Understanding the effect of hyperparameter optimization on machine learning models for structure design problems

To relieve the computational cost of design evaluations using expensive finite element simulations, surrogate models have been widely applied in computer-aided engineering design. Machine learning algorithms (MLAs) have been implemented as surrogate models due to their capability of learning the complex interrelations between the design variables and the response from big datasets. Typically, an MLA regression model contains model parameters and hyperparameters. The model parameters are obtained by fitting the training data. Hyperparameters, which govern the model structures and the training processes, are assigned by users before training. There is a lack of systematic studies on the effect of hyperparameters on the accuracy and robustness of the surrogate model. In this work, we proposed to establish a hyperparameter optimization (HOpt) framework to deepen our understanding of the effect. Four frequently used MLAs, namely Gaussian Process Regression (GPR), Support Vector Machine (SVM), Random Forest Regression (RFR), and Artificial Neural Network (ANN), are tested on four benchmark examples. For each MLA model, the model accuracy and robustness before and after the HOpt are compared. The results show that HOpt can generally improve the performance of the MLA models in general. HOpt leads to few improvements in the MLAs accuracy and robustness for complex problems, which are featured by high-dimensional mixed-variable design space. The HOpt is recommended for the design problems with intermediate complexity. We also investigated the additional computational costs incurred by HOpt. The training cost is closely related to the MLA architecture. After HOpt, the training cost of ANN and RFR is increased more than that of the GPR and SVM. To sum up, this study benefits the selection of HOpt method for the different types of design problems based on their complexity.

[1]  Qiang Gao,et al.  Multi-objective lightweight and crashworthiness optimization for the side structure of an automobile body , 2018 .

[2]  P. E. Uys,et al.  The ride comfort vs. handling compromise for off-road vehicles , 2007 .

[3]  Chao Sun,et al.  Evaluation of vehicle vibration comfort using deep learning , 2020 .

[4]  Michael A. Osborne,et al.  Gaussian process regression for forecasting battery state of health , 2017, 1703.05687.

[5]  Pingfeng Wang,et al.  Reliability-based design optimization of crane bridges using Kriging-based surrogate models , 2019, Structural and Multidisciplinary Optimization.

[6]  Gideon S. Mann,et al.  Efficient Transfer Learning Method for Automatic Hyperparameter Tuning , 2014, AISTATS.

[7]  Chris Eliasmith,et al.  Hyperopt: a Python library for model selection and hyperparameter optimization , 2015 .

[8]  Browne,et al.  Cross-Validation Methods. , 2000, Journal of mathematical psychology.

[9]  Ren-Jye Yang,et al.  Mixed-Variable Metamodeling Methods for Designing Multi-Material Structures , 2016, Design Automation Conference.

[10]  Kirolos Haleem,et al.  Effect of driver's age and side of impact on crash severity along urban freeways: a mixed logit approach. , 2013, Journal of safety research.

[11]  Ping Zhu,et al.  Metamodel-based lightweight design of B-pillar with TWB structure via support vector regression , 2010 .

[12]  E. Divo,et al.  Modeling the motion of small unmanned aerial system (sUAS) due to ground collision , 2018 .

[13]  Nando de Freitas,et al.  A Bayesian interactive optimization approach to procedural animation design , 2010, SCA '10.

[14]  Michael S. Eldred,et al.  OVERVIEW OF MODERN DESIGN OF EXPERIMENTS METHODS FOR COMPUTATIONAL SIMULATIONS , 2003 .

[15]  B. Schölkopf,et al.  General cost functions for support vector regression. , 1998 .

[16]  Xin Liu,et al.  An adaptive local range sampling method for reliability-based design optimization using support vector machine and Kriging model , 2017 .

[17]  Jun Chen,et al.  Robust design of sheet metal forming process based on adaptive importance sampling , 2009 .

[18]  Arun Mannodi-Kanakkithodi,et al.  Critical assessment of regression-based machine learning methods for polymer dielectrics , 2016 .

[19]  Yoshua Bengio,et al.  Algorithms for Hyper-Parameter Optimization , 2011, NIPS.

[20]  Wei Chen,et al.  Use of support vector regression in structural optimization: Application to vehicle crashworthiness design , 2012, Math. Comput. Simul..

[21]  Qing Li,et al.  Optimization of foam-filled bitubal structures for crashworthiness criteria , 2012 .

[22]  José Manuel García-Aznar,et al.  Computational evaluation of different numerical tools for the prediction of proximal femur loads from bone morphology , 2014 .

[23]  Filip De Turck,et al.  Automatic surrogate model type selection during the optimization of expensive black-box problems , 2011, Proceedings of the 2011 Winter Simulation Conference (WSC).

[24]  Hongren Gong,et al.  Use of random forests regression for predicting IRI of asphalt pavements , 2018, Construction and Building Materials.

[25]  O. Bilgen,et al.  Generating Pseudo-Data to Enhance the Performance of Classification-Based Engineering Design: A Preliminary Investigation , 2020, Volume 6: Design, Systems, and Complexity.

[26]  Kiran Solanki,et al.  Improving the accuracy of vehicle crashworthiness response predictions using an ensemble of metamodels , 2009 .

[27]  Guilin Wen,et al.  Crashworthiness optimization design for foam-filled multi-cell thin-walled structures , 2014 .

[28]  Bernd Bischl,et al.  mlr: Machine Learning in R , 2016, J. Mach. Learn. Res..

[29]  Erkan Gunpinar,et al.  GenYacht: An interactive generative design system for computer-aided yacht hull design , 2019, Ocean Engineering.

[30]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[31]  Hyeonjoon Moon,et al.  Background Information of Deep Learning for Structural Engineering , 2017 .

[32]  Timothy W. Simpson,et al.  Metamodels for Computer-based Engineering Design: Survey and recommendations , 2001, Engineering with Computers.

[33]  Vladimir Cherkassky,et al.  The Nature Of Statistical Learning Theory , 1997, IEEE Trans. Neural Networks.

[34]  Achille Messac,et al.  An adaptive hybrid surrogate model , 2012, Structural and Multidisciplinary Optimization.

[35]  Ali Osman Atahan,et al.  RBF surrogate model and EN1317 collision safety-based optimization of two guardrails , 2019, Structural and Multidisciplinary Optimization.

[36]  Joshua B. Tenenbaum,et al.  Structure Discovery in Nonparametric Regression through Compositional Kernel Search , 2013, ICML.

[37]  Jian Chang,et al.  Data-driven train set crash dynamics simulation , 2017 .

[38]  Kevin Leyton-Brown,et al.  Sequential Model-Based Optimization for General Algorithm Configuration , 2011, LION.

[39]  Jianguang Fang,et al.  On design optimization for structural crashworthiness and its state of the art , 2017 .

[40]  Rakesh K. Kapania,et al.  Applications of Artificial Neural Networks in Structural Engineering with Emphasis on Continuum Models , 1998 .

[41]  Feng Zhu,et al.  A new data-driven design methodology for mechanical systems with high dimensional design variables , 2018, Adv. Eng. Softw..

[42]  Jianguang Fang,et al.  On design of multi-cell tubes under axial and oblique impact loads , 2015 .

[43]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[44]  Jiawei Han,et al.  Data Mining: Concepts and Techniques , 2000 .

[45]  Aaron Klein,et al.  Fast Bayesian Optimization of Machine Learning Hyperparameters on Large Datasets , 2016, AISTATS.

[46]  Sylvain Arlot,et al.  A survey of cross-validation procedures for model selection , 2009, 0907.4728.

[47]  Jasbir S. Arora,et al.  Survey of multi-objective optimization methods for engineering , 2004 .

[48]  Ismail Mohamad,et al.  Standardization and Its Effects on K-Means Clustering Algorithm , 2013 .

[49]  Xianping Du A Data Mining Methodology for Vehicle Crashworthiness Design , 2019 .

[50]  Lionel Tomaso,et al.  Automatic selection for general surrogate models , 2018 .

[51]  Wallace G. Ferreira,et al.  Ensemble of metamodels: the augmented least squares approach , 2016 .

[52]  Guido Bugmann,et al.  NEURAL NETWORK DESIGN FOR ENGINEERING APPLICATIONS , 2001 .

[53]  In Gwun Jang,et al.  Deep learning for determining a near-optimal topological design without any iteration , 2018, Structural and Multidisciplinary Optimization.

[54]  Michèle Sebag,et al.  Collaborative hyperparameter tuning , 2013, ICML.

[55]  M. E. Botkin,et al.  Structural shape optimization with geometric description and adaptive mesh refinement , 1985 .

[56]  Feng Zhu,et al.  A novel principal components analysis (PCA) method for energy absorbing structural design enhanced by data mining , 2019, Adv. Eng. Softw..

[57]  Dirk Lukaszewicz,et al.  A Design Method for Robust Automotive and Aerospace Composite Structures Including Manufacturing Variations , 2015 .

[58]  Hongbing Fang,et al.  On the ensemble of metamodels with multiple regional optimized weight factors , 2018 .

[59]  Abhijit Mukherjee,et al.  Application of artificial neural networks in structural design expert systems , 1995 .

[60]  Nam H. Kim,et al.  Eulerian shape design sensitivity analysis and optimization with a fixed grid , 2005 .

[61]  V. R. Akula,et al.  Optimal rapid multidisciplinary response networks: RAPIDDISK , 2005 .

[62]  Dong Zhao,et al.  A comparative study of metamodeling methods considering sample quality merits , 2010 .

[63]  Ayat Ali Saleh,et al.  Comparison of different optimization techniques for optimal allocation of multiple distribution generation , 2018, 2018 International Conference on Innovative Trends in Computer Engineering (ITCE).

[64]  John H. Frazer,et al.  Capturing aesthetic intention during interactive evolution , 2006, Comput. Aided Des..

[65]  Victor F. Rodriguez-Galiano,et al.  Predictive modelling of gold potential with the integration of multisource information based on random forest: a case study on the Rodalquilar area, Southern Spain , 2014, Int. J. Geogr. Inf. Sci..

[66]  Jian Chen,et al.  Optimal design of aeroengine turbine disc based on kriging surrogate models , 2011 .

[67]  S. V. Novikova,et al.  Structural optimization of the neural network model for the gas turbine engine monitoring , 2016 .

[68]  Hu Wang,et al.  Probability-based least square support vector regression metamodeling technique for crashworthiness optimization problems , 2011 .

[69]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[70]  Wallace G. Ferreira,et al.  Ensemble of metamodels: extensions of the least squares approach to efficient global optimization , 2017 .

[71]  Jasper Snoek,et al.  Practical Bayesian Optimization of Machine Learning Algorithms , 2012, NIPS.

[72]  Alexander J. Smola,et al.  Efficient mini-batch training for stochastic optimization , 2014, KDD.

[73]  Feng Zhu,et al.  A New Data-Driven Design Method for Thin-Walled Vehicular Structures Under Crash Loading , 2017 .

[74]  Ashutosh Tiwari,et al.  Ergonomic Chair Design by Fusing Qualitative and Quantitative Criteria Using Interactive Genetic Algorithms , 2008, IEEE Transactions on Evolutionary Computation.

[75]  Weihong Zhang,et al.  Stress constrained shape and topology optimization with fixed mesh: A B-spline finite cell method combined with level set function , 2014 .

[76]  Pramudita Satria Palar,et al.  Efficient global optimization with ensemble and selection of kernel functions for engineering design , 2018, Structural and Multidisciplinary Optimization.

[77]  Zhiwei Guo,et al.  Application of Least Squares Support Vector Machine for Regression to Reliability Analysis , 2009 .

[78]  T. Simpson,et al.  Comparative studies of metamodelling techniques under multiple modelling criteria , 2001 .

[79]  Stéphane Grihon,et al.  A case study : Influence of Dimension Reduction on regression trees-based Algorithms -Predicting Aeronautics Loads of a Derivative Aircraft , 2018, ArXiv.

[80]  SunGuangyong,et al.  On design optimization for structural crashworthiness and its state of the art , 2017 .

[81]  Jun Hu,et al.  Crashworthiness optimal design of a new extruded octagonal multi-cell tube under dynamic axial impact , 2018 .

[82]  Kaisa Miettinen,et al.  A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms , 2017, Soft Computing.

[83]  Hongyi Xu,et al.  A data mining method for structure design with uncertainty in design variables , 2021 .

[84]  Jongsoo Lee,et al.  Derivative and GA-based methods in metamodeling of back-propagation neural networks for constrained approximate optimization , 2007 .

[85]  G. Belingardi,et al.  Surrogate modeling in design optimization of structures with discontinuous responses , 2018 .

[86]  V. Rodriguez-Galiano,et al.  Machine learning predictive models for mineral prospectivity: an evaluation of neural networks, random forest, regression trees and support vector machines , 2015 .

[87]  Guangyao Li,et al.  Crashworthiness optimization of foam-filled tapered thin-walled structure using multiple surrogate models , 2013 .

[88]  Ren-Jye Yang,et al.  Metamodeling development for vehicle frontal impact simulation , 2001, DAC 2001.

[89]  Erkan Gunpinar,et al.  A shape sampling technique via particle tracing for CAD models , 2018, Graph. Model..

[90]  Laurent Van Miegroet,et al.  Generalized Shape Optimization using XFEM and Level Set Description , 2012 .

[91]  Ping Zhu,et al.  A method for selecting surrogate models in crashworthiness optimization , 2012 .

[92]  Nikolaos V. Sahinidis,et al.  Derivative-free optimization: a review of algorithms and comparison of software implementations , 2013, J. Glob. Optim..

[93]  Bernd Bischl,et al.  mlrMBO: A Modular Framework for Model-Based Optimization of Expensive Black-Box Functions , 2017, 1703.03373.

[94]  Haobin Jiang,et al.  Parametric modeling and multiobjective crashworthiness design optimization of a new front longitudinal beam , 2018, Structural and Multidisciplinary Optimization.

[95]  Xiaojian Zhou,et al.  Metamodel selection based on stepwise regression , 2016, Structural and Multidisciplinary Optimization.

[96]  Wilfrido Gómez-Flores,et al.  On the selection of surrogate models in evolutionary optimization algorithms , 2011, 2011 IEEE Congress of Evolutionary Computation (CEC).

[97]  Masoud Rais-Rohani,et al.  Ensemble of Metamodels with Optimized Weight Factors , 2008 .

[98]  Moinul Hossain,et al.  Data mining in road crash analysis: the context of developing countries , 2018, International journal of injury control and safety promotion.

[99]  A. Messac,et al.  Concurrent surrogate model selection (COSMOS): optimizing model type, kernel function, and hyper-parameters , 2017, Structural and Multidisciplinary Optimization.

[100]  Jianguang Fang,et al.  Crashworthiness design of foam-filled bitubal structures with uncertainty , 2014 .