# 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  
In order to analyze each strategy clearly, three strategies are introduced into the SSA for solving 15 benchmark functions. The evaluation indexes of optimization performance include optimal value, mean value and standard deviation (Std.Dev) in order to prove the effectiveness of the proposed algorithm. The experimental results are shown in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithms** & **Parameter Settings** \\ \hline GWO & Decreases linearly from 2 to \(0,r_{1},r_{2}\in[0,\ 1]\) \\ \hline PSO & \(v_{i}=6,\omega_{\max}=0.9,\omega_{\min}=0.2,c_{1}=c_{2}=2\) \\ \hline DE & \(C_{R}\) = 0.9 \\ \hline SSA\(\backslash\)CSSA\(\backslash\)WSSA\(\backslash\)TSSA\(\backslash\)CWSA\(\backslash\)CTSS\(\backslash\)WTSSA & \(PD=0.7,SD=0.2,ST=0.6\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter settings for each algorithm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Functions** & **Algorithms** & **Optimal Value** & **Mean Value** & **Std.Dev** \\ \hline \multirow{8}{*}{\(f_{1}\)} & SSA & 0.0000E+00 & \(-1.1800\)E\(-246\) & 0.0000E+00 \\  & CSSA & 0.0000E+00 & \(-8.2624\)E\(-209\) & 0.0000E+00 \\  & WSSA & 5.3328E\(-165\) & \(-6.0757\)E\(-84\) & 1.2071E\(-83\) \\  & TSSA & 0.0000E+00 & \(1.3301\)E\(-182\) & 0.0000E+00 \\  & CWSSA & 4.8142E\(-44\) & 3.7280E\(-24\) & 4.0567E\(-23\) \\  & CTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\  & WTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\  & CWTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\ \hline \multirow{8}{*}{\(f_{2}\)} & SSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\  & CSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\  & WSSA & 5.1891E\(-220\) & 8.7820E\(-222\) & 0.0000E+00 \\  & TSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\  & CWSSA & 2.2862E\(-10\) & 5.1202E\(-12\) & 2.5566E\(-11\) \\  & CTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\  & WTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\  & CWTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\ \hline \multirow{8}{*}{\(f_{3}\)} & SSA & 0.0000E+00 & 3.4758E\(-171\) & 0.0000E+00 \\  & CSSA & 0.0000E+00 & 3.4785E\(-237\) & 0.0000E+00 \\  & WSSA & 1.0848E\(-173\) & 2.1891E\(-89\) & 5.8870E\(-88\) \\  & TSSA & 0.0000E+00 & \(-3.4143\)E\(-165\) & 0.0000E+00 \\  & CWSSSA & 5.6884E\(-09\) & \(-7.8547\)E\(-08\) & 2.6252E\(-05\) \\  & CTSSA & 0.0000E+00 & 3.0491E\(-168\) & 0.0000E+00 \\  & WTSSA & 0.0000E+00 & 5.2493E\(-211\) & 0.0000E+00 \\  & CWTSSA & 0.0000E+00 & 2.1387E\(-195\) & 0.0000E+00 \\ \hline \multirow{8}{*}{\(f_{4}\)} & SSA & 0.0000E+00 & 3.4758E\(-171\) & 0.0000E+00 \\  & CSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\ \cline{1-1}  & WSSA & 7.1761E\(-69\) & \(-5.4623E\)\(-71\) & 2.9230E\(-69\) \\ \cline{1-1}  & TSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\ \cline{1-1}  & CWSSA & 2.1638E\(-05\) & 3.4421E\(-07\) & 1.6619E\(-05\) \\ \cline{1-1}  & CTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\ \cline{1-1}  & WTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\ \cline{1-1}  & CWTSSA & 0.0000E+00 & 0.0000E+00 & 0.0000E+00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison results of the SSA with different strategies.