Imperialist competitive algorithm hybridized with multilayer perceptron to predict the load-settlement of square footing on layered soils

Abstract

To forecast the value of bearing capacity in shallow footings, a total of 2430 finite element modelling WEND simulation is performed. In this regard and to optimize the performance of the artificial neural network (ANN), it is combined with the imperialist competitive algorithm (ICA). The new combined technique is called ICA-MLP (multi-layer perceptron). To develop the ICA-MLP model, the input parameters were the soil type (i.e., having particular soil properties for each of the sandy soil types) installed at the top, the soil type installed at the bottom, the first-layer thickness ratio (h/B) and the applied stress on the footing (kPa), while the output was the vertical settlement (mm) under the square footing. The estimations were compared with a predeveloped ANN model to demonstrate the ability of the ICA-MLP hybrid model. The results showed a high ability of ICA metaheuristic ensembles for understanding the non-linear relationship between the influential factors and the selected target. Meanwhile, a comparison between the used models revealed that the best-combined structure is when the ICA algorithm is followed by the swarm size equal to 350. In this sense, the results from the predeveloped ANN model, based on R-2 values, were 0.83 and 0.89 for the training and testing data sets, respectively, whereas the R-2 and RMSE values for the ICA-MLP model for the training and testing datasets were 0.983, 0.062 and 0.977, 0.070, respectively. Therefore, the ICA-MLP model can be regarded as a new model that is superior to the conventional MLP technique.