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| A Variant Constrained Genetic Algorithm for Solving Conditional Nonlinear Optimal Perturbations简 | |
| 作者姓名： | ZHENG Qin SHA Jianxin SHU Hang LU Xiaoqing |
| 基金项目： | supported by the National Natural Science Foundation of China(Grant No.40975063);the National Natural Science Foundation of China(Grant No.41331174) |
| 摘 要： | A variant constrained genetic algorithm （VCGA） for effective tracking of conditional nonlinear optimal perturbations （CNOPs） is presented. Compared with traditional constraint handling methods, the treatment of the constraint condition in VCGA is relatively easy to implement. Moreover, it does not require adjustments to indefinite pararneters. Using a hybrid crossover operator and the newly developed multi-ply mutation operator, VCGA improves the performance of GAs. To demonstrate the capability of VCGA to catch CNOPS in non-smooth cases, a partial differential equation, which has ＂on off＂ switches in its forcing term, is employed as the nonlinear model. To search global CNOPs of the nonlinear model, numerical experiments using VCGA, the traditional gradient descent algorithm based on the adjoint method （ADJ）, and a GA using tournament selection operation and the niching technique （GA-DEB） were performed. The results with various initial reference states showed that, in smooth cases, all three optimization methods are able to catch global CNOPs. Nevertheless, in non-smooth situations, a large proportion of CNOPs captured by the ADJ are local. Compared with ADJ, the performance of GA-DEB shows considerable improvement, but it is far below VCGA. Further, the impacts of population sizes on both VCGA and GA-DEB were investigated. The results were used to estimate the computation time of ~CGA and GA-DEB in obtaining CNOPs. The computational costs for VCGA, GA-DEB and ADJ to catch CNOPs of the nonlinear model are also compared. |
| 关 键 词： | 非线性模型 遗传算法 扰动 变种 求解 偏微分方程 小生境技术 梯度下降法 |
A variant constrained genetic algorithm for solving conditional nonlinear optimal perturbations |
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| ZHENG Qin,SHA Jianxin,SHU Hang,LU Xiaoqing.A variant constrained genetic algorithm for solving conditional nonlinear optimal perturbations[J].Advances in Atmospheric Sciences,2014,31(1):219-229. | |
| Authors: | Qin Zheng Jianxin Sha Hang Shu Xiaoqing Lu |
| Institution: | 1. Institute of Science, PLA University of Science and Technology, Nanjing, 211101, China 2. State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China 3. Troop 94906, People’s Liberation Army, Suzhou, 215157, China |
| Abstract: | A variant constrained genetic algorithm (VCGA) for effective tracking of conditional nonlinear optimal perturbations (CNOPs) is presented. Compared with traditional constraint handling methods, the treatment of the constraint condition in VCGA is relatively easy to implement. Moreover, it does not require adjustments to indefinite parameters. Using a hybrid crossover operator and the newly developed multi-ply mutation operator, VCGA improves the performance of GAs. To demonstrate the capability of VCGA to catch CNOPS in non-smooth cases, a partial differential equation, which has “onoff” switches in its forcing term, is employed as the nonlinear model. To search global CNOPs of the nonlinear model, numerical experiments using VCGA, the traditional gradient descent algorithm based on the adjoint method (ADJ), and a GA using tournament selection operation and the niching technique (GA-DEB) were performed. The results with various initial reference states showed that, in smooth cases, all three optimization methods are able to catch global CNOPs. Nevertheless, in non-smooth situations, a large proportion of CNOPs captured by the ADJ are local. Compared with ADJ, the performance of GA-DEB shows considerable improvement, but it is far below VCGA. Further, the impacts of population sizes on both VCGA and GA-DEB were investigated. The results were used to estimate the computation time of VCGA and GA-DEB in obtaining CNOPs. The computational costs for VCGA, GA-DEB and ADJ to catch CNOPs of the nonlinear model are also compared. |
| Keywords: | genetic algorithm conditional nonlinear optimal perturbation "on-off" switch adjoint method |
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