###### Abstract  
The determination of the rock elasticity modulus (EM) is an indispensable key step for the design of rock engineering problems. Traditional experimental analysis can accurately measure the rock EM, but it requires manpower and material resources, and it is time consuming. The EM estimation of new rocks using former published empirical formulas is also a possibility but can be attached of high uncertainties. In this paper, four types of metaheuristic optimization algorithms (MOA), named the backtracking search optimization algorithm (BSA), multi-verse optimizer (MVO), golden eagle optimizer (GEO) and poor and rich optimization algorithm (PRO), were utilized to optimize the random forest (RF) model for predicting the rock EM. A data-driven technology was used to generate an integrated database consisting of 120 rock samples from the literature. To verify the predictive performance of the proposed models, five common machine-learning models and one empirical formula were also developed to predict the rock EM. Four popular performance indices, including the root-mean-square error (RMSE), mean absolute error (MAE), the coefficient of determination (R\({}^{2}\)) and Willmott's index (WI), were adopted to evaluate all models. The results showed that the PRO-RF model has obtained the most satisfactory prediction accuracy. The porosity (Pn) is the most important variable for predicting the rock EM based on the sensitive analysis. This paper compares the performance of the RF models optimized by using four MOA for the rock EM prediction. It provides a good example for the subsequent application of soft techniques on the EM and other important rock parameter estimations. elasticity modulus; rock materials; data-driven; soft techniques; poor and rich optimization algorithm +
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(SHRN) and EM. The prediction accuracy of R\({}^{2}\) was equal to 0.85. [PERSON] et al. [20] only utilized the point load index (PLI) to forecast the granite EM. The prediction accuracy was not satisfactory, resulting in a low R\({}^{2}\) of 0.58. [PERSON] et al. [21] developed an MR formula consisting of the above four variables to predict the traverting EM. By reviewing the developed empirical formula, the Pn, Vp, SHRN and PLI are usually considered into these empirical equations, which can be obtained directly from tests [13]. However, the original data used to develop each empirical formula are fixed and different, and the formula performance decreases once it is used to predict the EM of a new rock [22]. From the prediction accuracy perspective, the intrinsic relationship of the SR and MR formulas cannot well describe the complex and nonlinear correlation between the rock properties and the EM [23]. In recent years, soft techniques have been widely used to solve prediction problems in rock engineering [24; 25; 26; 27; 28; 29; 30], especially machine-learning (ML) methods. For the rock EM prediction, [PERSON] and [PERSON] [31] proposed an artificial neural network (ANN) model to predict the EM of intact rock. The results showed that the ANN model obtained a higher accuracy for the root-mean-square error (RMSE is equal to 0.191) than those of previous approaches. [PERSON] and [PERSON] [32] utilized ANN models to estimate the EM statis of rock samples. The results indicated that this artificial intelligence model is of more practical value in estimating the rock EM. [PERSON] et al. [33] used an adaptive neurofuzzy inference system (ANFIS) to predict the EM values of 85 rock samples. The performance evaluation results illustrated that the ANFIS model has a better performance than the initial ANN model and fuzzy inference system (FIS) model by means of the lower RMSE value of 6.799. [PERSON] et al. [34] developed an ANFIS to estimate the EM of 45 heterogenous sedimentary rocks. This model has obtained a satisfactory prediction accuracy of R\({}^{2}\) = 0.935.