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Due to the heterogeneous nature of granular soils and the involvement of many effective parameters in the geotechnical behavior of soil-foundation systems, the accurate prediction of shallow foundation settlements on cohesionless soils is a complex engineering problem. In this study, three new evolutionary-based techniques, including evolutionary polynomial regression (EPR), classical genetic programming (GP), and gene expression programming (GEP), are utilized to obtain more accurate predictive settlement models. The models are developed using a large databank of standard penetration test (SPT)-based case histories. The values obtained from the new models are compared with those of the most precise models that have been previously proposed by researchers. The results show that the new EPR and GP-based models are able to predict the foundation settlement on cohesionless soils under the described conditions with R2 values higher than 87%. The artificial neural networks (ANNs) and genetic programming (GP)-based models obtained from the literature, have R2 values of about 85% and 83%, respectively which are higher than 80% for the GEP-based model. A subsequent comprehensive parametric study is further carried out to evaluate the sensitivity of the foundation settlement to the effective input parameters. The comparison results prove that the new EPR and GP-based models are the most accurate models. In this study, the feasibility of the EPR, GP and GEP approaches in finding solutions for highly nonlinear problems such as settlement of shallow foundations on granular soils is also clearly illustrated. The developed models are quite simple and straightforward and can be used reliably for routine design practice.