Comparison of efficiency between differential evolution and evolution strategy: application of the LST model to the Be River catchment in Vietnam

Parameter calibration is an important step in the development of rainfall–runoff models. Recently, there has been a significant focus on automatic calibration. In this paper, two evolutionary optimization algorithms were applied to calibration of the long- and short-term runoff model (LST model) to simulate the daily rainfall–runoff process in the Be River catchment located in southern Vietnam. The differential evolution (DE) and evolution strategy (ES) algorithms were employed to optimize three objective functions: the Nash–Sutcliffe efficiency coefficient, root mean square error, and mean absolute error, which are indices for evaluating the simulation accuracy of the LST model. Hydrometeorological data for the periods 1985–1989 and 1990–1991 were used for calibration and validation, respectively. The LST model was calibrated for each objective function using five different parent and offspring population conditions. The results show that both the DE and ES algorithms are efficient methods for automatic calibration of the LST model. After 1000 generations, the best values of the fitness indices found by the DE technique were slightly better and more stable than those found by the ES technique in both calibration and validation. The average computation time for each generation using the DE algorithm was approximately two-thirds as long as that using the ES algorithm.