# 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
The experiment selects 21 benchmark functions from reference [15; 33; 34; 35], which include the low dimensional unimodal functions (F1, F2), the low dimensional multimodal functions (F3-F10), the high dimensional unimodal functions (F11-F17) and the high dimensional multimodal functions (F18-F21). The specific functions are shown in Table 1:

### The Influence of Parameter on ISSA

ISSA divides the whole evolutionary process into \(n\) substages and selects the proper strategy when a substage is completed. In order to obtain good performances as fast as possible, take \(n=0\), \(n=5\), \(n=10\), \(n=15\) and \(n=20\) and test the ISSA on low dimensional unimodal function F2, the low dimensional multimodal functions F6 and F10, the high dimensional unimodal functions F16 and F17, the high dimensional multimodal functions F18 and the total number of evolutions at 18,000, respectively. \(N_{\beta}\) is 3 which is the same as the reference [30]. The population size is 30, and every function runs 30 times independently in order to avoid the occasionality of the single execution. The results are as follows: the number before '\(\pm\)' is the mean and the number after '\(\pm\)' is the deviation of the obtained best fitness value. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Name** & **Function** & **D** & **Range** & **Optimal** \\ \hline F1 Eason & \(f(x)=-\cos(x_{1})\cos(x_{2})\exp(-(x_{1}-n)^{2}-(x_{2}-n)^{2})\) & 2 & [-10,100] & \(-1\) \\ F2 Matyas & \(f(x)=0.261+x_{1}^{2}-(x_{2}-0.48x_{1})^{2}\) & 2 & [-10,10] & 0 \\ F3 Bchahevsky1 & \(f(x)=x_{1}^{2}+2x_{2}^{2}-0.30x(37x_{1})-0.40x(44x_{2})+0.7\) & 2 & [-100,100] & 0 \\ F4 Bchahevsky2 & \(f(x)=x_{1}^{2}+2x_{2}^{2}-0.30x(37x_{1})(44x_{2})+0.3\) & 2 & [-100,100] & 0 \\ F5 [PERSON] & \(f(x)=x_{1}^{2}+2x_{2}^{2}-0.30x(37x_{1}+47x_{2})+0.3\) & 2 & [-100,100] & 0 \\ F6 [PERSON] & \(f(x)=(x_{1}+2x_{2}+7)^{2}+(2x_{1}+2x_{2}-5)^{2}\) & 2 & [-10,10] & 0 \\ F7 [PERSON] & \(f(x)=-\sum\limits_{i=1}^{N}{\sin(x_{i})(sin(x_{i}^{2}/n))^{20}}\) & 2 & [0,\pi] & \(-1.8013\) \\ F8 [PERSON] & \(f(x)=0.5+\frac{\sin^{2}(\sqrt{\frac{1}{2}+4})-0.5}{(1+0.001((x_{i}^{2}+4)))^{2}}\) & 2 & [-100,100] & 0 \\ F9 [PERSON] & \(f(x)=-\sum\limits_{i=1}^{D}{\sin(x_{i})(sin(x_{i}^{2}/n))^{20}}\) & 5 & [0,\pi] & \(-4.6877\) \\ F10 [PERSON] & \(f(x)=\sum\limits_{i=1}^{D}{\sin(x_{i})(sin(x_{i}^{2}/n))^{20}}\) & 10 & [0,\pi] & \(-9.6602\) \\ F11 [PERSON] & \(f(x)=\sum\limits_{i=1}^{D}{x_{i}^{2}+(\sum\limits_{i=1}^{D}{0.5\sin x_{i}})^{2} }+(\sum\limits_{i=1}^{D}{0.5\sin x_{i}})^{4}\) & 30/50/100 & [-5,10] & 0 \\ F12 Sphere & \(f(x)=\sum\limits_{i=1}^{D}{x_{i}^{2}}\) & 30/50/100 & [-100,100] & 0 \\ F13 SumSquares & \(f(x)=\sum\limits_{i=1}^{D}{\frac{1}{2}\sum\limits_{i=1}^{D}{x_{i}^{2}}}\) & 30/50/100 & [-10,10] & 0 \\ F14 Schwefel 1.2 & \(f(x)=\sum\limits_{i=1}^{D}{(\sum\limits_{i=1}^{D}{x_{i}})^{2}}\) & 30/50/100 & [-100,100] & 0 \\ F15 Schwefel 2.21 & \(f(x)=\sum\limits_{i=1}^{D}{\frac{1}{2}\sum\limits_{i=1}^{D}{\frac{1}{2}\sum \limits_{i=1}^{D}{\frac{1}{2}\sum\limits_{i=1}^{D}{\frac{1}{2}\sum\limits_{i=1}^{D}{ \frac{1}{2}\sum\limits_{i=1}^{D}{\frac{1}{2}\sum\limits_{i=1}^{D}{\frac{1}{2} \sum\limits_{i=1}^{D}{\frac{1}{2}\sum\limits_{i=1}^{According to Table 2, there is almost no impact of different \(n\) on low dimensional unimodal function; for low dimensional multimodal functions, the results of \(n=0\) are much worse than that of \(n\
eq 0\). According to 3.4, ISSA starts with the jumping search method and ISSA is same as the jumping search method in total when \(n=0\). ISSA is the combination of two strategies and the searching strategy may turn to the progressive search method when \(n\
eq 0\). The results of F2 and F6 mean that different strategies are fit for different problems and the linear regression selection strategy is effective. Aside from this, the results of F2 and F6 are better with a higher selection frequency; for high dimensional unimodal functions, the experimental results are not much different.