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

The lower bound of maximum predictable time can be formulated into a constrained nonlinear opti- mization 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 ad- joint 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.

On the application of a genetic algorithm to the predictability problems involving “on-off” switches

The lower bound of maximum predictable time can be formulated into aconstrained nonlinear optimization problem, and the traditional solutions tothis problem are the filtering method and the conditional nonlinear optimalperturbation (CNOP) method. Usually, the CNOP method is implemented with thehelp of a gradient descent algorithm based on the adjoint method, which isnamed the ADJ-CNOP. However, with the increasing improvement of actualprediction models, more and more physical processes are taken intoconsideration in models in the form of parameterization, thus giving rise tothe on--off switch problem, which tremendously affects the effectiveness ofthe conventional gradient descent algorithm based on the adjoint method. Inthis study, we attempted to apply a genetic algorithm (GA) to the CNOPmethod, named GA-CNOP, to solve the predictability problems involvingon--off switches. As the precision of the filtering method depends uniquelyon the division of the constraint region, its results were taken asbenchmarks, and a series of comparisons between the ADJ-CNOP and the GA-CNOPwere performed for the modified Lorenz equation. Results show that theGA-CNOP can always determine the accurate lower bound of maximum predictabletime, even in non-smooth cases, while the ADJ-CNOP, owing to the effect ofon--off switches, often yields the incorrect lower bound of maximumpredictable time. Therefore, in non-smooth cases, using GAs to solvepredictability problems is more effective than using the conventionaloptimization algorithm based on gradients, as long as genetic operators inGAs are properly configured.