# NSGA-III-XGBoost-Based Stochastic Reliability Analysis of Deep Soft Rock Tunnel
## 3 NSGA-III Algorithm
The calculation time of each forward construction finite difference simulation (FDS) (three-step construction method, excavation length 12 m, and each excavation length is 1 m) is about one hour, while the calculation time of the surrogate model is generally only 30-40 s. Using NSGA-III-XGBoost to establish the surrogate model of the nonlinear mapping relationship between geo-mechanical parameters and their responses can significantly reduce the time cost of numerical simulation calculations. 3. A nonlinear mapping model with the interaction between rock mechanics parameters and displacement has been established. Then, by training the relevant XGBoost-based model to represent the displacement response model of the surrounding rock mechanical parameters, it has a lower computational cost and higher efficiency. 4. There are the obvious advantages of the calculation stability and accuracy of the proposed method (NSGA-III-XGBoost-MCS) compared with SVR and BP. The XGBoost algorithm is suitable for use with a small number of samples. The number of samples used in this paper is only 1000, and further research will need to compare engineering cases with over 1000 samples. In further research, the proposed method also will be compared with the Bayesian updating method and deep learning algorithms, such as the deep Gaussian process and Bayesian optimization of hyperparameters, so as to find out the advantages and disadvantages of the proposed method and promote its engineering applications. Due to the fact that one and a half months are required to complete more than 1000 3D numerical simulation calculations, this study only conducted one engineering verification. In further research, we will add more engineering cases for verification of the proposed method. J.X. : conceptualization, funding acquisition, software, supervision, writing--original draft preparation, and writing--review and editing; C.S. : software; numerical simulations, formal analysis; G.R. : investigation, resources. All authors have read and agreed to the published version of the manuscript. This research was funded by National Natural Science Foundation of China--Yalong River Joint Fund, grant number U1765110, and China Postdoctoral Science Foundation, grant number 20060390165. Not applicable. Data Availability Statement: Data are contained within this article. Author [PERSON] was employed by the company POWERCHINA Chengdu Engineering Co., Ltd. Author [PERSON] was employed by the company China Railway 20 th Bureau Group Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. ## References

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