Vol.:(0123456789) 1 3 Engineering with Computers https://doi.org/10.1007/s00366-019-00808-y ORIGINAL ARTICLE Developing GEP tree‑based, neuro‑swarm, and whale optimization models for evaluation of bearing capacity of concrete‑flled steel tube columns Payam Sarir 1  · Jun Chen 1  · Panagiotis G. Asteris 2  · Danial Jahed Armaghani 3  · M. M. Tahir 4 Received: 2 May 2019 / Accepted: 18 June 2019 © Springer-Verlag London Ltd., part of Springer Nature 2019 Abstract The type of materials used in designing and constructing structures signifcantly afects the way the structures behave. The performance of concrete and steel, which are used as a composite in columns, has a considerable efect upon the structure behavior under diferent loading conditions. In this paper, several advanced methods were applied and developed to predict the bearing capacity of the concrete-flled 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 artifcial 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 coefcient of determi- nation (R 2 ) results. R 2 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 R 2 values of 0.910 and 0.904 and ANN with R 2 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 signifcantly the bearing capacity of CFST columns. Keywords The concrete-flled steel tube columns · Bearing capacity · GEP-based tree · Neuro-swarm · WOA · Optimization 1 Introduction In the area of structural performance, one of the key issues is how to use the available materials in an optimized way. In current construction processes, the two most widely used materials are steel and concrete. They can be used together in such a way that each one of them can improve the oth- er’s performance, which fnally results in a better overall behavior of the structure under various loads. As a result, when concrete and steel are combined appropriately, their performance will be more improved compared to the cases where they are utilized separately. Recently, composite material has been widely applied to diferent construction projects [1, 2] as well as to retroftting and rehabilitation purposes [3, 4] across the world. Composite columns ofer many benefts; they can be easily produced, they enjoy some improved features compared to other columns such as steel structures, and they reduce the construction expenses [1]. Accordingly, several researchers have attempted to test how the concrete-flled hollow steel columns behave in dif- ferent conditions [5–8]. Based on the fndings of the study conducted by He et al. [9], among diferent types of compos- ite columns, the concrete-flled steel tube (CFST) can out- perform the other types of columns. The concrete in CFST is employed inside, while the steel’s hollow sections are in the surrounding periphery. It helps the steel column not to be suddenly buckled, improves the way it performs, and delays * Jun Chen chen_jun@sjtu.edu.cn * Danial Jahed Armaghani danialarmaghani@gmail.com Extended author information available on the last page of the article