Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem  

作　　者：PENG Fei SUN Guo-Dong 

机构地区：[1]State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics (LASG),Institute of Atmospheric Physics,Chinese Academy of Sciences [2]University of Chinese Academy of Sciences

出　　处：《Atmospheric and Oceanic Science Letters》2014年第6期499-504,共6页大气和海洋科学快报（英文版）

基　　金：provided by grants from the LASG State Key Laboratory Special Fund;the National Natural Science Foundation of China (Grant Nos. 40905050, 40830955, and 41375111)

摘　　要：Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP), which has been applied widely in predictability studies. In this study, the Differential Evolution(DE) algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers' equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the Spectral Projected Gradient(SPG2) algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or for optimization problems with non-differentiable cost functions. A projection skill was first explanted to the DE algorithm to calculate the CNOPs. To validate the algorithm, the SPG2 algorithm was also applied to obtain the CNOPs for the same optimization problems. The results showed that the CNOPs obtained by the DE algorithm were nearly the same as those obtained by the SPG2 algorithm in terms of their spatial distributions and nonlinear evolutions. The implication is that the DE algorithm could be employed to calculate the optimal values of optimization problems, especially for non-differentiable and nonlinear optimization problems associated with the atmospheric and oceanic sciences.Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation（CNOP）, which has been applied widely in predictability studies. In this study, the Differential Evolution（DE） algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers＇ equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the Spectral Projected Gradient（SPG2） algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or for optimization problems with non-differentiable cost functions. A projection skill was first explanted to the DE algorithm to calculate the CNOPs. To validate the algorithm, the SPG2 algorithm was also applied to obtain the CNOPs for the same optimization problems. The results showed that the CNOPs obtained by the DE algorithm were nearly the same as those obtained by the SPG2 algorithm in terms of their spatial distributions and nonlinear evolutions. The implication is that the DE algorithm could be employed to calculate the optimal values of optimization problems, especially for non-differentiable and nonlinear optimization problems associated with the atmospheric and oceanic sciences.

关 键 词：differential evolution algorithm spectral projected gradient algorithm CNOP Burgers＇ equation optimization problem 

分 类 号：P456.7[天文地球—大气科学及气象学]