A predictive model based on an optimized ANN combined with ICA for predicting the stability of slopes

In this study, we optimized artificial neural network (ANN) with imperialist competition algorithm (ICA) for the problem of slope stability design charts. To prepare training and testing datasets for the ANN and ICA–ANN predictive models, an extensive number of limit equilibrium analysis modelings (e.g., for the lower bound, LB, limit analysis and upper bound, UB, limit analysis) was conducted. The analyses were conducted using OptumG2 computer software and implemented on two-layered cohesive soil layer sets. For each of the LB and UB limit analysis, the database consisted of 320 training datasets and 80 testing datasets. Variables of the ICA algorithm such as the number of countries, the number of initial imperialists and the number of decades were optimized using a series of trial-and-error process. The input parameters that used thorough the OptumG2 finite element modeling (FEM) analysis include depth factor (i.e., the ratio of first soil layer thickness to the slope height), slope angle, undrained shear strength ratio where the output was taken dimensionless stability number. The estimated results for both of datasets (e.g., training and testing) from ANN and ICA–ANN models were assessed based on three known statistical indices namely value account for (VAF), root means squared error (RMSE), and coefficient of determination ( R 2 ). To evaluate the performance of proposed models, color intensity rating (CER) and total ranking method (TRM), i.e., based on the result of statistical indices, was used. After 72 trial-and-error processes (e.g., sensitivity analysis on some neurons) the optimal architecture of 3 × 6 × 1 were found for both of the ANN–UB and ANN–LB models. As a result, both models presented excellent performance, however according to the introduced ranking system the ICA–ANN model could slightly perform a better performance compared to ANN. Based on R 2 , RMSE and VAF values of (0.9999, 0.0107 and 99.9924) and (0.9991, 0.0102 and 99.9913), respectively, were found for training and testing of the optimized ICA–ANN–LB predictive model. Similarly, for the ICA–ANN–UB predictive model, values of (0.9984, 0.0129 and 99.9659) and (0.9984, 0.01047 and 99.9915) were obtained for the R 2 , RMSE and VAF of training and testing datasets, respectively. However, in the ANN model, the R 2 and RMSE for both of the training and testing datasets were (0.9982 and 0.01815) and (0.9972 and 0.01748), respectively. This proves a better performance of the ICA–ANN mo