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Multiple Surrogate-Model-Based Optimization Method Using the Multimodal Expected Improvement Criterion for Expensive Problems

Author

Listed:
  • Mingyang Li

    (Smart Transportation Key Laboratory of Hunan Province, School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China)

  • Jinjun Tang

    (Smart Transportation Key Laboratory of Hunan Province, School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China)

  • Xianwei Meng

    (Smart Transportation Key Laboratory of Hunan Province, School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China)

Abstract

In this article, a multiple surrogate-model-based optimization method using the multimodal expected improvement criterion (MSMEIC) is proposed. In MSMEIC, an important region is first identified and used alternately with the whole space. Then, in each iteration, three common surrogate models, kriging, radial basis function (RBF), and quadratic response surface (QRS), are constructed, and a multipoint expected improvement (EI) criterion that selects the highest peak and other peaks of EI is proposed to obtain several potential candidates. Furthermore, the optimal predictions of the three surrogate models are regarded as potential candidates. After deleting redundant candidates, the remaining points are saved as the new sampling points. Finally, several well-known benchmark functions and an engineering application are employed to assess the performance of MSMEIC. The testing results demonstrate that, compared with four recent counterparts, the proposed method can obtain more precise solutions more efficiently and with strong robustness.

Suggested Citation

  • Mingyang Li & Jinjun Tang & Xianwei Meng, 2022. "Multiple Surrogate-Model-Based Optimization Method Using the Multimodal Expected Improvement Criterion for Expensive Problems," Mathematics, MDPI, vol. 10(23), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4467-:d:984981
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    References listed on IDEAS

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    1. Felipe Viana & Raphael Haftka & Layne Watson, 2013. "Efficient global optimization algorithm assisted by multiple surrogate techniques," Journal of Global Optimization, Springer, vol. 56(2), pages 669-689, June.
    2. Dawei Zhan & Jiachang Qian & Yuansheng Cheng, 2017. "Balancing global and local search in parallel efficient global optimization algorithms," Journal of Global Optimization, Springer, vol. 67(4), pages 873-892, April.
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