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A lower confidence bounding approach based on the coefficient of variation for expensive global design optimization

Ji Cheng (The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, HuBei, China)
Ping Jiang (The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, HuBei, China)
Qi Zhou (School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan, HuBei, China)
Jiexiang Hu (The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, HuBei, China and Georgia Institute of Technology, Atlanta, Georgia, USA)
Tao Yu (School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan, HuBei, China)
Leshi Shu (The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, HuBei, China)
Xinyu Shao (The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 25 March 2019

Issue publication date: 8 May 2019

Abstract

Purpose

Engineering design optimization involving computational simulations is usually a time-consuming, even computationally prohibitive process. To relieve the computational burden, the adaptive metamodel-based design optimization (AMBDO) approaches have been widely used. This paper aims to develop an AMBDO approach, a lower confidence bounding approach based on the coefficient of variation (CV-LCB) approach, to balance the exploration and exploitation objectively for obtaining a global optimum under limited computational budget.

Design/methodology/approach

In the proposed CV-LCB approach, the coefficient of variation (CV) of predicted values is introduced to indicate the degree of dispersion of objective function values, while the CV of predicting errors is introduced to represent the accuracy of the established metamodel. Then, a weighted formula, which takes the degree of dispersion and the prediction accuracy into consideration, is defined based on the already-acquired CV information to adaptively update the metamodel during the optimization process.

Findings

Ten numerical examples with different degrees of complexity and an AIAA aerodynamic design optimization problem are used to demonstrate the effectiveness of the proposed CV-LCB approach. The comparisons between the proposed approach and four existing approaches regarding the computational efficiency and robustness are made. Results illustrate the merits of the proposed CV-LCB approach in computational efficiency and robustness.

Practical implications

The proposed approach exhibits high efficiency and robustness in engineering design optimization involving computational simulations.

Originality/value

CV-LCB approach can balance the exploration and exploitation objectively.

Keywords

Acknowledgements

This research has been supported by the National Natural Science Foundation of China (NSFC) under Grant No. 51805179, No. 51775203, No. 51505163 and No. 51721092, and the Fundamental Research Funds for the Central Universities, HUST: Grant No. 2016YXMS272. The authors also would like to thank the anonymous referees for their valuable comments.

Citation

Cheng, J., Jiang, P., Zhou, Q., Hu, J., Yu, T., Shu, L. and Shao, X. (2019), "A lower confidence bounding approach based on the coefficient of variation for expensive global design optimization", Engineering Computations, Vol. 36 No. 3, pp. 830-849. https://doi.org/10.1108/EC-08-2018-0390

Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited