Prediction of California bearing ratio using multi-layer perceptron model based on multiple meta-heuristic optimizers

The California bearing ratio (CBR) is commonly employed within the field of geotechnical engineering and its associated applications, including but not limited to highway embankments, earth dams, and bridge abutments. This index can typically be ascertained through laboratory analyses or field test procedures. Nonetheless, the method of determining CBR is both time- and cost-intensive. Consequently, this research endeavors to present three hybrid models that integrate the multi-layer perceptron model (MLP) with three meta-heuristic algorithms, namely, the flow direction algorithm (FDA), Prairie dog optimization (PDO), and red deer algorithm (RDA). These models offer a cost-effective and efficient methodology for predicting CBR values while concurrently exhibiting enhanced precision in dealing with real-world complexities. The present study determined that 70% of the developed hybrid models were assigned to the training phase, while the 30% remaining were designated testing models. This study assessed the influence of eight distinct factors on the anticipated CBR values. To assess the precision of the models developed for two categories, an analysis is conducted that involves a comparative examination of projected outcomes versus observed results. This evaluation utilizes five distinct statistical measures, namely, the coefficient of determination (R²), root mean squared error (RMSE), mean squared error (MSE), mean absolute relative error (MARE), and uncertainty (U_95%).