTTopology optimization of elastic continua using restrictionArch Comput Methods Eng2001843513851876438 Alibrahim H, Ludwig SA (2021) Hyperparameter optimization: comparing genetic algorithm against grid search and Bayesian optimization. In: 2021 IEEE congress on evolutionary computation (CEC), pp 1551–1559 SigmundOOn the usefulness of non-gradient approaches in topology optimizationStruct Multidiscip Optim20114355895962795757 Snoek J, Larochelle H, Adams RP (2012) Practical Bayesian optimization of machine learning algorithms. 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PhD thesis, The Technical University of Denmark, Lyngby, Denmark FerrariFSigmundOA new generation 99 line MATLAB code for compliance topology optimization and its extension to 3dStruct Multidiscip Optim202062221122284156382 Lessmann S, Stahlbock R, Crone SF (2018) Optimizing hyperparameters of support vector machines by genetic algorithms. In: Proceedings of the 2005 international conference on artificial intelligence, ICAI 2005, vol 1, pp 74–80 Jiang X, Wang H, Li Y, Mo K (2020) Machine learning based parameter tuning strategy for mmc based topology optimization. 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PLOS ONE 10(12) FerrariFSigmundOGuestJKTopology optimization with linearized buckling criteria in 250 lines of MATLABStruct Multidiscip Optim2021636304530664268366 O Sigmund (3850_CR44) 2009; 25 3850_CR46 3850_CR49 J Bergstra (3850_CR8) 2012; 13 F Ferrari (3850_CR19) 2021; 63 MP Bendsøe (3850_CR6) 1999; 69 O Sigmund (3850_CR45) 2011; 43 T Borrvall (3850_CR11) 2001; 8 3850_CR40 L Yang (3850_CR57) 2020; 415 O Sigmund (3850_CR41) 1997; 25 3850_CR16 B Shahriari (3850_CR38) 2016; 104 F Wang (3850_CR53) 2011; 43 O Sigmund (3850_CR43) 2007; 33 B Zhu (3850_CR58) 2020; 143 JK Guest (3850_CR24) 2004; 61 O Amir (3850_CR2) 2008; 78 J Liu (3850_CR30) 2018; 57 AT Gaynor (3850_CR23) 2016; 54 J Wu (3850_CR55) 2019; 17 3850_CR10 M Stolpe (3850_CR50) 2001; 22 TE Bruns (3850_CR13) 2001; 190 E Andreassen (3850_CR3) 2011; 43 3850_CR27 3850_CR29 S Xu (3850_CR56) 2010; 41 B Bourdin (3850_CR12) 2001; 50 M Kuhn (3850_CR28) 2013 F Ferrari (3850_CR18) 2020; 62 H-M Gutmann (3850_CR26) 2001; 13 3850_CR9 X Guo (3850_CR25) 2013; 253 O Sigmund (3850_CR48) 1998; 16 O Sigmund (3850_CR42) 2001; 21 MP Bendsøe (3850_CR5) 1989; 1 3850_CR1 3850_CR4 H Cho (3850_CR14) 2020; 8 3850_CR21 3850_CR20 RE Christiansen (3850_CR15) 2015; 52 3850_CR22 S Rojas-Labanda (3850_CR36) 2015; 52 GIN Rozvany (3850_CR37) 1992; 4 K Svanberg (3850_CR52) 2002; 12 MP Bendsøe (3850_CR7) 2003 NV Queipo (3850_CR35) 2005; 41 K Svanberg (3850_CR51) 1987; 24 O Sigmund (3850_CR47) 2013; 48 S Shin (3850_CR39) 2023; 10 3850_CR32 3850_CR31 A Diaz (3850_CR17) 1995; 10 3850_CR34 3850_CR33 RV Woldseth (3850_CR54) 2022; 65 |
| References_xml | – reference: BorrvallTTopology optimization of elastic continua using restrictionArch Comput Methods Eng2001843513851876438 – reference: SigmundOMauteKTopology optimization approachesStruct Multidiscip Optim2013486103110553138124 – reference: Müller J (2014) MATSuMoTo: the MATLAB surrogate model toolbox for computationally expensive black-box global optimization problems. Optimization and Control. arXiv:1404.4261 – reference: WuJChenX-YZhangHXiongL-DLeiHDengS-HHyperparameter optimization for machine learning models based on Bayesian optimizationJ Electron Sci Technol20191712640 – reference: KuhnMJohnsonKApplied predictive modeling20131New YorkSpringer – reference: SigmundOPeterssonJNumerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minimaStruct Multidiscip Optim19981616875 – reference: SvanbergKA class of globally convergent optimization methods based on conservative convex separable approximationsSIAM J Optim20021225555731885575 – reference: WoldsethRVAageNBærentzenJASigmundOOn the use of artificial neural networks in topology optimisationStruct Multidiscip Optim20226510294 – reference: BendsøeMPSigmundOMaterial interpolation schemes in topology optimizationArch Appl Mech1999699–10635654 – reference: GutmannH-MA radial basis function method for global optimizationJ Global Optim2001132012271833217 – reference: RozvanyGINZhouMBirkerTGeneralized shape optimization without homogenizationStruct Optim199243–4250252 – reference: SigmundOOn the usefulness of non-gradient approaches in topology optimizationStruct Multidiscip Optim20114355895962795757 – reference: Sigmund O (1994) Design of material structures using topology optimization. PhD thesis, The Technical University of Denmark, Lyngby, Denmark – reference: GuoXZhangWZhangLRobust structural topology optimization considering boundary uncertaintiesComput Methods Appl Mech Eng20132533563683002798 – reference: Bardenet R, Brendel M, Kégl B, Sebag M (2013) Collaborative hyperparameter tuning. In: International conference on machine learning. PMLR, pp 199–207 – reference: SigmundOMorphology-based black and white filters for topology optimizationStruct Multidiscip Optim2007334–5401424 – reference: BourdinBFilters in topology optimizationInt J Numer Methods Eng2001509214321581818051 – reference: ChoHKimYLeeEChoiDLeeYRheeWBasic enhancement strategies when using Bayesian optimization for hyperparameter tuning of deep neural networksIEEE Access202085258852608 – reference: Feurer M, Springenberg J, Hutter F (2015) Initializing Bayesian hyperparameter optimization via meta-learning. In: Proceedings of the AAAI conference on artificial intelligence, vol 29 – reference: Sigmund O (2022) On benchmarking and good scientific practise in topology optimization. Struct Multidiscip Optim 65(315) – reference: ChristiansenRELazarovBSJensenJSSigmundOCreating geometrically robust designs for highly sensitive problems using topology optimizationStruct Multidiscip Optim2015527377543406629 – reference: SigmundOOn the design of compliant mechanisms using topology optimizationMech Struct Mach1997254493524 – reference: BergstraJBengioYRandom search for hyper-parameter optimizationJ Mach Learn Res2012132813052913701 – reference: Alibrahim H, Ludwig SA (2021) Hyperparameter optimization: comparing genetic algorithm against grid search and Bayesian optimization. In: 2021 IEEE congress on evolutionary computation (CEC), pp 1551–1559 – reference: Lorenzo PR, Nalepa J, Kawulok M, Sanchez L, Ranilla J (2017) Particle swarm optimization for hyper-parameter selection in deep neural networks. In: Proceedings of the genetic and evolutionary computation conference – reference: BrunsTETortorelliDATopology optimization of non-linear elastic structures and compliant mechanismsComput Methods Appl Mech Eng20011902634433459 – reference: WangFLazarovBSSigmundOOn projection methods, convergence and robust formulations in topology optimizationStruct Multidiscip Optim2011436767784 – reference: Jiang X, Wang H, Li Y, Mo K (2020) Machine learning based parameter tuning strategy for mmc based topology optimization. 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| SubjectTerms | Algorithms Computational Mathematics and Numerical Analysis Design factors Design optimization Engineering Engineering Design Machine learning Optimization Parameter identification Research Paper Theoretical and Applied Mechanics Topology optimization Tuning |
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| Title | Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization |
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