# A Novel Adaptive Sparrow Search Algorithm Based on Chaotic Mapping and T-Distribution Mutation
## 4 Numerical Experiments and Analysis
### Experimental Results and Analysis
#### 4.3.2 Optimization Results for Different Dimensions  
In order to further prove the optimization performance of the CWTSSA, the GWO, PSO, and sparrow search algorithm based on Cauchy distribution and reverse learning (CASSA) are selected for comparative analysis in three different dimensions. The obtained optimal value, average value and standard deviation after 30 independent experiments are used as the evaluation index to illustrate the convergence accuracy and convergence speed of the CWTSSA. The comparison results of five different algorithms under 30, 50, and 100 dimensions are shown in Table 4.  
It can be seen from Table 4 that for simple unimodal functions, the CWTSSA and DE, GWO, PSO, SSA, CASSA have achieved better optimization results, and they do not cause great obstacles with the increase in dimensionality. The CWTSSA performs well, and can even converge to the global optimal value under the different dimensions. However, for more complex multimodal functions \(f_{5}-f_{8}\), the increased dimensionality greatly increases the difficulty and weakens the optimization performance of all algorithms. It can also be seen that the convergence accuracy of the CWTSSA has been improved, and the standard deviation is kept at a small value. The experimental results show that the stability of the CWTSSA is stronger than that of the other compared algorithms. For \(f_{13},f_{14}\), the CWTSSA algorithm performs well by in comparison with other algorithms, which fully illustrates the increased necessity of the strategy. From the perspective of horizontal comparison, the solution accuracy of the CWTSSA has not been reduced by the gradual increase in dimensionality. The experimental results show that the CWTSSA has withstood the test of increases in dimensionality.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Functions**} & \multirow{2}{*}{**Algorithms**} & \multicolumn{3}{c}{**D = 30**} & \multicolumn{3}{c}{**D = 100**} \\ \cline{3-11}  & & & **Optimal Value** & **Mean Value** & **[PERSON]. [PERSON]** & **Optimal Value** & **Mean Value** & **[PERSON]. [PERSON]** & **Optimal Value** & **Mean Value** & **[PERSON]. [PERSON]** \\ \hline \multirow{9}{*}{_f_} & DE & 1.3464E-04 & 2.8733E-04 & 2.7606E-09 & 1.0268E-02 & 1.7215E-02 & 2.7988E-05 & 1.0798E-02 & 2.1346E-02 & 4.1207E-04 \\  & GAVO & 1.3002E-85 & 9.5404E-04 & 6.4873E-04 & 2.1438E-03 & 5.5300E-04 & 4.6982E-03 & 2.9413E-01 & -5.8436E-02 & 5.5405E-02 \\  & PSO & 2.7828E-16 & 1.9463E-10 & 3.0802E-09 & 1.1708E-07 & 6.4312E-06 & 4.8564E-05 & 2.5273E-02 & -5.5001E-04 & 2.5314E-02 \\  & SA & 0.0006E-01 & 1.1300E-126 & 0.0002E-00 & 0.0004E-00 & 1.1325E-04 & 0.0000E-00 & 0.0030E-00 & 0.3387E-01 & 3.0000E-00 \\  & CASSA & 0.0000E-00 & 5.8842E-164 & 0.0000E-00 & 2.0081E-00 & 8.9421E-15 & 6.0007E-13 & 0.0000E-00 & -1.02096E-164 & 0.0000E-00 \\  & CUTSSA & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 4.3077E-220 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 \\ \hline \multirow{9}{*}{_f_} & DE & 2.7131E-04 & 2.0742E-01 & 2.3728E-06 & 2.2846E-02 & 4.6104E-02 & -5.0244E-05 & 3.3144E-02 & 4.6484E-02 & 2.7252E-05 \\  & GAVO & 1.5422E-04 & 6.6672E-02 & 5.2454E-02 & 6.0229E-06 & 2.6356E-02 & 1.2727E-07 & 1.4056E-03 & 3.3562E-02 & 2.8260E-08 \\  & PSO & 1.1001E-07 & 2.3028E-09 & 9.2759E-09 & 1.6616E-03 & 1.6700E-08 & 5.7870E-06 & 1.8975E-03 & -1.0870E-04 & 5.4940E-04 \\  & S8A & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 \\  & CSSA & 2.2145E-02 & -.7831E-04 & 1.0700E-00 & 1.0000E-00 & 4.6641E-02 & 3.4774E-09 & 1.1000E-01 & 1.1735E-01 & 9.7374E-15 \\  & CVTSSA & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 & 0.0000E-00 \\ \hline \multirow{9}{*}{_f_} & DE & 3.8978E-10 & 2.1354E-09 & 1.7181E-08 & 7.6264E-06 & 2.6607E-05 & 5.0914E-06 & 7.6284E-06 & 2.6607E-05 & 5.0914E-06 \\  & GAVO & 1.1110E-08 & -6.4612E-03 & 3.3140E-05 & 6.7648E-15 & 1.3980E-01 & 1.1916E-08 & 4.0997E