Sedimentation in open channels occurs frequently and is relative to system inflow. The long-term retention of sediments on channel beds can increase the possibility of variations in deposits and their eventual consolidation. This study compares three hybrid artificial intelligence methods in estimating sediment transport without sedimentation (STWS). We employed the Particle Swarm Optimization (PSO), Imperialist Competitive Algorithm (ICA) and Genetic Algorithm (GA) methods in combination with the Artificial Neural Network (ANN) to overcome the weakness of ANN training with conventional algorithms. We used the ICA, GA and PSO methods to optimize the weights of the ANN layers. Using dimensional analysis, we placed the effective parameters in predicting sediment transport into five non-dimensional groups. Six models are proposed and run using three hybrid methods (18 models in total). As the comparisons demonstrate, the proposed combined models are more accurate than ANN and existing equations in estimating the densimetric Froude number (Fr). However, we found the ICA–ANN superior to GA–ANN and PSO–ANN, as it produces explicit solutions to the problem. The ICA–ANN has the lowest prediction uncertainty band for Fr of all developed models. Moreover, the variation trend of the Fr for all input variables (except overall friction factor of sediment) is a second-order polynomial.