Enhanced Calibration of Multi-Partition Nonlinear Muskingum Flood Routing Models Using an Improved Biogeography-Based Optimization Algorithm

Flood routing is a critical component of hydrological modeling and flood risk management. An improved biogeography-based optimization (IBBO) algorithm is proposed for determining the optimal parameter values of a multi-partition nonlinear Muskingum flood routing model. The evaluation was conducted for two model structures, namely, the three-partition (3P) and five-partition (5P) configurations, using three benchmark datasets: Wilson, Wyre River, and Viessman–Lewis. IBBO was compared with six algorithms—artificial bee colony (ABC), differential evolution (DE), grey wolf optimizer (GWO), chaotic salp swarm algorithm (CSSA), hybridizing sum-local search optimizer (HSLSO), and standard biogeography-based optimization (BBO)—using 30 independent runs for each case. Across the six benchmark scenarios, IBBO achieved the lowest best and mean SSQ values, with best SSQ values of 0.93, 5.99, and 9673.51 for the Wilson, Wyre, and Viessman–Lewis events, respectively. Moreover, IBBO provided an excellent fit to the hydrographs, with VarexQ values (variance explained) ranging from 99.62% to 99.99%, and substantially reduced the total absolute deviation (SAD = 3.11 for Wilson 5P and 9.83 for Wyre 5P) and the peak discharge error (DPO = 0.01). Across all benchmarks, the 5P configuration improved routing accuracy relative to the 3P configuration, owing to its greater model flexibility. Finally, the robustness of the proposed 5P configuration against over-parameterization is rigorously verified using an extended dataset from the Dinavar River, which provides a higher data-to-parameter ratio and confirms the model’s superior predictive accuracy. Overall, the results demonstrate that IBBO provides superior calibration accuracy and convergence stability for multi-partition nonlinear Muskingum models across the benchmark events investigated in this study.