Parameter evaluation of a nonlinear Muskingum model using a constrained self-adaptive differential evolution algorithm

The precise evaluation of the Muskingum model (MM) parameters is quite critical for routing flood waves for achieving flood control in open channels. The MM is one of the popular techniques adopted for flood routing. Estimation of the MM parameters so as to provide the best fit for the observed and computed flow values is a global optimization problem. Several optimization techniques have been adopted in the past to serve this purpose, but efficient optimization algorithms are needed to overcome the local optima issues and improvement of accuracy. In this paper, the efficiency of three optimization algorithms, namely Jaya, Covariance Matrix Adaption-Evolution Strategy (CMAES) and self-adaptive differential evolution (SaDE), has been assessed in the evaluation of the Muskingum parameters. The sum of the square deviation of the observed outflow and computed outflow (SSQ) is considered an objective in this MM optimization problem. Also, a constraint is proposed in this paper to help the optimization algorithms in finding the global optimal solutions. The simulation results show that the sum of the square deviation of the observed outflow and computed outflow (SSQ) was the least for SaDE, followed by CMAES.