Application of a Hybrid Optimization Method in Muskingum Parameter Estimation

Abstract

Two new mathematical forms of the nonlinear Muskingum model called NL4 and NL5, involving four and five parameters, respectively, can be used in river flood routing. The accuracy of the estimation of the Muskingum model parameters is essential for flood routing. This paper proposes a novel hybrid algorithm, based on the shuffled frog leaping algorithm (SFLA) and Nelder-Mead simplex (NMS), for the estimation of parameters of two new nonlinear Muskingum models. The proposed methodology is applied by considering minimization of the sum of the square deviation (SSD) between observed and routed outflows in (1) experimental, (2) real, and (3) multimodal examples. Results show that the SSD is 0.91, 3.97, and 4.44% smaller (better) than pertinent values obtained by the genetic algorithm-generalized reduced gradient (GA-GRG) method in experimental, real, and multimodal examples, respectively.