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Abstract In this study, the capabilities of classical and novel integrated machine learning models were investigated to predict sediment discharge (Qs) in free-flow flushing. Developed models include Multivariate Linear Regression (MLR), Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), Group Method of Data Handling (GMDH), and four hybrid forms of GMDH and Support Vector Regression (SVR) in combination with Henry Gas Solubility Optimization (HGSO) and Equilibrium Optimizer (EO) algorithms. The number of 160 datasets that were applied to assess these models was extracted from the Janssen (PhD’s Thesis, Engineering, Civil and Environmental Engineering. University of California, 1999) experimental study. Input parameters to predict Qs included the water level in the reservoir (hw), bed level in the flushing channel (hb), outflow (Qout), inflow (Qin), and elapsed time of flushing (T). The performance of all models was evaluated by four statistical indices of root mean square error (RMSE), mean absolute error (MAE), correlation coefficient (R2), and Mean absolute relative error (MARE). Evaluation of results demonstrated that the HGSO and EO algorithms could enhance the accuracy of the GMDH model (up to 26% and 22% in terms of RMSE), respectively. According to statistical criteria, the SVR-EO and SVR-HGSO provided the highest accuracy in both training (R2 = 0.98) and validation phases (R2 = 0.96). Moreover, among the developed models, the GMDH-HGSO algorithm provided excellent fitness to the observed data (R2 = 0.96, RMSE = 22.37, MAE = 15.65, and MARE = 0.26). The results indicated the high efficiency of the HGSO and EO algorithms in improving the accuracy of the GMDH and SVR models. However, among the developed models, the GMDH-HGSO is the most accurate model and is recommended for sediment transport modelling.