摘要
Nelder-Mead Simplex(NMS)算法是一种查找多元函数局地最小值的无微分算法,在现代科学计算中得到广泛应用,该文提出了一种对NMS算法的改进方法。改进后,大大简化了其计算过程,提高了该算法的收敛速度。利用改进后的算法对陆面过程参数进行了拟合计算,结果表明:改进的NMS算法对非线性公式具有非常高的拟合精度,可将其应用于气象学上非线性问题计算或非线性方程组求解。
Owing to computers providing great advantage in iterative calculation, the nonderivative algorithms have great potential applications to scientific research. Nelder-Mead Simplex （NMS） algorithm is a technique for minimizing an objective function in a multipledimensional space without differentiation, proposed by Nelder and Mead （1965）. As a simple non-derivative technique, NMS algorithm is widely introduced in many computational books and used in numerical computations, and Matlab implements this algorithm for instance. Unfortunately, the method has some disadvantages such as slow converging and low precision, which need to be improved. Meteorological problems, usually nonlinear, are very complicated to solve, which require nonlinear fittings, solving the relationships between different meteorological variables, determining parameters in empirical formulas, solving the system of nonlinear equations and so forth. Conventionally, nonlinear problems are usually transformed into linear ones to solve, but this is not always practical. Fortunately the non derivative algorithm could do this work, and an introduction to the application of the NMS algorithm to meteorological computations could be beneficial for meteorological community. An improvement on the NMS algorithm is proposed. To avoid the problems existing in the original NM simplex algorithm, a constraint is introduced to obtain next iterative point rather than finding the points of reflection, expansion, contraction and shrink, similar to that in the Powell＇s Method or in the Steepest Gradient algorithm. However, the searching direction is still along the downhill direction, i. e. , the direction along the segment line between the vertex with the greatest functional value and the gravity center point. By introduction of the constraint, the multi-variable function will be transformed into a func- tion with one variable, i. e. , the constraint, which can be solved by the algorithms to calculate the mini- mum of a function with one variable, such as the Golden Section Search, Fibonacci Search and so forth. This approach will still keep the calculation without differentiation. After the improvement, the computa- tion is greatly simplified, and its convergence will be accelerated. Some possible applications of the NMS algorithm to meteorology are also introduced, and it＇s also described how to implement the algorithm in fitting parameters in empirical formulas and solving the system of nonlinear equations. To testify this improvement, fitting experiments to some parameters in land surface process are made using the modified algorithm. Relationships between zero plane displacement and leaf area index （II.A） and between aerodynamic resistance and ILA at ground surface are calculated using the Least Square Method and the NMS algorithm to determine parameters. Experimental results show that the proposed algorithm have very high precision when fitting nonlinear formulas, therefore it can be used in computations for solving nonlinear issues or the system of nonlinear equations.
出处
《应用气象学报》
CSCD
北大核心
2011年第5期584-589,共6页
Journal of Applied Meteorological Science
关键词
NMS算法
改进
无微分
气象学
非线性应用
NMS algorithm
improvement
non-derivative
meteorology
nonlinear application
