# Path Planning of Obstacle-Crossing Robot Based on Golden Sine Grey Wolf Optimizer
## 5 Simulation Experiment and Analysis
### Algorithm Performance Test  
In order to verify the optimization performance of GSGWO shown in Algorithm 1, four test functions are selected to compare the GSGWO and the other three algorithms. The information of the functions is shown in Table 2. Before the experiment, the preset parameters of the function need to be set, and the detailed setting information is shown in Table 3. The other parameters of the GWO and TGWO are shown in ref. [8], and the other parameters of the IGWO are shown in ref. [32]. Each test function in the experiment runs 30 times. The average represents the optimization performance of the algorithm, and the standard deviation represents the stability of the test results; both are shown in Table 4. In order to clearly see the convergence process of the algorithm in the experiment, a certain convergence process curve in each group of experiments is selected to draw the graph shown in Figure 5.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function** & **Performance** & **GWO** & **TGWO** & **IGWO** & **GSGWO** \\ \hline \multirow{2}{*}{Sphere} & average & \(2.35\times 10^{-14}\) & \(2.41\times 10^{-25}\) & \(3.61\times 10^{-57}\) & \(6.18\times 10^{-81}\) \\  & standard deviation & \(2.01\times 10^{-14}\) & \(8.27\times 10^{-26}\) & \(3.36\times 10^{-57}\) & \(2.16\times 10^{-81}\) \\ \multirow{2}{*}{Schwefel} & average & \(9.80\times 10^{-7}\) & \(2.14\times 10^{-14}\) & \(1.06\times 10^{-29}\) & \(1.35\times 10^{-47}\) \\  & standard deviation & \(4.13\times 10^{-7}\) & \(6.52\times 10^{-15}\) & \(8.15\times 10^{-30}\) & \(7.21\times 10^{-48}\) \\ \multirow{2}{*}{Perm} & average & \(6.57\times 10^{0}\) & \(2.60\times 10^{-1}\) & \(3.54\times 10^{-3}\) & \(5.58\times 10^{-5}\) \\  & standard deviation & \(8.15\times 10^{1}\) & \(1.48\times 10^{-2}\) & \(4.98\times 10^{-4}\) & \(6.14\times 10^{-6}\) \\ \multirow{2}{*}{Ellipsoid} & average & \(2.17\times 10^{-25}\) & \(1.65\times 10^{-49}\) & \(0\) & \(0\) \\  & standard deviation & \(1.85\times 10^{-25}\) & \(7.56\times 10^{-50}\) & \(0\) & \(0\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Test results.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Function Name** & **Function Expressions** & **Region of Search** & **Solution** \\ \hline Sphere & \(f(x)=\sum_{i=1}^{D}x_{i}^{2}\) & \([100,-100]\) & \(0\) \\ Schwefel & \(f(x)=\sum_{i=1}^{D}|x_{i}|+\prod_{i=1}^{D}|x_{i}|\) & \([-10,10]\) & \(0\) \\ Prem & \(f(x)=\sum_{i=1}^{D}\left(\sum_{j=1}^{D}(j+\beta)\left(x_{i}^{j}-\frac{1}{f} \right)\right)^{2}\) & \([-30,30]\) & \(0\) \\ Ellipsoid & \(f(x)=\sum_{i=1}^{D}\sum_{j=1}^{D}x_{j}^{2}\) & \([-65.536,65.536]\) & \(0\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Test function information.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Numerical Value** \\ \hline \(t_{max}\) & \(100\) \\ \(num_{p}\) & \(50\) \\ \(func(x)\) & Function Expressions in Table 2 \\ \(I_{max}\) & Region of Search in Table 2 \\ \(I_{min}\) & \(30\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Algorithm parameters.  
It can be seen from the data in Table 4 that the average and standard deviation of the convergence results after 30 runs of the algorithm that the GSGWO was better than the GWO, TGWO and IGWO, and the performance of the algorithm was greatly improved. Through the comparison of the convergence curves in Figure 5, it can be seen that in the early global search, the convergence mode of the GSGWO is similar to that of the former three; it is faster than the GWO and TGWO but slower than the IGWO. In the later local search state, the convergence speed of the other algorithms gradually decreases, but due to the effect of the golden sine strategy, the GSGWO algorithm can still ensure a high convergence speed.