Concrete-filled steel tube columns (CFSTCs) are important elements in the construction sector and predictive analysis of their behavior is essential. Recent works have revealed the potential of metaheuristic-assisted approximators for this purpose. The main idea of this paper, therefore, is to introduce a novel integrative model for appraising the axial compression capacity (Pu) of CFSTCs. The proposed model represents an artificial neural network (ANN) supervised by satin bowerbird optimizer (SBO). In other words, this metaheuristic algorithm trains the ANN optimally to find the best contribution of input parameters to the Pu. In this sense, column length and the compressive strength of concrete, as well as the characteristics of the steel tube (i.e., diameter, thickness, yield stress, and ultimate stress), are considered input data. The prediction results are compared to five ANNs supervised by backtracking search algorithm (BSA), earthworm optimization algorithm (EWA), social spider algorithm (SOSA), salp swarm algorithm (SSA), and wind-driven optimization. Evaluating various accuracy indicators showed that the proposed model surpassed all of them in both learning and reproducing the Pu pattern. The obtained values of mean absolute percentage error of the SBO-ANN was 2.3082% versus 4.3821%, 17.4724%, 15.7898%, 4.2317%, and 3.6884% for the BSA-ANN, EWA-ANN, SOSA-ANN, SSA-ANN and WDA-ANN, respectively. The higher accuracy of the SBO-ANN against several hybrid models from earlier literature was also deduced. Moreover, the outcomes of principal component analysis on the dataset showed that the yield stress, diameter, and ultimate stress of the steel tube are the three most important factors in Pu prediction. A predictive formula is finally derived from the optimized SBO-ANN by extracting and organizing the weights and biases of the ANN. Owing to the accurate estimation shown by this model, the derived formula can reliably predict the Pu of concrete-filled steel tube columns.