Improving the Performance of Hydrological Model Parameter Uncertainty Analysis Using a Constrained Multi-Objective Intelligent Optimization Algorithm

Abstract

In the field of hydrological model parameter uncertainty analysis, sampling methods such as Differential Evolution based on Monte Carlo Markov Chain (DE-MC) and Shuffled Complex Evolution Metropolis (SCEM-UA) algorithms have been widely applied. However, there are two drawbacks which may introduce bad effects into the uncertainty analysis. The first disadvantage is that few optimization algorithms consider the physical meaning and reasonable range of the model parameters. The traditional sampling algorithms may generate non-physical parameter values and poorly simulated hydrographs when carrying out the uncertainty analysis. The second disadvantage is that the widely used sampling algorithms commonly involve only a single objective. Such sampling procedures implicitly introduce too strong an “exploitation” property into the sampling process, consequently destroying the diversity property of the sampled population, i.e., the “exploration” property is bad. Here, “exploitation” refers to using good already-existing solutions and making refinements to them, so that their fitness will improve further; meanwhile, “exploration” denotes that the algorithm searches for new solutions in new regions. With the aim of improving the performance of uncertainty analysis algorithms, in this research, a constrained multi-objective intelligent optimization algorithm is proposed that preserves the physical meaning of the model parameter using the penalty function method and maintains the population diversity using a Non-dominated Sorted Genetic Algorithm-II (NSGA-II) multi-objective optimization procedure. The representativeness of the parameter population is estimated on the basis of the mean and standard deviation of the Nash–Sutcliffe coefficient, and the diversity is evaluated on the basis of the mean Euclidean distance. The Chengcun watershed is selected as the study area, and uncertainty analysis is carried out. The numerical simulations indicate that the performance of the proposed algorithm is significantly improved, preserving the physical meaning and reasonable range of the model parameters while significantly improving the diversity and reliability of the sampled parameter population.