Proposing two new metaheuristic algorithms of ALO-MLP and SHO-MLP in predicting bearing capacity of circular footing located on horizontal multilayer soil

In this study, for the issue of shallow circular footing’s bearing capacity (also shown as F_ult), we used the merits of artificial neural network (ANN), while optimized it by two metaheuristic algorithms (i.e., ant lion optimization (ALO) and the spotted hyena optimizer (SHO)). Several studies demonstrated that ANNs have significant results in terms of predicting the soil’s bearing capacity. Nevertheless, most models of ANN learning consist of different disadvantages. Accordantly, we focused on the application of two hybrid models of ALO–MLP and SHO–MLP for predicting the F_ult placed in layered soils. Moreover, we performed an Extensive Finite Element (FE) modeling on 16 sets of soil layer (soft soil placed onto stronger soil and vice versa) considering a database that consists of 703 testing and 2810 training datasets for preparing the training and testing datasets. The independent variables in terms of ALO and SHO algorithms have been optimized by taking into account a trial and error process. The input data layers consisted of (i) upper layer foundation/thickness width (h/B) ratio, (ii) bottom and topsoil layer properties (for example, six of the most important properties of soil), (iii) vertical settlement (s), (iv) footing width (B), where the main target was taken F_ult. According to RMSE and R², values of (0.996 and 0.034) and (0.994 and 0.044) are obtained for training dataset and values of (0.994 and 0.040) and (0.991 and 0.050) are found for the testing dataset of proposed SHO–MLP and ALO–MLP best-fit prediction network structures, respectively. This proves higher reliability of the proposed hybrid model of SHO–MLP in approximating shallow circular footing bearing capacity.