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Surrogate-based optimisation using adaptively scaled radial basis functions

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Title: Surrogate-based optimisation using adaptively scaled radial basis functions
Authors: Urquhart, Magnus, 1990, Ljungskog, Emil, 1990, Sebben, Simone, 1961
Source: Applied Soft Computing Journal. 88
Subject Terms: Radial Basis Function interpolation, Optimisation, Surrogate model, Evolutionary algorithm, Latin Hypercube Sampling, Bayesian optimisation, Global optimisation, Proper Orthogonal Decomposition, Benchmarking, Black box optimisation, Aerodynamics, Gradient-free
Description: Aerodynamic shape optimisation is widely used in several applications, such as road vehicles, aircraft and trains. This paper investigates the performance of two surrogate-based optimisation methods; a Proper Orthogonal Decomposition-based method and a force-based surrogate model. The generic passenger vehicle DrivAer is used as a test case where the predictive capability of the surrogate in terms of aerodynamic drag is presented. The Proper Orthogonal Decomposition-based method uses simulation results from topologically different meshes by interpolating all solutions to a common mesh for which the decomposition is calculated. Both the Proper Orthogonal Decomposition- and force-based approaches make use of Radial Basis Function interpolation. The Radial Basis Function hyperparameters are optimised using differential evolution. Additionally, the axis scaling is treated as a hyperparameter, which reduces the interpolation error by more than 50% for the investigated test case. It is shown that the force-based approach performs better than the Proper Orthogonal Decomposition method, especially at low sample counts, both with and without adaptive scaling. The sample points, from which the surrogate model is built, are determined using an optimised Latin Hypercube sampling plan. The Latin Hypercube sampling plan is extended to include both continuous and categorical values, which further improve the surrogate's predictive capability when categorical design parameters, such as on/off parameters, are included in the design space. The performance of the force-based surrogate model is compared with four other gradient-free optimisation techniques: Random Sample, Differential Evolution, Nelder–Mead and Bayesian Optimisation. The surrogate model performed as good as, or better than these algorithms, for 17 out of the 18 investigated benchmark problems.
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Items – Name: Title
  Label: Title
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  Data: Surrogate-based optimisation using adaptively scaled radial basis functions
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  Data: <searchLink fieldCode="AR" term="%22Urquhart%2C+Magnus%22">Urquhart, Magnus</searchLink>, 1990<br /><searchLink fieldCode="AR" term="%22Ljungskog%2C+Emil%22">Ljungskog, Emil</searchLink>, 1990<br /><searchLink fieldCode="AR" term="%22Sebben%2C+Simone%22">Sebben, Simone</searchLink>, 1961
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  Data: <i>Applied Soft Computing Journal</i>. 88
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Radial+Basis+Function+interpolation%22">Radial Basis Function interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22Optimisation%22">Optimisation</searchLink><br /><searchLink fieldCode="DE" term="%22Surrogate+model%22">Surrogate model</searchLink><br /><searchLink fieldCode="DE" term="%22Evolutionary+algorithm%22">Evolutionary algorithm</searchLink><br /><searchLink fieldCode="DE" term="%22Latin+Hypercube+Sampling%22">Latin Hypercube Sampling</searchLink><br /><searchLink fieldCode="DE" term="%22Bayesian+optimisation%22">Bayesian optimisation</searchLink><br /><searchLink fieldCode="DE" term="%22Global+optimisation%22">Global optimisation</searchLink><br /><searchLink fieldCode="DE" term="%22Proper+Orthogonal+Decomposition%22">Proper Orthogonal Decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Benchmarking%22">Benchmarking</searchLink><br /><searchLink fieldCode="DE" term="%22Black+box+optimisation%22">Black box optimisation</searchLink><br /><searchLink fieldCode="DE" term="%22Aerodynamics%22">Aerodynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Gradient-free%22">Gradient-free</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: Aerodynamic shape optimisation is widely used in several applications, such as road vehicles, aircraft and trains. This paper investigates the performance of two surrogate-based optimisation methods; a Proper Orthogonal Decomposition-based method and a force-based surrogate model. The generic passenger vehicle DrivAer is used as a test case where the predictive capability of the surrogate in terms of aerodynamic drag is presented. The Proper Orthogonal Decomposition-based method uses simulation results from topologically different meshes by interpolating all solutions to a common mesh for which the decomposition is calculated. Both the Proper Orthogonal Decomposition- and force-based approaches make use of Radial Basis Function interpolation. The Radial Basis Function hyperparameters are optimised using differential evolution. Additionally, the axis scaling is treated as a hyperparameter, which reduces the interpolation error by more than 50% for the investigated test case. It is shown that the force-based approach performs better than the Proper Orthogonal Decomposition method, especially at low sample counts, both with and without adaptive scaling. The sample points, from which the surrogate model is built, are determined using an optimised Latin Hypercube sampling plan. The Latin Hypercube sampling plan is extended to include both continuous and categorical values, which further improve the surrogate's predictive capability when categorical design parameters, such as on/off parameters, are included in the design space. The performance of the force-based surrogate model is compared with four other gradient-free optimisation techniques: Random Sample, Differential Evolution, Nelder–Mead and Bayesian Optimisation. The surrogate model performed as good as, or better than these algorithms, for 17 out of the 18 investigated benchmark problems.
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.asoc.2019.106050
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: Radial Basis Function interpolation
        Type: general
      – SubjectFull: Optimisation
        Type: general
      – SubjectFull: Surrogate model
        Type: general
      – SubjectFull: Evolutionary algorithm
        Type: general
      – SubjectFull: Latin Hypercube Sampling
        Type: general
      – SubjectFull: Bayesian optimisation
        Type: general
      – SubjectFull: Global optimisation
        Type: general
      – SubjectFull: Proper Orthogonal Decomposition
        Type: general
      – SubjectFull: Benchmarking
        Type: general
      – SubjectFull: Black box optimisation
        Type: general
      – SubjectFull: Aerodynamics
        Type: general
      – SubjectFull: Gradient-free
        Type: general
    Titles:
      – TitleFull: Surrogate-based optimisation using adaptively scaled radial basis functions
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            NameFull: Urquhart, Magnus
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            NameFull: Ljungskog, Emil
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            NameFull: Sebben, Simone
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              M: 01
              Type: published
              Y: 2020
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              Value: 88
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            – TitleFull: Applied Soft Computing Journal
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