Rockbursts are often sudden and random, and they negatively affect the construction of tunnels and mines, creating unsafe conditions. Accurately predicting rockburst intensity is critical for disaster prevention and control and to ensure safety in underground spaces. Predicting rockbursts with traditional machine learning methods has become increasingly common; however, black-box effects limit the interpretability of the prediction mechanism. This study proposes a novel rockburst prediction method that combines a multistrategy improved optimization (quantum computation and good point sets and harmonizing sand cat swarm optimization (QGHSCSO)) with the CatBoost model. An interpretable technique (Shapley additive explanations (SHAPs)) is introduced to decipher the black-box effect of the QGHSCSO-CatBoost model, revealing the algorithm’s prediction mechanism. A comprehensive and multiangle performance comparison analysis is conducted with the whale optimization algorithm (WOA), northern goshawk optimization (NGO), and Harris hawk optimization (HHO) algorithms, using 10 test functions to verify the robustness and convergence of the QGHSCSO algorithm. The contributions of input factors to the prediction results are evaluated via a SHAP analysis. The results indicate that model classification predictions are governed by the elastic deformation energy coefficient  (W_et), particularly in intense rockbursts. The rock stress coefficient (σ_θ∕σ_c) and rock brittleness coefficient (σ_c∕σ_t) have minor SHAP contributions, indicating that they serve as supporting factors in low-to-moderate predictions. The QGHSCSO-CatBoost model, based on interpretable techniques, provides accurate and stable rockburst prediction (prediction accuracies of 90.74% for the test set); therefore, the QGHSCSO-CatBoost algorithm is a feasible approach for rockburst intensity prediction.