On efficient global optimization via universal Kriging surrogate models

Pramudita Satria Palar, Koji Shimoyama

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


In this paper, we investigate the capability of the universal Kriging (UK) model for single-objective global optimization applied within an efficient global optimization (EGO) framework. We implemented this combined UK-EGO framework and studied four variants of the UK methods, that is, a UK with a first-order polynomial, a UK with a second-order polynomial, a blind Kriging (BK) implementation from the ooDACE toolbox, and a polynomial-chaos Kriging (PCK) implementation. The UK-EGO framework with automatic trend function selection derived from the BK and PCK models works by building a UK surrogate model and then performing optimizations via expected improvement criteria on the Kriging model with the lowest leave-one-out cross-validation error. Next, we studied and compared the UK-EGO variants and standard EGO using five synthetic test functions and one aerodynamic problem. Our results show that the proper choice for the trend function through automatic feature selection can improve the optimization performance of UK-EGO relative to EGO. From our results, we found that PCK-EGO was the best variant, as it had more robust performance as compared to the rest of the UK-EGO schemes; however, total-order expansion should be used to generate the candidate trend function set for high-dimensional problems. Note that, for some test functions, the UK with predetermined polynomial trend functions performed better than that of BK and PCK, indicating that the use of automatic trend function selection does not always lead to the best quality solutions. We also found that although some variants of UK are not as globally accurate as the ordinary Kriging (OK), they can still identify better-optimized solutions due to the addition of the trend function, which helps the optimizer locate the global optimum.

Original languageEnglish
Pages (from-to)2377-2397
Number of pages21
JournalStructural and Multidisciplinary Optimization
Issue number6
Publication statusPublished - 2018 Jun 1


  • Efficient global optimization
  • Single-objective
  • Surrogate model
  • Universal Kriging

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Control and Optimization


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