# 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
However, there are obvious differences on a high dimensional multimodal function between \(n=5\) and \(n=0\), \(n=10\), \(15\) and \(20\). In order to guarantee the convergence performance and the operating efficiency of ISSA at the same time, take \(n=10\) for the remaining experiments in this paper. ### The Efficiency of the Proposed Methods

The proposed ISSA selects the jumping search method or the progressive method according to the linear regression selection strategy automatically. In order to verify the efficiency of the proposed methods, compare the standard SSA, the jumping search method, the progressive method and the ISSA through the 21 benchmark functions in terms of convergence speed, population diversity and convergence precision. #### 4.3.1 Comparison of Convergence Speed on Four Methods

For each method mentioned above, the total number of evolution is 30,000 and \(N_{f_{8}}\) is 3, the population size is 30, which is aimed at comparing the methods fairly effectively. Every method runs 30 times independently in order to avoid the randomness of the single execution. Figure 4a-i shows the convergence curves of SSA, the jumping search method, the progressive search method and ISSA on the low dimensional unimodal functions F2, the low dimensional multimodal functions F3 and F5, the high dimensional unimodal functions F11, F13, F14 and F16 and the high dimensional multimodal functions F18 and F21 when the evaluation time is 30,000. The blue, green, yellow and red curves refer to SSA, the jumping search method, the progressive method and ISSA, respectively. The abscissa of each figure is the iteration and the ordinate of each figure is the best value found so far. The title of each figure is given as the name F2, F3, F5, F11, F13, F14 and F16. For the low dimensional functions, the jumping search method, the progressive method and ISSA all have obvious improvements on convergence speed compared with SSA. The convergence speed from high to low is the jumping search method, ISSA and the progressive search method. In relation to the high dimensional functions, the convergence speed of the jumping search method and ISSA is still much better than SSA and the jumping search method performs better, but the improvement of the progressive search method is not as obvious as that on the low dimensional functions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**F**} & \multicolumn{5}{c}{\(n\)} \\ \cline{2-6}  & **0** & **5** & **10** & **15** & **20** \\ \hline F2 & \(0\pm 0\) & \(0\pm 0\) & \(0\pm 0\) & \(0\pm 0\) & \(0\pm 0\) \\ F6 & \(6.2502\)e\(-04\pm\) & \(1.7129\)e\(-10\pm\) & \(3.5323\)e\(-08\pm\) & \(7.7188\)e\(-07\pm\) & \(7.5656\)e\(-07\pm\) \\  & \(1.9021\)e\(-04\) & \(9.2634\)e\(-11\) & \(1.2626\)e\(-09\) & \(2.8698\)e\(-08\) & \(1.9151\)e\(-08\) \\ F10 & \(-7.6632\pm 0.7985\) & \(-9.4261\pm 0.0680\) & \(-9.2260\pm 0.7780\) & \(-8.1919\pm 1.3054\) & \(-8.0299\pm 1.1781\) \\ F16 & \(6.2909\)e\(-163\pm 0\) & \(7.4432\)e\(-162\pm 0\) & \(1.0302\)e\(-164\pm 0\) & \(2.0455\)e\(-165\pm 0\) & \(7.1391\)e\(-164\pm 0\) \\ F17 & \(0\pm 0\) & \(0\pm 0\) & \(0\pm 0\) & \(0\pm 0\) & \(0\pm 0\) \\ F18 & \(1.8504\)e\(-15\pm\) & \(4.4095\)e\(-08\pm\) & \(2.1945\)e\(-15\pm\) & \(2.9976\)e\(-15\pm\) & \(3.1826\)e\(-15\pm\) \\  & \(1.0135\)e\(-15\) & \(1.9301\)e\(-07\) & \(8.2481\)e\(-16\) & \(6.5204\)e\(-15\) & \(7.1639\)e\(-15\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The experimental results of ISSA with different \(n\). #### 4.3.2 Comparison of Population Diversity on Four Methods

In order to compare the population diversity of the four methods intuitively, all the population sizes are 30. Table 3 is the comparison of the individuals' distribution on the 2-dimensional unimodal function F2 and the 2-dimensional multimodal function F5 when the convergence accuracy is up to \(10^{-6}\), \(10^{-8}\) and \(10^{-10}\).