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An online variable-fidelity optimization approach for multi-objective design optimization

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Abstract

Multi-objective genetic algorithms (MOGAs) are effective ways for obtaining Pareto solutions of multi-objective design optimization problems. However, the high computational cost of MOGAs limits their applications to practical engineering optimization problems involving computational expensive simulations. To address this issue, a novel variable-fidelity (VF) optimization approach for multi-objective design optimization is proposed, in which a VF metamodel is embedded in the computation process of MOGA to replace the expensive simulation model. The VF metamodel is updated in the optimization process of MOGA, considering the cost of simulation models with different fidelity and the influence of the VF metamodel uncertainty. A normalized distance constraint is introduced to avoid selecting clustered sample points. Four numerical examples and two engineering cases are used to demonstrate the applicability and efficiency of the proposed approach. The results show that the proposed approach can obtain Pareto solutions with good quality and outperforms the other four approaches considered here as references in terms of computational efficiency.

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Abbreviations

C(x):

the difference between HF response and prediction value of LF metamodel at x

\( \widehat{\boldsymbol{C}}\left(\boldsymbol{x}\right) \) :

the prediction value of the scaling function metamodel at x

F Motor :

the weight of the engine in the front of the micro-aerial vehicle (N)

F Payload :

the payload of the micro-aerial vehicle (N/mm2)

F Tail :

the weight of the tail of the micro-aerial vehicle (N)

f h :

vector of HF responses of given HF sample set

f l :

vector of LF responses of given LF sample set

f h(x):

the function value of HF model at x

\( {\widehat{f}}_l\left(\boldsymbol{x}\right) \) :

the prediction value of LF metamodel at x

\( {\widehat{f}}_{vf}\left(\boldsymbol{x}\right) \) :

the prediction value of VF metamodel at x

I(x):

the prediction interval of VF metamodel at x

P1, P2:

forces placed at the center of the right end of the torque arm (N)

x l :

LF sample set

x h :

HF sample set

σ C(x):

the standard deviation of scaling function metamodel at x

σ l(x):

the standard deviation of LF metamodel at x

σ vf (x):

the standard deviation of VF metamodel at x

h:

quantities associated with high fidelity

l:

quantities associated with low fidelity

vf:

quantities associated with variable fidelity

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Acknowledgments

The authors also would like to thank the anonymous referees for their valuable comments.

Funding

This research has been supported by the National Natural Science Foundation of China (NSFC) under Grant No. 51775203, No. 51805179, No. 51721092, and the Fundamental Research Funds for the Central Universities, HUST: Grant No. 2016YXMS272.

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Authors and Affiliations

  1. The State Key Laboratory of Digital Manufacturing Equipment and Technology, School of Mechanical Science and Engineering, Huazhong University of Science & Technology, Wuhan, 430074, People’s Republic of China

    Leshi Shu, Ping Jiang & Tingli Xie

  2. School of Aerospace Engineering, Huazhong University of Science & Technology, Wuhan, 430074, Hubei, People’s Republic of China

    Qi Zhou

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  1. Leshi Shu
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  2. Ping Jiang
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Correspondence to Qi Zhou.

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Shu, L., Jiang, P., Zhou, Q. et al. An online variable-fidelity optimization approach for multi-objective design optimization. Struct Multidisc Optim 60, 1059–1077 (2019). https://doi.org/10.1007/s00158-019-02256-0

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