School of Electronic and Information Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China.
College of Information Science and Technology, Gansu Agricultural University, Lanzhou 730070, China.
Comput Intell Neurosci. 2020 Mar 10;2020:8594727. doi: 10.1155/2020/8594727. eCollection 2020.
Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions' combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions' combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.
水文模型参数优化本质上是一个高维、非线性、多变量、组合优化问题，涉及一组不同的目标。目前，水文模型优化结果的评估通常通过模拟和观测变量的目标函数值的计算和比较来进行。因此，水文模型参数优化中目标函数组合的适当选择对水文预报具有重要影响。存在各种目标函数，如何分析和评估目标函数组合以选择最优参数尚未得到深入研究。因此，为了选择适当的目标函数组合，以平衡各种设计目标之间的权衡，实现整体最佳效益，迫切需要一个简单方便的框架来比较不同目标函数组合对优化结果的影响。本文从文献中收集了与水文模型参数优化相关的各种目标函数，并构建了九个组合。然后，提出了一种用于水文模型参数优化的目标函数选择和评价框架，其中采用了一种名为 RMOABC 的多目标人工蜂群算法来优化水文模型并获得 Pareto 最优解。以黑河流域长期径流预测为例，将新安江水文模型的参数优化问题作为应用案例。最后，采用基于熵理论的逼近理想解排序法（TOPSIS）对 Pareto 最优解进行排序，比较这些目标函数组合，得到综合最优目标函数组合。实验结果表明，在研究区域内，目标函数组合 2 可以为实际水文预报提供更全面、更可靠的主导选项（即参数集）。基于熵的方法已被证明，它可以有效地分析和评估不同目标函数组合的性能，并为水文预报提供更全面、客观的决策支持。
