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Multiple Metamodels for Robustness Estimation in Multi-objective Robust Optimization

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Evolutionary Multi-Criterion Optimization (EMO 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10173))

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Abstract

Due to the excessive cost of Monte Carlo simulation, metamodel is now frequently used to accelerate the process of robustness estimation. In this paper, we explore the use of multiple metamodels for robustness evaluation in multi-objective evolutionary robust optimization under parametric uncertainty. The concept is to build several different metamodel types, and employ cross-validation to pick the best metamodel or to create an ensemble of metamodels. Three types of metamodel were investigated: sparse polynomial chaos expansion (PCE), Kriging, and 2\(^\text {nd}\) order polynomial regression (PR). Numerical study on robust optimization of two test problems was performed. The result shows that the ensemble approach works well when all the constituent metamodel is sufficiently accurate, while the best scheme is more favored when there is a constituent metamodel with poor quality. Moreover, besides the accuracy, we found that it is also important to preserve the trend and smoothness of the decision variables-robustness relationship. PR, which is the less accurate metamodel from all, can found a better representation of the Pareto front than the sparse PCE.

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Authors and Affiliations

  1. Institute of Fluid Science, Tohoku University, Sendai, Miyagi Prefecture, 980-8577, Japan

    Pramudita Satria Palar & Koji Shimoyama

Authors
  1. Pramudita Satria Palar
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  2. Koji Shimoyama
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Correspondence to Pramudita Satria Palar .

Editor information

Editors and Affiliations

  1. University of Münster, Münster, Germany

    Heike Trautmann

  2. TU Dortmund University, Dortmund, Germany

    Günter Rudolph

  3. University of Wuppertal, Wuppertal, Germany

    Kathrin Klamroth

  4. CINVESTAV-IPN, Mexico City, Mexico

    Oliver Schütze

  5. Clemson University, Clemson, South Carolina, USA

    Margaret Wiecek

  6. University of Surrey, Guildford, United Kingdom

    Yaochu Jin

  7. University of Münster, Münster, Germany

    Christian Grimme

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Palar, P.S., Shimoyama, K. (2017). Multiple Metamodels for Robustness Estimation in Multi-objective Robust Optimization. In: Trautmann, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2017. Lecture Notes in Computer Science(), vol 10173. Springer, Cham. https://doi.org/10.1007/978-3-319-54157-0_32

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  • DOI: https://doi.org/10.1007/978-3-319-54157-0_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54156-3

  • Online ISBN: 978-3-319-54157-0

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