The development of four efficient optimal neural network methods in forecasting shallow foundation's bearing capacity

This research aimed to appraise the effectiveness of four optimization approaches - cuckoo optimization algorithm (COA), multi-verse optimization (MVO), particle swarm optimization (PSO), and teaching-learning-based optimization (TLBO) - that were enhanced with an artificial neural network (ANN) in predicting the bearing capacity of shallow foundations located on cohesionless soils. The study utilized a database of 97 laboratory experiments, with 68 experiments for training data sets and 29 for testing data sets. The ANN algorithms were optimized by adjusting various variables, such as population size and number of neurons in each hidden layer, through trial-and-error techniques. Input parameters used for analysis included width, depth, geometry, unit weight, and angle of shearing resistance. After performing sensitivity analysis, it was determined that the optimized architecture for the ANN structure was 5×5×1. The study found that all four models demonstrated exceptional prediction performance: COA-MLP, MVO-MLP, PSO-MLP, and TLBO-MLP. It is worth noting that the MVO-MLP model exhibited superior accuracy in generating network outputs for predicting measured values compared to the other models. The training data sets showed R² and RMSE values of (0.07184 and 0.9819), (0.04536 and 0.9928), (0.09194 and 0.9702), and (0.04714 and 0.9923) for COA-MLP, MVO-MLP, PSO-MLP, and TLBO-MLP methods respectively. Similarly, the testing data sets produced R² and RMSE values of (0.08126 and 0.07218), (0.07218 and 0.9814), (0.10827 and 0.95764), and (0.09886 and 0.96481) for COA-MLP, MVO-MLP, PSO-MLP, and TLBO-MLP methods respectively.