# Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model
## 3 Model Construction and Optimal Selection of Dataset Balancing Methods
### Construction of Optimized Model
The mine pillar sample dataset was randomly divided into a 70% training set and a 30% testing set, and the data were normalized for model training. Step 2. Build the initial LSSVM model. First, we determined the type of kernel function to be used in the LSSVM model. Common options include linear kernel, polynomial kernel, and radial basis function (RBF). In this study, a commonly used RBF function was selected. Second, we defined the range of model parameters that needed to be optimized, namely, the regularization parameter, \(\gamma\), and kernel function parameter, \(\sigma\). Based on the experience of the grid search optimization mentioned earlier, the optimal parameter combinations were concentrated in the range of \([2^{-4},2^{4}]\). Therefore, the lower and upper bounds for the search of parameters \(\gamma\) and \(\sigma\) were set to \(2^{-4}\) and \(2^{4}\). Step 3. Initialize the SABO optimization algorithm. Before applying this algorithm, we input the optimization problem and relevant information, and determined the population size and number of iterations for SABO. It is worth mentioning that compared to other optimization algorithms, SABO does not require complex control parameter settings. It only requires the determination of the number of population members and the maximum  
Figure 7: Flowchart of the SABO-LSSVM prediction model. number of iterations to initialize the optimization algorithm. This is an advantage of the SABO algorithm. Step 4. The search agent positions are updated. After completing the initialization settings, the search agents can be optimized using the \"\(-v\)\" operator in Formula (13). After each position update, the search agent must obtain the corresponding fitness function value. Only when this value meets the screening condition in Equation (14) will it be saved and used in the next iteration. Step 5. Iterative loop. If the fitness values of the search agents and number of iterations during the optimization process do not meet the requirements, return to Step 4 and repeat the process until the termination condition is satisfied. After the optimization was completed, the optimized hyperparameter values were input into the LSSVM model, and the entire process of optimizing the model for mine pillar state prediction was finalized. Step 6. Multiple runs and average results. The results of the optimized model may fluctuate within a certain range for each run. Therefore, to comprehensively evaluate the accuracy of the model predictions, all steps need to be repeated, and the results of each prediction should be recorded. In addition to the SABO optimization model, the five comparative optimization models used in this study also needed to complete the prediction under the same conditions. Considering that the WOA-LSSVM model requires 90 s for a single prediction, completing the entire prediction process for the five parameter combinations, M-1, M-2, M-3, M-4, and M-5, would take a total of 25 h. Increasing the number of repetitions would incur significant time costs, which is not in line with the efficiency requirements. Therefore, this study attempted to set the number of repetitions to 200.