基于全局搜索和局部收敛能力均衡的快速稳定高斯牛顿算法研究

With the progress in model structure and simulation functionality, there is a significant increment in the number of parameters, as well as computational cost during model simulation. In the meanwhile, the complexity of the problems to be solved increased, together with the requests of high real-time performance. The number of objective function calls for stochastic based optimization algorithms increased exponential when the dimension of the problem increased; thus are no longer the prevailing optimization algorithm for high dimension and excessive cost problems. Therefore, there is an urgent demanding for hydrological modelling community to develop a fast and robust optimization algorithm tailored to the geometrically problematic features of hydrological model response surface and less sensitive to the dimensionality of parameters..This research focuses on gradient-based Gauss-Newton algorithm. In order to enhance exploration ability in high dimension problem and exploration ability in irregular hydrology response surface of Gauss-Newton algorithm, this research intends to carry out the research with the following three aspects. Firstly, attention will be paid to investigate exploration ability and exploitation ability enhancement mechanism for optimization algorithms. Secondly, the research will focus on possible solutions for improving the exploration and exploitation balance for Gauss-Newton algorithm on hydrology model calibration; Finally, a comprehensive framework is tailored to further improve the speed for hydrology model calibration with Gauss-Newton algorithm by using the parallel computation technique, in order to meet the requests of high real-time performance..The aim of the research per se is to develop a fast and robust Gauss-Newton algorithm tailored to problematic features of hydrological model response surface, which opens up some fruitful areas of research for hydrological model calibration.

随着水文模型结构和模拟功能的不断完善，水文模型的参数维度增加，模型模拟时间也随之增长。与此同时水文模型在应用过程中问题的复杂度提高，问题的实时性需求也显著增加。全局随机优化算法需要的模型运算次数随着参数维度增加呈指数增长趋势，已经很难满足应用过程中的实时性需求。因此亟需研究一种适合于水文模型复杂目标函数响应面，同时又少受维度影响的快速稳定参数优化算法。本项目以基于梯度的高斯牛顿算法为研究对象，针对算法在高维度参数空间上全局探索能力以及非常态水文模型响应面上局部探究能力的不足，拟展开如下三个方面的研究：1）系统性挖掘优化算法全局探索和局部探究能力提升机制; 2）提出非常态响应面上全局探索和局部探究能力提升应对策略；3）实现梯度算法主要模型运算的并行化以削弱维度对优化效率的影响。本项目目标是建立一种适用于水文模型复杂目标函数响应面上的快速稳定高斯牛顿算法，满足水文模型应用过程中的实时性需求。

水文模型的参数优化是水文模型建模中的重要环节。随着水文模型地不断发展完善，待优化的参数数量及模型复杂度逐渐增加。由于水文模型的复杂性，包括非连续性、不可微性及多极值等特点，当前高维度参数空间上基于梯度的优化算法在水文模型参数优化中的应用效果受限。因此亟需研究一种适合于水文模型复杂目标函数响应面，同时又少受维度影响的快速稳定参数优化算法。本项目首先分析了水文模型目标函数响应面上的复杂特性，并提出了梯度算法在水文模型非常态响应面上全局搜索和局部收敛能力改善的关键因子；在此基础上提出了一种综合考虑稳定性和计算效率的稳定高斯牛顿算法，并在不同维度水文模型参数空间上实现了快速稳定参数优化；最后通过并行化方案对梯度算法海森矩阵计算和线搜索计算进行并行化设计，充分利用了服务器计算资源，大大提升了基于梯度的参数优化算法在高维度参数空间上的优化效率，为复杂水文模型水环境水动力模型的快速稳定参数优化提供了可行的解决方案。

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