In present study, the comprehension of different types of bedforms generated by different bed roughness, in rectangular and circular cross-sectional rigid boundary channels and the resistance generated by the bed roughness against the flow are evaluated. Moreover, the critical condition of sediment motion under bed roughness influence is investigated. This study presents novel contributions in solving engineering problems that suffer from the lack of knowledge on the incipient motion of sediment particles in rigid boundary channels under bed roughness effects. Furthermore, soft computing and evolutionary computation methods have been combined to develop a new novel predictive model. The Evolutionary GENOFIS also aims at improving the ANFIS tool depends on Sugeno Fuzzy Inference System. The advantages of the proposed hybrid GENOFIS approach over the ANFIS tool is its novel ability to tackle the incipient prediction problem by using less fuzzy based rules and to represent the consequent part of the model as a constant, linear or non-linear function as well as with possible simultaneous combinations of them. For validation and comparison purposes, model performances of hybrid GENOFIS, ANFIS and data-based linear regression approaches are evaluated via experimental data partitioned for testing purposes. The model results are compared through corresponding RMSE and CE values. It is found that the hybrid GENOFIS model results outperformed the ANFIS and linear regression models. Consequently, novel experimental data-driven incipient motion formula and the hybrid GENOFIS approach are proposed to modeling complex incipient motion problems that are full of uncertainty and complication.