Study on Optimization of Hydrological Watershed Model using Multi-Objective Programming

多目标优化方法对于多输出通量水文模型的参数估计是非常有用的，即使对于单输出的全径流模型，它也适用于同时使用不同目标的参数校准。例如最小化峰值流量、低流量和总体积的误差。本研究针对一个概念性的河川径流模型--Sugawara Tank模型，进行多目标参数优化的研究。以均方根误差（RMSE）和相对误差的均方根（RR）为目标函数，在允许水量平衡误差的约束下，使目标函数最小化。在单目标全局优化算法SCE-UA方法的基础上，采用经典加权方法求出离散Pareto最优解，然后采用一种新的基于随机搜索的简单方法有效地估计大量Pareto解，并逼近整个Pareto空间。此外，还讨论了全局搜索方法之一的进化策略（ES）的使用。将专家系统应用于坦克模型的单目标和多目标优化。结果表明，在单目标优化问题中，ES比GA和SCE-UA更有效，在多目标优化问题中，ES能更有效地求出Pareto解。本文还探讨了径流模型率定中目标函数的选择与模拟过程拟合优度的关系。结果表明，RMSE法强调高流量时的拟合优度，RR法强调低流量时的估计误差。

The multi-objective optimization is very useful for parameter estimation of multi-output-flux hydrological models and even in the case of single-output rainfall-runoff models, it is applicable and useful for parameter calibration using different objectives simultaneously. e.g. minimization of errors of peak flows, low flows and overall volume. In this study, parameter optimization of a conceptual rainfall-runoff model, the Sugawara Tank Model using the multi-objectives was investigated. The root mean square error (RMSE) and the root mean square of relative error (RR), which show obvious trade-off relationship, were adopted as objective functions and these objectives were minimized under the constraint of the permitted water balance error. The discrete Pareto optimal solutions were obtained by using the classical weighting method based on the SCE-UA method of the single-objective global optimization algorithm and then a new simple approach based on the random search was applied to estimate a large number of Pareto solutions efficiently and approximate the entire Pareto space. Moreover, the use of the Evolution Strategy (ES) which is one of the global search methods was discussed. The ES was applied to the single- and multi-objective optimization of the Tank Model. Results showed that the ES is more effective than the GA and the SCE-UA in the single-objective optimization and the Pareto solutions of multi-objective optimization can be obtained quite efficiently by using the ES. The relationship between the selection of objective functions used in calibration of rainfall-runoff models and the goodness of fit of simulated hydrograph was also investigated. Results showed that the RMSE emphasizes most the goodness of fit at high flows and the RR emphasizes estimated errors at low flows.