The Muskingum model is one of the most widely used hydrological methods in food routing, and calibrating its parameters is an ongoing research challenge. We optimized Muskingum model parameters to accurately simulate hourly output hydrographs of three foodprone rivers in the Karun watershed, Iran. We evaluated model performance using the correlation coefcient (CC), the ratio of the root-mean-square error to the standard deviation of measured data (PSR), Nash–Sutclife efciency (NSE), and index of agreement (d). The results show that the gray wolf optimization (GWO) algorithm, with CC=0.99455, PSR=0.155, NSE=0.9757, and d=0.9945, performed better in simulating the food in the frst study area. The Kalman flter (KF) improved these measures by+0.00516,−0.12 46,+0.02328, and+0.00527, respectively. Our fndings for the second food show that the gravitational search algorithm (GSA), with CC=0.9941, PSR=0.1669, NSE=0.9721, and d=0.9921, performed better than all other algorithms. The Kalman flter enhanced each of the measures by+0.00178,−0.0175,+0.0055 and+0.0021, respectively. The gravitational search algorithm also performed best in the third food, with CC=0.9786, PSR=0.2604, NSE=0.9321, and d=0.9848, and with improvements in accuracy using the Kalman flter of+0.01081,−0.0971,+0.394, and+0.0078, respectively. We recommend the use of GWO-KF for food routing studies with food events of high volumes and hydrograph base times, and u
