Developing GEP tree-based, neuro-swarm, and whale optimization models for evaluation of bearing capacity of concrete-filled steel tube columns

The type of materials used in designing and constructing structures significantly affects the way the structures behave. The performance of concrete and steel, which are used as a composite in columns, has a considerable effect upon the structure behavior under different loading conditions. In this paper, several advanced methods were applied and developed to predict the bearing capacity of the concrete-filled steel tube (CFST) columns in two phases of prediction and optimization. In the prediction phase, bearing capacity values of CFST columns were estimated through developing gene expression programming (GEP)-based tree equation; then, the results were compared with the results obtained from a hybrid model of artificial neural network (ANN) and particle swarm optimization (PSO). In the modeling process, the outer diameter, concrete compressive strength, tensile yield stress of the steel column, thickness of steel cover, and the length of the samples were considered as the model inputs. After a series of analyses, the best predictive models were selected based on the coefficient of determination (R²) results. R² values of 0.928 and 0.939 for training and testing datasets of the selected GEP-based tree equation, respectively, demonstrated that GEP was able to provide higher performance capacity compared to PSO–ANN model with R² values of 0.910 and 0.904 and ANN with R² values of 0.895 and 0.881. In the optimization phase, whale optimization algorithm (WOA), which has not yet been applied in structural engineering, was selected and developed to maximize the results of the bearing capacity. Based on the obtained results, WOA, by increasing bearing capacity to 23436.63 kN, was able to maximize significantly the bearing capacity of CFST columns.