# 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} \hline \hline \multirow{2}{*}{**Name**} & \multicolumn{4}{c}{**Method**} \\ \cline{2-5}  & **SSA** & \begin{tabular}{c} **Jumping Search** \\ **Method** \\ \end{tabular} & \
\begin{tabular}{c} **Progressive** \\ **Search Method** \\ \end{tabular} &
\begin{tabular}{c} **ISSA** \\ **(1)** \\ \end{tabular} \\ \hline F1 & \(-1\pm 0\) (=) & \(-1\pm 1.090\)e\(-16\) & \(-1\pm 0\) (=) & \(-1\pm 3.9171\)e\(-16\) \\ F2 & \(4.4212\)e\(-21\pm\) & \(0\pm 0\) (=) & \(9.7986\)e\(-149\pm\) & \(0\pm 0\) \\ F3 & \(7.4015\)e\(-18\pm\) & \(0\pm 0\) (=) & \(0\pm 0\) (=) & \(0\pm 0\) \\  & \(4.0540\)e\(-17\) (\(-\)) & \(0\pm 0\) (=) & \(0\pm 0\) (=) & \(0\pm 0\) \\ F4 & \(1.0191\)e\(-20\pm\) & \(0\pm 0\) (=) & \(0\pm 0\) (=) & \(0\pm 0\) \\  & \(2.9625\)e\(-20\) (\(-\)) & \(0\pm 0\) (=) & \(0\pm 0\) (=) & \(0\pm 0\) \\ F5 & \(1.2019\)e\(-20\pm\) & \(0\pm 0\) (=) & \(0\pm 0\) (=) & \(0\pm 0\) \\  & \(4.4285\)e\(-20\) (\(-\)) & \(0\pm 0\) (=) & \(0\pm 0\) (=) & \(0\pm 0\) \\  & \(1.4402\)e\(-18\pm\) & \(0.0202\)e\(0.0238\) (\(-\)) & \(2.6295\)e\(-33\pm\) & \(4.9331\)e\(-12\pm\) \\  & \(3.0624\)e\(-18\) (\(+\)) & \(0.0202\)e\(0.0238\) (\(-\)) & \(1.4403\)e\(-32\) (\(+\)) & \(1.6068\)e\(-11\) \\  & \(-1.8468\pm 0.0838\) & \(-1.7911\pm 0.0116\) & \(-1.8013\pm\) & \(-1.8013\pm\) \\  & \((-)\) & \((-)\) & \(6.8344\)e\(-16\) (=) & \(8.5739\)e\(-16\) \\ F8 & \(0\pm 0\) (=) & \(0\pm 0\) (=) & \(0\pm 0\) (=) & \(0\pm 0\) \\ P9 & \(-4.6459\pm\) & \(-4.4543\pm 0.1818\) & \(-4.6808\pm 0.1336\) & \(-4.6617\pm 0.0304\) \\  & \(2.7201\)e\(-15\) (\(-\)) & \((-)\) & \((+)\) & \\ F10 & \(-9.5333\pm 0.2598\) & \(-8.2037\pm 0.3744\) & \(-9.6602\pm 0\) (\(+\)) & \(-9.5882\pm 0.0891\) \\  & \((-)\) & \((-)\) & \(2.1318\)e\(-16\pm\) & \(0\pm 0\) \\ F11 & \(1.1640\)e\(-12\) (\(-\)) & \(0\pm 0\) (=) & \(1.1676\)e\(-15\) (\(-\)) & \(0\pm 0\) \\  & \(8.0478\)e\(-13\pm\) & \(0\pm 0\) (=) & \(1.9301\)e\(-15\pm\) & \(0\pm 0\) \\  & \(4.3612\)e\(-12\) (\(-\)) & \(1.0572\)e\(-14\) (\(-\)) & \(0\pm 0\) (=) & \(3.5232\)e\(-11\pm\) \\ F13 & \(2.0435\)e\(-10\pm\) & \(0\pm 0\) (=) & \(1.9297\)e\(-10\) (\(-\)) & \(0\pm 0\) \\  & \(1.0129\)e\(-10\) (\(-\)) & \(0\pm 0\) (=) & \(1.9297\)e\(-10\) (\(-\)) & \(0\pm 0\) \\ F14 & \(0.5472\pm 2.7161\) (\(-\)) & \(0\pm 0\) (=) & \(0.0865\pm 0.4149\) (\(-\)) & \(0\pm 0\) \\  & \(7.2194\)e\(-08\) (\(+\)) & \(0\pm 0\) (=) & \(0.0241\pm 0.1321\) (\(-\)) & \(0\pm 0\) \\  & \(6.4247\)e\(-08\) (\(-\)) & \(0\pm 0\) (=) & \(1.4322\)e\(-11\pm\) & \(0\pm 0\) \\  & \(1.4322\)e\(-11\pm\) & \(0\pm 0\) (=) & \(7.8443\)e\(-11\) (\(-\)) & \(0\pm 0\) \\  & \(9.7812\)e\(+03\pm\) & \(0\pm 0\) (=) & \(2.3545\)e\(-15\pm\) & \(0\pm 0\) \\  & \(3.5168\)e\(+04\) (\(-\)) & \(1.2896\)e\(-14\) (\(-\)) & \(0\pm 0\) \\  & \(1.9614\)e\(-16\pm\) & \(0\pm 0\) (=) & \(1.9614\)e\(-16\pm\) \\ F18 & \(0.6323\pm 0.3594\) (\(-\)) & \(0\pm 0\) (+) & \(0.0129\pm 0.0650\) (\(-\)) & \(3.6843\)e\(-16\) \\ F19 & \(0.1099\pm 0.0548\) (\(-\)) & \(0\pm 0\) (=) & \(0.0233\pm 0.0773\) (\(-\)) & \(0\pm 0\) \\  & \(9.1222\)e\(-13\pm\) & \(0\pm 0\) (=) & \(9.1222\)e\(-13\pm\) & \(0\pm 0\) \\  & \(4.9964\)e\(-12\) (\(-\)) & \(0\pm 0\) (=) & \(7.3093\)e\(-05\pm\) & \(0\pm 0\) \\ F21 & \(8.6605\pm 38.6332\) (\(-\)) & \(0\pm 0\) (=) & \(2.2255\)e\(-05\) (\(-\)) & \(0\pm 0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The comparison of the convergence precision. according to the Chi-square distribution table. Therefore, the four methods are considered to have significant differences at the 5% significance level. To further compare the performance of the four methods, assuming that the convergence performance of ISSA is better than the other three methods, a Holm test was carried out and the results are shown in Table 7:

It can be seen from Table 7 that \(P_{1}<\alpha(k-1)\), \(P_{2}>\alpha(k-2)\), \(P_{3}>\alpha(k-3)\). The original hypothesis is rejected at the 5% significance level. Therefore, compared with SSA, ISSA has significantly better performance.