The application of the Differential Evolution (DE) algorithm (a derivative-free approach) in calculating the Conditional Nonlinear Optimal Perturbation (CNOP) with ball constraint was investigated by employing a projection skill. To verify the CNOPs calculated by the DE algorithm, the Spectral Projected Gradient (SPG2) algorithm (a derivative-based algorithm) was also applied to get CNOPs. Through comparisons results showed that the DE algorithm could be employed to calculate the optimal values of optimization problems; for example CNOPs.

Citation: Peng, F., and G.-D. Sun, 2014: Application of a derivative-free method with projection skill to solve an optimization problem, Atmos. Oceanic Sci. Lett., 7, doi:10.3878/AOSL20140041.

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Spatial distributions of CNOPs (m s^？1) calculated by the (a, d, g) SPG2 algorithm and (b, e, h) DE algorithm, and the (c, f, i) CNOP differences (m s^？1) (DE minus SPG2) when T = 30 s and n = 101, 201, 301, respectively.