Critical shear stress (CSS) of sediment governs its transport in open channel flow. Earlier, mathematical models were developed to compute CSS of sediment under clay influence which was limited to their own experimental data. The present study aims to develop an ANN model to compute CSS of coarser sediment present in mobile channel bed made of cohesive sediment mixture. The proposed model was optimized using parent-selected operator GA (genetic algorithm), which helped to determine the optimal process parameters responsible for CSS. Initially, the mathematical model was implemented with the help of ANN (artificial neural network) and later on it was optimized by three well-known parent-selected operator genetic algorithms. Data from the literature along with current experimental data was used to develop ANN-based model to compute CSS for coarser particle under clay influence. It was found that linear ranked selected GA-ANN is the best-fitted model for both training and testing data. The CSS obtained for optimized input values for clay fraction by weight (CP), weighted geometric standard deviation of sediment mixture (SM), and dimensionless dry bulk unit weight of cohesive sediment (DB) are 0.104, 2.9523, and 1.6921 respectively which were quite satisfactory and performing better than the existed mathematical models.