Structural and Multidisciplinary Optimization

, Volume 57, Issue 3, pp 1233–1250 | Cite as

An adaptive RBF-HDMR modeling approach under limited computational budget

  • Haitao Liu
  • Jaime-Rubio Hervas
  • Yew-Soon Ong
  • Jianfei Cai
  • Yi Wang


The metamodel-based high-dimensional model representation (e.g., RBF-HDMR) has recently been proven to be very promising for modeling high dimensional functions. A frequently encountered scenario in practical engineering problems is the need of building accurate models under limited computational budget. In this context, the original RBF-HDMR approach may be intractable due to the independent and successive treatment of the component functions, which translates in a lack of knowledge on when the modeling process will stop and how many points (simulations) it will cost. This article proposes an adaptive and tractable RBF-HDMR (ARBF-HDMR) modeling framework. Given a total of N m a x points, it first uses N i n i points to build an initial RBF-HDMR model for capturing the characteristics of the target function f, and then keeps adaptively identifying, sampling and modeling the potential cuts with the remaining N m a x N i n i points. For the second-order ARBF-HDMR, N i n i ∈ [2n + 2,2n 2 + 2] not only depends on the dimensionality n but also on the characteristics of f. Numerical results on nine cases with up to 30 dimensions reveal that the proposed approach provides more accurate predictions than the original RBF-HDMR with the same computational budget, and the version that uses the maximin sampling criterion and the best-model strategy is a recommended choice. Moreover, the second-order ARBF-HDMR model significantly outperforms the first-order model; however, if the computational budget is strictly limited (e.g., 2n + 1 < N m a x ≪ 2n 2 + 2), the first-order model becomes a better choice. Finally, it is noteworthy that the proposed modeling framework can work with other metamodeling techniques.


Metamodeling Adaptive high dimensional model representation Limited computational budget Tractable process 



The majority of this work was finished before joining the Lab. We appreciate the support from the National Research Foundation (NRF) Singapore under the Corp Lab@University Scheme for completing the research. It is also partially supported by the Data Science and Artificial Intelligence Research Center (DSAIR) and the School of Computer Science and Engineering at Nanyang Technological University.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Haitao Liu
    • 1
  • Jaime-Rubio Hervas
    • 2
  • Yew-Soon Ong
    • 2
    • 3
  • Jianfei Cai
    • 2
  • Yi Wang
    • 4
  1. 1.Rolls-Royce@NTU Corporate LaboratoryNanyang Technological UniversitySingaporeSingapore
  2. 2.School of Computer Science and EngineeringNanyang Technological UniversitySingaporeSingapore
  3. 3.Data Science and Artificial Intelligence Research CenterNanyang Technological UniversitySingaporeSingapore
  4. 4.Applied Technology GroupRolls-Royce SingaporeSingaporeSingapore

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