New hybrid models integrating the aquila optimizer with machine learning algorithms to predict the strength of geosynthetic-reinforced subgrade soil

Abstract

Accurately predicting the California Bearing Ratio (CBR) of geosynthetic-reinforced subgrades is critical for pavement design but remains challenging due to the complex, nonlinear soil-reinforcement interaction. This study develops a novel hybrid modeling framework that integrates the Aquila Optimization Algorithm (AOA) with machine learning models such as Artificial Neural Networks (ANN), Ridge Regression, and XGBoost to enhance the prediction of soaked CBR values. A comprehensive database of 90 tests, encompassing key soil properties and reinforcement parameters, was used for model development. The AOA significantly boosted the predictive performance of all base models. The proposed AOA-XGBoost hybrid model demonstrated superior accuracy, achieving a convincing coefficient of determination (R 2 = 0.980), a low mean squared error (MSE = 1.78), and a minimal mean absolute error (MAE = 5.075) on the testing dataset. This performance notably surpassed the plain XGBoost model (R 2 = 0.954, MSE = 1.99, MAE = 11.82), corresponding to a 2.8% gain in R 2 , a 10.6% reduction in MSE, and a 57.1% reduction in MAE. Similarly, the AOA-ANN model (R 2 = 0.945, MSE = 2.87, MAE = 13.87) showed a clear improvement over the plain ANN (R 2 = 0.929, MSE = 3.06, MAE = 18.09), reflecting a 1.8% gain in R 2 , a 6.2% reduction in MSE, and a 23.3% reduction in MAE. Five-fold cross-validation, reported as mean ± standard deviation, confirmed the robustness and generalization capability of this ranking. AOA-XGBoost produced the best cross-validated results: R 2 = 0.8819 ± 0.0765, RMSE = 6.4218 ± 3.1846, MAE = 3.5217 ± 1.4826, MAPE = 19.6842 ± 4.7315%, and A20 = 0.6427 ± 0.1186. Sensitivity analysis revealed that reinforcement characteristics, particularly the number of layers (29.4% contribution) and tensile strength (21.8%), are the most dominant factors influencing CBR values. Hence, the results conclusively demonstrate that the AOA-assisted hybrid framework, particularly AOA-XGBoost, provides a robust and highly accurate tool for forecasting reinforced subgrade strength, supporting process innovation in pavement design through data‐driven assessment, with substantial potential to reduce reliance on time-consuming laboratory tests and improve pavement design efficiency.