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Purpose This study aims to examine the potential of two artificial intelligence (AI)-based algorithms, namely, adaptive neuro-fuzzy inference system (ANFIS) and gene expression programming (GEP), for indirect estimation of the ultimate bearing capacity (qult) of rock foundations, which is a considerable civil and geotechnical engineering problem. Design/methodology/approach The input-processing-output procedures taking place in ANFIS and GEP are represented for developing predictive models. The great importance of simultaneously considering both qualitative and quantitative parameters for indirect estimation of qult is taken into account and explained. This issue can be considered as a remarkable merit of using AI-based approaches. Furthermore, the evaluation procedure of various models from both engineering and accuracy viewpoints is also demonstrated in this study. Findings A new and explicit formula generated by GEP is proposed for the estimation of the qult of rock foundations, which can be used for further engineering aims. It is also presented that although the ANFIS approach can predict the output with a high degree of accuracy, the obtained model might be a black-box. The results of model performance analyses confirm that ANFIS and GEP can be used as alternative and useful approaches over previous methods for modeling and prediction problems. Originality/value The superiorities and weaknesses of GEP and ANFIS techniques for the numerical analysis of engineering problems are expressed and the performance of their obtained models is compared to those provided by other approaches in the literature. The findings of this research provide the researchers with a better insight to using AI techniques for resolving complicated problems.

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