关键词: 代理模型, 隧洞支护方案, 多目标优化, 类别型特征梯度提升（CatBoost）, 沙普利加和解释模型（SHAP）, 第三代非支配排序遗传算法（NSGA-III）

Abstract: To overcome the shortcomings of traditional numerical simulation methods in optimizing tunnel support schemes, this paper presents a new multi-objective optimization method based on surrogate models and NSGA-III, to balance the schemes’ safety and economy under various geological conditions and to improve the computational efficiency of the traditional methods. First, we construct a categorical feature gradient boosting (CatBoost) surrogate model that is equipped with the support parameters of surrounding rock and its mechanical parameters as input parameters, and its deformation and plastic zones depth as output parameters. A nonlinear mapping relationship between these input and output parameters is worked out. We optimize the hyperparameters of CatBoost using the dung beetle optimizer (DBO) thereby achieving efficient prediction of tunnel surrounding rock stability, and evaluate the contribution of these parameters using the Shapley Additive exPlanations (SHAP) model. Then, a multi-objective optimization model for the support schemes is constructed with tunnel safety and support cost as objective functions, the support parameters as design variables, and the ranges of support parameter values as constraints, so that the surrogate model is combined with the Non-dominated Sorting Genetic Algorithm III (NSGA-III) to solve the multi-objective optimization problem of support schemes. Finally, this method is applied in real project cases. The results indicate that compared with the original scheme for surrounding rocks Class III and Class IV, the optimized support schemes reduce tunnel vault deformation by 1.23% and 9.78% respectively, decrease the depth of plastic zones by 8.98% and 10.53% respectively, and lower support cost by 17.39% and 4.94% respectively, which are all verified by the on-site monitoring results. Our new method is more efficient and intelligent than traditional support optimization methods, and helps design better tunnel support schemes.

Key words: surrogate model, tunnel support scheme, multi-objective optimization, categorical boosting (CatBoost), Shapley additive explanations model (SHAP), non-dominated sorting genetic algorithm III (NSGA-III)