A bi-fidelity Bayesian optimization method for multi-objective optimization with a novel acquisition function

Xu, Kaiqin; Shu, Leshi; Zhong, Linjun; Jiang, Ping; Zhou, Qi

doi:10.1007/s00158-023-03509-9

Cited by 3 publications

(1 citation statement)

References 43 publications

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“…However, the EI related to the LF model only reflects the sample effect on the model at this fidelity rather than on the MF model, and it cannot be used to indicate the sample fidelity. Therefore, some studies [22][23][24][25] evaluate the acquisition functions such as EI, LCB, and MES with the different parts of the prediction variance of MF model, which are brought by lack of corresponding fidelity samples, for comparison. In addition, He 26 simply considered the prediction variance associated with different fidelity models as the potential effect of the corresponding fidelity samples, and took the HF sample only when the potential effect of LF sample was low enough.…”

Section: Introductionmentioning

confidence: 99%

Decreased Max-value Entropy Search for Multi-fidelity Bayesian Optimization

Gong

Wang

Duan

et al. 2023

Preprint

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Bayesian Optimization is a widely applied efficient framework for updating the surrogate model sequentially. To improve the efficiency, multi-fidelity Bayesian Optimization is developed to combine the information of samples in different fidelity levels. However, the multi-fidelity levels brings the challenge for sequential sampling. In multi-fidelity Bayesian Optimization, the sampling strategy is applied to determine not only the sample location but also the sample fidelity level for updating the model. To balance the benefit and the experiment cost, it is vital to measure the potential effect of each fidelity sample. Some sampling strategies, which is categorized as direct-type methods, can measure the potential effect of different samples in a easy way, but they cannot figure out the difference of samples that has little uncertainty and it has the risk for redundant sampling. Some other strategies, which is categorized as direct-type methods, can measure the potential effect appropriately, but the calculation of them are much complicated and time-consuming. In this paper, a new type method combining the direct-type and indirect-type methods is presented for measuring the potential effect of different fidelity sample. It is convenient enough and can avoid the problems occurring in the direct-type method. Based on this paradigm, a sampling strategy named decreased max-value entropy search(DMES) is proposed and applied in the multi-fidelity Bayesian Optimization framework. The characteristics of DMES and how it is different from direct-type method are detailed in some examples. Besides, two numerical experiments and one simulation experiment demonstrate the efficiency of DMES.

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Section: Introductionmentioning

confidence: 99%

Decreased Max-value Entropy Search for Multi-fidelity Bayesian Optimization

Gong

Wang

Duan

et al. 2023

Preprint

View full text Add to dashboard Cite

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An efficient parallel multi-fidelity multi-objective Bayesian optimization method and application to 3-stage axial compressor with 144 variables

He,

Gui,

Luo

2024

Aerospace Science and Technology

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A Multi-Fidelity Bayesian Optimization Approach for Constrained Multi-Objective Optimization Problems

Lin,

Hu,

Zhou

et al. 2024

Journal of Mechanical Design

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In this paper, a multi-fidelity Bayesian optimization approach is presented to tackle computationally expensive constrained multi-objective optimization problems (MOPs). The proposed approach consists of a three-stage optimization framework designed to search for promising candidate points. In the first stage, an acquisition function is proposed to identify a feasible solution if none are available in the current set of sampling points. Subsequently, a new multi-fidelity weighted expected hypervolume improvement function is developed to find better solutions. In the third stage, a constrained weighted lower confidence bound acquisition function is presented to enhance the constraint predictions and refine the solutions near the constraint boundary. Additionally, a filter strategy is suggested to determine whether constraint updating is necessary, aiming to save computational resources and improve optimization efficiency. Moreover, to expedite the optimization process, a parallel optimization approach is further developed based on the suggested three-stage optimization framework. To achieve this, a multi-fidelity influence function is introduced, allowing the proposed approach to determine a desired number of candidate points within a single iteration. Lastly, the proposed approach is demonstrated through six numerical benchmark examples, which verifies its significant advantages in addressing expensive constrained MOPs. Besides, the proposed approach is applied to the multi-objective optimization of a metamaterial vibration isolator, resulting in the attainment of satisfactory solutions.

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A bi-fidelity Bayesian optimization method for multi-objective optimization with a novel acquisition function

Cited by 3 publications

References 43 publications

Decreased Max-value Entropy Search for Multi-fidelity Bayesian Optimization

Decreased Max-value Entropy Search for Multi-fidelity Bayesian Optimization

An efficient parallel multi-fidelity multi-objective Bayesian optimization method and application to 3-stage axial compressor with 144 variables

A Multi-Fidelity Bayesian Optimization Approach for Constrained Multi-Objective Optimization Problems

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