Bitumen rheological properties significantly influence pavement performance in terms of resistance to rutting and cracking. Various approaches, such as polymer modification and the incorporation of nanomaterials, have been employed to improve bitumen properties. This study aims to characterize bitumen modified with different concentrations of nano-hydrated lime (NHL), nano-clay (NC), and nano-olive husk (NOH). The rutting parameter (G*/Sinδ) of these materials was evaluated using the dynamic shear rheometer (DSR) under unaged and short-term aged conditions at various temperatures. Consequently, a robust experimental dataset was employed to develop prediction models for each nanomodified bitumen using genetic expression programming (GEP). The models incorporated various variables: temperature, loading frequency, rutting parameter of the unmodified bitumen, and the concentration of nanomaterials. The findings demonstrated that GEP provided precise and insightful expressions for estimating the G*/Sinδ of nanomodified bitumen. The results demonstrated that incorporating 10% NC significantly enhanced rutting resistance. While using 5% NOH improved the bitumen property, its effectiveness diminished at a higher concentration of 10% due to potential issues like agglomeration and NOH's oil content. Using 5% NHL was the most viable option when considering performance alongside cost-effectiveness. Evaluating cost, compatibility with bitumen, and environmental impact is crucial when considering various nanomaterials as binder modifiers.