# A Novel Adaptive Sparrow Search Algorithm Based on Chaotic Mapping and T-Distribution Mutation
## 4 Numerical Experiments and Analysis
### Experimental Results and Analysis
#### 4.3.1 SSA with Different Strategies
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Functions** & **Algorithms** & **Optimal Value** & **Mean Value** & **Std.Dev** \\ \hline \multirow{8}{*}{\(f_{12}\)} & SSA & 6.9451E\(-\)05 & 4.9734E\(-\)05 & 3.9537E\(-\)08 \\  & CSSA & 4.6432E\(-\)13 & \(-\)1.0000E+00 & 1.5557E\(-\)06 \\  & WSSA & 4.3067E\(-\)10 & \(-\)1.0000E+00 & 4.7613E\(-\)05 \\  & TSSA & 6.2419E\(-\)12 & \(-\)1.0000E+00 & 5.6778E\(-\)06 \\  & CWTSSA & 1.6996E\(-\)32 & \(-\)1.0000E+00 & 8.2465E\(-\)17 \\  & CTSSA & 7.2381E\(-\)12 & \(-\)1.0000E+00 & 6.1476E\(-\)06 \\  & WTSSA & 2.2723E\(-\)12 & \(-\)1.0000E+00 & 3.4413E\(-\)06 \\  & CWTSSA & 7.1167E\(-\)09 & \(-\)9.9998E\(-\)01 & 1.9048E\(-\)04 \\ \hline \multirow{8}{*}{\(f_{13}\)} & SSA & 6.9451E\(-\)05 & 4.9734E\(-\)05 & 3.9537E\(-\)08 \\  & CSSA & 1.0023E\(-\)05 & 1.0000E+00 & 4.3812E\(-\)09 \\  & WSSA & 8.0951E\(-\)05 & 1.0000E+00 & 3.1108E\(-\)07 \\  & TSSA & 2.2859E\(-\)05 & 1.0000E+00 & 9.3112E\(-\)08 \\  & CWSSA & 2.8343E\(-\)06 & 1.0000E+00 & 8.5164E\(-\)07 \\  & CTSSA & 6.1355E\(-\)05 & 1.0000E+00 & 1.8308E\(-\)08 \\  & WTSSA & 9.3486E\(-\)07 & 1.0000E+00 & 2.4531E\(-\)08 \\  & CWTSSA & 1.6516E\(-\)05 & 2.6485E\(-\)05 & 1.6149E\(-\)09 \\ \hline \multirow{8}{*}{\(f_{14}\)} & SSA & 0.0000E+00 & 2.2507E\(-\)178 & 0.0000E+00 \\  & CSSA & 0.0000E+00 & 4.6834E\(-\)197 & 0.0000E+00 \\  & WSSA & 0.0000E+00 & \(-\)5.2254E\(-\)94 & 03.4224E\(-\)182 \\  & TSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\  & CWSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\  & CTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\  & CWTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\ \hline \multirow{8}{*}{\(f_{15}\)} & SSA & 0.0000E+00 & \(-\)1.7863E\(-\)138 & 0.0000E+00 \\  & CSSA & 0.0000E+00 & 1.1245E\(-\)165 & 0.0000E+00 \\  & WSSA & 0.0000E+00 & 1.3890E\(-\)140 & 1.6568E\(-\)278 \\ \cline{1-1}  & TSSA & 0.0000E+00 & 3.0445E\(-\)180 & 0.0000E+00 \\ \cline{1-1}  & CWSSA & 0.0000E+00 & 6.0872E\(-\)206 & 0.0000E+00 \\ \cline{1-1}  & TTSSA & 0.0000E+00 & 1.1566E\(-\)168 & 0.0000E+00 \\ \cline{1-1}  & WTSSA & 0.0000E+00 & 6.4927E\(-\)199 & 0.0000E+00 \\ \cline{1-1}  & CWTSSA & 0.0000E+00 & 5.3679E\(-\)206 & 0.0000E+00 \\ \cline{1-1}  & CWTSSA & 0.0000E+00 & 5.3679E\(-\)206 & 0.0000E+00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._ferent performance on different test functions. For function \(f_{9}\), the combination of the sine chaotic mapping strategy and adaptive weighting strategy makes the standard deviation and the mean value obtain the theoretical optimal value. Because of the particularity of the functions, when all the strategies are used, the satisfactory result cannot be obtained. The example for function \(f_{10}\) is a function with added random noise. When the domain is positive, the value range tends to positive infinity, so the function has only a global minimum. High accuracy cannot be achieved in several cases. This may be related to the limitations of the algorithm, and also related to the ability of the algorithm to optimize. Therefore, the test function also has an impact on the performance of the algorithm. For functions \(f_{14}\) and \(f_{15}\), CWTSSA has also achieved better results than a single strategy or combination strategy, which further illustrates the superior performance of the algorithm. To sum up, when the three strategies are used at the same time for SSA, most of the test functions have better convergence speed and convergence accuracy, and the stability is also better. This is inseparable from the use of the three strategies. In general, the SSA with each strategy has certain improvements compared with the basic SSA.