Multi-gene GP and GA-FIS models to deal with scaling problem in the ANFIS model for estimating roughness coefficient in erodible channels

Estimation of the roughness coefficient is important for reliable hydraulic design in erodible channels. In this paper, the capability of multi-gene Genetic Programming (GP), a combined Genetic Algorithm and Fuzzy Inference System (GA-FIS) model, and Multi Regression (MR) methods are employed to estimate the roughness coefficient. These methods try to extract either an explicit or an implicit relationship between the roughness coefficient and input variables. In addition, traditional GP, widely used by researchers, and conventional empirical formulas are implemented to evaluate the models. Results show that the employed methods are more accurate than empirical methods. In addition, the effects of some other parameters, such as non-dimensional water depth and shear Reynolds number, are highlighted over the roughness coefficient while previously ignored in the empirical methods. Also, findings prove that the GA is a helpful tool to optimize a FIS compared with gradient-based models like ANFIS, while the scale of input variables is not in the same order. The R2 for multi-gene GP and GA-FIS are 0.8504 and 0.8842, respectively, while this value for the most accurate empirical method (Yalin, 1992) is 0.6286.