# 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
Best, Worst, Mean and SD respectively represent the best fitness value, the worst fitness value, the mean fitness value and the standard deviation obtained by 30 independent executions. R represents the times of the algorithm converges to the appointed precision. The appointed precision is \(10^{-8}\) for the benchmark functions, whose optimal is 0. For the benchmark functions F1, F7, F9 and F10 whose optimal is not equal to 0, the appointed precision is \(-0.6\), \(-1.6\), \(-3.6\) and \(-8.6\) respectively. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Name** & **Method** & **Best** & **Worst** & **Mean** & **SD** & **R** \\ \hline \multirow{8}{*}{F1} & Modified differential evolution & \multirow{2}{*}{\(-1\)} & \(-1\) & \(-1\) & \(0\) & \(30\) \\  & (MDE) & & & & & \\  & Improved artificial bee colony & & & & & \\  & (distABC) & & & & & \\  & Improved gravitational search & & & & & \\  & algorithm (IGSA/PSO) & & & & & \\ F1 & All-dimension neighborhood & & & & & \\  & based particle swarm & & & & & \\  & optimization with randomly & & & & & \\  & selected neighbors & & & & & \\  & (ADN-RSN-PSO) & & & & & \\  & Improved grey wolf & & & & & \\  & optimization (PSO-GWO) & & & & & \\  & ISSA & \(-1\) & \(-1.0000\) & \(-1\) & \(4.1233\)e\(-17\) & \(30\) \\ \hline \multirow{8}{*}{F2} & MDE & \(1.8981\)e\(-124\) & \(6.0392\)e\(-111\) & \(2.0134\)e\(-112\) & \(1.1026\)e\(-111\) & \(30\) \\  & distABC & \(6.4478\)e\(-12\) & \(1.3143\)e\(-04\) & \(4.5038\)e\(-06\) & \(2.3974\)e\(-05\) & \(21\) \\  & ISSA/PSO & \(3.5151\)e\(-20\) & \(1.2328\)e\(-18\) & \(4.3235\)e\(-19\) & \(3.5081\)e\(-19\) & \(30\) \\  & ADN-RSN-PSO & \(1.5194\)e\(-14\) & \(9.3798\)e\(-06\) & \(3.8898\)e\(-07\) & \(1.7203\)e\(-06\) & \(20\) \\  & PSO-GWO & \(8.0797\)e\(-271\) & \(5.0693\)e\(-225\) & \(1.6898\)e\(-226\) & \(0\) & \(30\) \\  & ISSA & \(0\) & \(0\) & \(0\) & \(0\) & \(30\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The convergence results of F1–F10. It can be seen from Table 8 that MDE can converge to the optimal on F1, F3, F4, F5, F6, F7 and F8, but the performances of F7 and F8 are not stable enough; distABC only converges to the optimal stably on F4 and has a certain probability to converge to the optimal on F3 and F5; IGSA/PSO has no stable convergence performance on all the functions but still has a certain probability to converge to the optimal on F1, F3, F4 and F5; ADN-RSN-PSO has the worst performance without any function convergences to the optimal; PSO-GWO can converge stably to the optimal on F3, F4, F5 and F8, and there is also a certain probability for F7 to converge to the optimal. For ISSA, all the low dimensional functions can converge to the optimal and have the stable convergence performances on F2, F3, F4, F5 and F8. Aside from this, ISSA obtains the minimum mean on all functions except F6. In order to compare the differences of each method, we used the Friedman test to check the data in Table 8. The specific process is shown below, and the results can be obtained by Table 9: