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694566,A couple of), (Only two.000000,One particular), (A couple of.000000,Some), (Several.000000,Four), (A couple of.000000,1), (Three.000000,One), (A couple of.000000,Some), (Some.000000,Several), (4.000000,Four), (One.000000,One particular), (A couple of.000000,A single), (4.000000,Several), (A single.000000,Your five), (1.000000,A single), (Only two.000000,A single), (Five.713432,Only two), (Four.000000,One), (One particular.000000,One)}, and the simplified form of the corresponding decoded equation is xt=9.784395yt?2?10.134447yt?4?0.175026zt?1. (20) It can be seen from (20) that the values of x-variable can be extrapolated by the previous values of y-variable and z-variable. The forecasting performance is verified by taking the remaining 200-step values. The prediction values and real values of Rossler time series are shown in Figure 6, and it can be seen from Figure 6 that the forecasting values are very close to the real values; the mean square error (MSE) is 2.755001E ? 03. Figure 7 indicates that the fitness value converges to the best value with a high speed and the final [https://en.wikipedia.org/wiki/RecBCD RecBCD] best fitness value is calculated as Fitnesstest = 0.999903 (accurately to sixth place of decimal). Figure 6 Real values of Rossler time series and short-term prediction values. Figure 7 Convergence process of IGSA during the iterations. 5. Effect of Noise in the Chaotic Time Series As the actual chaotic systems always contain noise, in order to test the influence of noise on the forecasting precision, the noise-free time series of [http://www.selleckchem.com/screening/anti-diabetic-compound-library.html Antidiabetic Compound Library datasheet] Quadratic and Rossler maps were corrupted using Gaussian white noise with the different signal-to-noise ratios (SNR) values (see Table 2). The fitness values obtained by taking the same procedure described earlier were also listed in the table. Table 2 Fitness values for noisy time series with different SNR. It can be observed from Table 2 that the fitness values are all decreased, and none of the forecasting precisions matched the precision when noise-free data were used. However, it can be found that the precisions are generally satisfactory when the values of SNR are larger than 25?dB, and when the SNR decreased, the fitness value was decreased a lot. It can be concluded that the proposed method possesses a certain capability of noise immunity and can effectively perform in the noisy time series with large SNR values (in this case, the SNR value should be larger than 25?dB). However, the limit is also obvious that the precisions are not acceptable and the method is not effective in a highly corrupted time series. 6. [http://www.selleckchem.com/products/crenolanib-cp-868596.html this website] Discussion In order to demonstrate that the proposed method is robust to parameter variations and to evaluate the effect of parameter variations, different parameters are also set to test the performances of the method, such as the number of generations and initial individuals and the probability of mutation and the initial temperature. The results are varied slightly. However, the following rules of setting the parameters may prove helpful to improve the efficiency and accuracy of the method.