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A Kriging-based constrained global optimization algorithm for expensive black-box functions with infeasible initial points

Author

Listed:
  • Yaohui Li

    (Huazhong University of Science and Technology
    Xuchang University)

  • Yizhong Wu

    (Huazhong University of Science and Technology)

  • Jianjun Zhao

    (Huazhong University of Science and Technology)

  • Liping Chen

    (Huazhong University of Science and Technology)

Abstract

In many engineering optimization problems, the objective and the constraints which come from complex analytical models are often black-box functions with extensive computational effort. In this case, it is necessary for optimization process to use sampling data to fit surrogate models so as to reduce the number of objective and constraint evaluations as soon as possible. In addition, it is sometimes difficult for the constrained optimization problems based on surrogate models to find a feasible point, which is the premise of further searching for a global optimal feasible solution. For this purpose, a new Kriging-based Constrained Global Optimization (KCGO) algorithm is proposed. Unlike previous Kriging-based methods, this algorithm can dispose black-box constrained optimization problem even if all initial sampling points are infeasible. There are two pivotal phases in KCGO algorithm. The main task of the first phase is to find a feasible point when there is no feasible data in the initial sample. And the aim of the second phase is to obtain a better feasible point under the circumstances of fewer expensive function evaluations. Several numerical problems and three design problems are tested to illustrate the feasibility, stability and effectiveness of the proposed method.

Suggested Citation

  • Yaohui Li & Yizhong Wu & Jianjun Zhao & Liping Chen, 2017. "A Kriging-based constrained global optimization algorithm for expensive black-box functions with infeasible initial points," Journal of Global Optimization, Springer, vol. 67(1), pages 343-366, January.
  • Handle: RePEc:spr:jglopt:v:67:y:2017:i:1:d:10.1007_s10898-016-0455-z
    DOI: 10.1007/s10898-016-0455-z
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    References listed on IDEAS

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    1. Andrea Cassioli & Fabio Schoen, 2013. "Global optimization of expensive black box problems with a known lower bound," Journal of Global Optimization, Springer, vol. 57(1), pages 177-190, September.
    2. Rommel Regis & Christine Shoemaker, 2005. "Constrained Global Optimization of Expensive Black Box Functions Using Radial Basis Functions," Journal of Global Optimization, Springer, vol. 31(1), pages 153-171, January.
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    Cited by:

    1. Hau T. Mai & Jaewook Lee & Joowon Kang & H. Nguyen-Xuan & Jaehong Lee, 2022. "An Improved Blind Kriging Surrogate Model for Design Optimization Problems," Mathematics, MDPI, vol. 10(16), pages 1-19, August.
    2. Yaohui Li & Jingfang Shen & Ziliang Cai & Yizhong Wu & Shuting Wang, 2021. "A Kriging-Assisted Multi-Objective Constrained Global Optimization Method for Expensive Black-Box Functions," Mathematics, MDPI, vol. 9(2), pages 1-20, January.
    3. Li, Yaohui & Shi, Junjun & Cen, Hui & Shen, Jingfang & Chao, Yanpu, 2021. "A kriging-based adaptive global optimization method with generalized expected improvement and its application in numerical simulation and crop evapotranspiration," Agricultural Water Management, Elsevier, vol. 245(C).

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