In this paper, a hybrid harmony search (HS) algorithm is proposed for the parameter estimation of the nonlinear Muskingum model. The BFGS algorithm is used as local search algorithm with a low probability for accelerating the HS algorithm. In the proposed technique, an indirect penalty function approach is imposed on the model to prevent negativity of outflows and storages. The proposed algorithm finds the global or near-global minimum regardless of the initial parameter values with fast convergence. The proposed algorithm found the best solution among 12 different methods. The results demonstrate that the proposed algorithm can be applied confidently to estimate optimal parameter values of the nonlinear Muskingum model. Moreover, this hybrid methodology may be applicable to any continuous engineering optimization problems.

A new nonlinear Muskingum flood routing model taking the contribution from lateral flow into consideration was developed in the present study. The cuckoo search algorithm, a quite novel and robust algorithm, was used in the calibration and verification of the model parameters. The success and the dependability of the proposed model were tested on five different sets of synthetic and real flood data. The optimal solutions for the test cases were determined by the currently proposed model rather than by different models taken from the literature, indicating that this model could be suitable for use in flood routing problems.