On the Application of a Genetic Algorithm to the Predictability  Problems Involving ``On--Off'' Switches

ZHENG Qin; DAI Yi; ZHANG Lu; SHA Jianxin; LU Xiaoqing

doi:10.1007/s00376-011-1054-z

Impact Factor: 5.8

Volume 29 Issue 2

Mar. 2012

Article Contents

Article > ADVANCES IN ATMOSPHERIC SCIENCES > 2012 > 29(2): 422-434

On the Application of a Genetic Algorithm to the Predictability Problems Involving ``On--Off'' Switches

1.
Institute of Science, PLA University of Science and Technology, Nanjing 211101, State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;Institute of Science, PLA University of Science and Technology, Nanjing 211101;Institute of Science, PLA University of Science and Technology, Nanjing 211101;Institute of Science, PLA University of Science and Technology, Nanjing 211101;Institute of Science, PLA University of Science and Technology, Nanjing 211101

doi: 10.1007/s00376-011-1054-z

Abstract
References
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Abstract:
The lower bound of maximum predictable time can be formulated into a constrained nonlinear optimization problem, and the traditional solutions to this problem are the filtering method and the conditional nonlinear optimal perturbation (CNOP) method. Usually, the CNOP method is implemented with the help of a gradient descent algorithm based on the adjoint method, which is named the ADJ-CNOP. However, with the increasing improvement of actual prediction models, more and more physical processes are taken into consideration in models in the form of parameterization, thus giving rise to the on--off switch problem, which tremendously affects the effectiveness of the conventional gradient descent algorithm based on the adjoint method. In this study, we attempted to apply a genetic algorithm (GA) to the CNOP method, named GA-CNOP, to solve the predictability problems involving on--off switches. As the precision of the filtering method depends uniquely on the division of the constraint region, its results were taken as benchmarks, and a series of comparisons between the ADJ-CNOP and the GA-CNOP were performed for the modified Lorenz equation. Results show that the GA-CNOP can always determine the accurate lower bound of maximum predictable time, even in non-smooth cases, while the ADJ-CNOP, owing to the effect of on--off switches, often yields the incorrect lower bound of maximum predictable time. Therefore, in non-smooth cases, using GAs to solve predictability problems is more effective than using the conventional optimization algorithm based on gradients, as long as genetic operators in GAs are properly configured.
- predictability,
- on--off switch,
- conditional nonlinear optimal perturbation (CNOP),
- genetic algorithm (GA)
References

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Manuscript History

Manuscript received: 10 March 2012

Manuscript revised: 10 March 2012

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

On the Application of a Genetic Algorithm to the Predictability Problems Involving ``On--Off'' Switches

1. Institute of Science, PLA University of Science and Technology, Nanjing 211101, State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029;Institute of Science, PLA University of Science and Technology, Nanjing 211101;Institute of Science, PLA University of Science and Technology, Nanjing 211101;Institute of Science, PLA University of Science and Technology, Nanjing 211101;Institute of Science, PLA University of Science and Technology, Nanjing 211101

Manuscript received: 2012-03-10
Manuscript revised: 2012-03-10

Abstract: The lower bound of maximum predictable time can be formulated into a constrained nonlinear optimization problem, and the traditional solutions to this problem are the filtering method and the conditional nonlinear optimal perturbation (CNOP) method. Usually, the CNOP method is implemented with the help of a gradient descent algorithm based on the adjoint method, which is named the ADJ-CNOP. However, with the increasing improvement of actual prediction models, more and more physical processes are taken into consideration in models in the form of parameterization, thus giving rise to the on--off switch problem, which tremendously affects the effectiveness of the conventional gradient descent algorithm based on the adjoint method. In this study, we attempted to apply a genetic algorithm (GA) to the CNOP method, named GA-CNOP, to solve the predictability problems involving on--off switches. As the precision of the filtering method depends uniquely on the division of the constraint region, its results were taken as benchmarks, and a series of comparisons between the ADJ-CNOP and the GA-CNOP were performed for the modified Lorenz equation. Results show that the GA-CNOP can always determine the accurate lower bound of maximum predictable time, even in non-smooth cases, while the ADJ-CNOP, owing to the effect of on--off switches, often yields the incorrect lower bound of maximum predictable time. Therefore, in non-smooth cases, using GAs to solve predictability problems is more effective than using the conventional optimization algorithm based on gradients, as long as genetic operators in GAs are properly configured.

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