# An Improved Squirrel Search Algorithm for Global Function Optimization
## 3 The improved Squirrel Search Algorithm
### The Jumping Search Method
#### 3.2.3 Characters of the Jumping Search Method
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Name** & **Method** & **Best** & **Worst** & **Mean** & **SD** & **R** \\ \hline \multirow{6}{*}{F3} & MDE & 0 & 0 & 0 & 0 & 30 \\  & distABC & 0 & 6.6613e\(-\)16 & 2.2204e\(-\)17 & 1.2162e\(-\)16 & 30 \\  & IGSA/PSO & 0 & 6.6613e\(-\)16 & 5.1810e\(-\)17 & 5.1810e\(-\)17 & 30 \\  & ADN-RSN-PSO & 1.7529e\(-\)09 & 0.3443 & 0.0209 & 0.0670 & 1 \\  & PSO-GWO & 0 & 0 & 0 & 0 & 30 \\  & ISSA & 0 & 0 & 0 & 0 & 30 \\ \hline \multirow{6}{*}{F4} & MDE & 0 & 0 & 0 & 0 & 30 \\  & distABC & 0 & 0 & 0 & 0 & 30 \\  & IGSA/PSO & 0 & 5.5511e\(-\)17 & 1.8504e\(-\)18 & 1.0135e\(-\)17 & 30 \\  & ADN-RSN-PSO & 2.2204e\(-\)16 & 0.0025 & 1.5597e\(-\)04 & 4.6084e\(-\)04 & 6 \\  & PSO-GWO & 0 & 0 & 0 & 0 & 30 \\  & ISSA & 0 & 0 & 0 & 0 & 30 \\ \hline \multirow{6}{*}{F5} & MDE & 0 & 0 & 0 & 0 & 30 \\  & distABC & 0 & 2.2128e\(-\)10 & 7.3769e\(-\)12 & 4.0400e\(-\)11 & 30 \\  & IGSA/PSO & 0 & 1.6653e\(-\)16 & 2.9606e\(-\)17 & 4.3081e\(-\)17 & 30 \\  & ADN-RSN-PSO & 4.3178e\(-\)12 & 0.5315 & 0.0194 & 0.0968 & 3 \\  & PSO-GWO & 0 & 0 & 0 & 0 & 30 \\  & ISSA & 0 & 0 & 0 & 0 & 30 \\ \hline \multirow{6}{*}{F6} & MDE & 0 & 0 & 0 & 0 & 30 \\  & distABC & 9.3892e\(-\)04 & 0.9114 & 0.1484 & 0.1747 & 0 \\  & IGSA/PSO & 2.3141e\(-\)19 & 6.8399e\(-\)17 & 1.4187e\(-\)17 & 1.5244e\(-\)17 & 30 \\  & ADN-RSN-PSO & 4.6791e\(-\)13 & 3.3521e\(-\)04 & 2.3684e\(-\)05 & 7.2434e\(-\)05 & 7 \\  & PSO-GWO & 4.7856e\(-\)07 & 9.8150e\(-\)04 & 1.4743e\(-\)04 & 2.1193e\(-\)04 & 0 \\  & ISSA & 0 & 1.5479e\(-\)12 & 5.1596e\(-\)14 & 5.1956e\(-\)14 & 30 \\ \hline \multirow{6}{*}{F7} & MDE & \(-\)1.8013 & \(-\)1.9996 & \(-\)1.8206 & 0.0587 & 30 \\  & distABC & \(-\)1.7576 & \(-\)1.1419 & \(-\)1.4170 & 0.1852 & 12 \\  & IGSA/PSO & \(-\)1.8381 & \(-\)1.9969 & \(-\)1.9554 & 0.0443 & 30 \\  & ADN-RSN-PSO & \(-\)1.7829 & \(-\)1.4155 & \(-\)1.7056 & 0.1385 & 25 \\  & PSO-GWO & \(-\)1.8013 & \(-\)1.2138 & \(-\)1.7697 & 0.1218 & 27 \\  & ISSA & \(-\)1.8013 & \(-\)1.8013 & \(-\)1.8013 & 7.5040e\(-\)16 & 30 \\ \hline \multirow{6}{*}{F8} & MDE & 0 & 0.0097 & 6.4773e\(-\)04 & 0.0025 & 28 \\  & distABC & 0.0014 & 0.0103 & 0.0085 & 0.0027 & 0 \\  & IGSA/PSO & 5.7927e\(-\)04 & 0.0097 & 0.0071 & 0.0034 & 0 \\  & ADN-RSN-PSO & 0.2325 & 0.4767 & 0.3792 & 0.0769 & 0 \\  & PSO-GWO & 0 & 0 & 0 & 0 & 30 \\  & ISSA & 0 & 0 & 0 & 0 & 30 \\ \hline \multirow{6}{*}{F9} & MDE & \(-\)4.6459 & \(-\)4.9833 & \(-\)4.7363 & 0.0866 & 30 \\  & distABC & \(-\)2.6563 & \(-\)1.7364 & \(-\)2.2089 & 0.2644 & 0 \\  & IGSA/PSO & \(-\)4.3109 & \(-\)2.5452 & \(-\)3.6519 & 0.4646 & 19 \\  & ADN-RSN-PSO & \(-\)3.4226 & \(-\)2.1793 & \(-\)2.6879 & 0.3210 & 0 \\  & PSO-GWO & \(-\)4.4527 & \(-\)2.7246 & \(-\)3.4183 & 0.4289 & 14 \\  & ISSA & \(-\)4.6877 & \(-\)4.6459 & \(-\)4.6856 & 0.0093 & 30 \\ \hline \multirow{6}{*}{F10} & MDE & \(-\)9.6552 & \(-\)9.1153 & \(-\)9.5328 & 0.1095 & 30 \\  & distABC & \(-\)3.5674 & \(-\)2.7672 & \(-\)3.1627 & 0.1969 & 0 \\  & IGSA/PSO & \(-\)8.6839 & \(-\)3.8323 & \(-\)5.9454 & 1.2127 & 12 \\  & ADN-RSN-PSO & \(-\)4.49021 & \(-\)3.3798 & \(-\)3.7563 & 0.3143 & 0 \\  & PSO-GWO & \(-\)6.7936 & \(-\)4.1522 & \(-\)5.4923 & 0.6488 & 0 \\  & ISSA & \(-\)9.6602 & \(-\)9.5403 & \(-\)9.6241 & 0.0411 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: _Cont._\(\chi_{r}^{5}=\frac{12}{nk(k+1)}\sum\limits_{j=1}^{k}R_{j}^{2}-3n(k+1)=\frac{12}{10 0\times 6\times(6+1)}(20.5^{2}+51.5^{2}+39^{2}+53^{2}+29^{2}+17^{2})-3\times 10 \times(6+1)=33.7857\); \(\alpha=0.05\), \(d_{f}=6-1=5\) at the 5% significant level and \(\chi_{0.05}^{5}=11.07<33.7857\) according to the Chi-square distribution table. Therefore, the six algorithms are considered to have significant differences at the 5% significance level. To further compare the performance of the six algorithms, assume that the convergence performance of ISSA is better than the other five algorithms.