# Improvement of Dung Beetle Optimization Algorithm Application to Robot Path Planning
## 4 Results of the Experiment and Discussion
### Analysis of the Effectiveness of Improvement Strategies  
TSDBO includes three improvements to DBO, and three different algorithms are obtained by fusing DBO with these three kinds of improvements, respectively.  
1. Adding the improved Tent chaotic mapping to initialize the population in DBO to obtain DBO1;
2. Introducing a dynamic spiral search strategy in DBO to obtain DBO2;
3. DBO is used with an adaptive t-distribution perturbation technique to produce DBO3.  
The four algorithms of TSDBO with DBO, DBO1, DBO2, and DBO3 are experimented with the 12 test functions in Table 1. The optimization outcomes for 30 separate iterations of each algorithm, including the three metrics, are displayed in Table 2. Best indicates the algorithm's correctness, while Mean and Std indicate its stability.  
\begin{table}
\begin{tabular}{l l l l} \hline \multicolumn{1}{c}{**Function Name**} & \multicolumn{1}{c}{**D**} & \multicolumn{1}{c}{**S**} & \multicolumn{1}{c}{\(\boldsymbol{f_{\min}}\)} \\ \hline \(f_{1}(x)=\sum_{i=1}^{n}x_{i}^{2}\) & 30 & \([-100,100]\) & 0 \\ \(f_{2}(x)=\sum_{i=1}^{n}|\,x_{i}|+\prod_{i=1}^{n}|\,x_{i}|\) & 30 & \([-10,10]\) & 0 \\ \(f_{3}(x)=\sum_{i=1}^{n}\biggl{(}\sum_{j=1}^{j}x_{j}\biggr{)}^{2}\) & 30 & \([-100,100]\) & 0 \\ \(f_{4}(x)=\max_{i}\{|\,x_{i}|,1\leq i\leq n\}\) & 30 & \([-100,100]\) & 0 \\ \(f_{5}(x)=\sum_{i=1}^{n-1}\biggl{[}100\bigl{(}x_{i+1}-x_{i}^{2}\bigr{)}^{2}+(x _{i}-1)^{2}\biggr{]}\) & 30 & \([-30,30]\) & 0 \\ \(f_{6}(x)=\sum_{i=1}^{n}-x_{i}\sin\left(\sqrt{|\,x_{i}|}\right)\) & 30 & \([-500,500]\) & \(-12,569.5\) \\ \(f_{7}(x)=\sum_{i=1}^{n}\bigl{[}x_{i}^{2}-10\cos(2\pi x_{i})+10\bigr{]}\) & 30 & \([-5.12,5.12]\) & 0 \\ \(f_{8}(x)=-20\exp\left(-0.2\sqrt{\frac{1}{n}\sum_{i=1}^{n}x_{i}^{2}}\right)-\) & 30 & \([-32,32]\) & 0 \\ \(\exp\left(\frac{1}{n}\sum_{i=1}^{n}\cos(2\pi x_{i})\right)+20+e\) & & & \\ \(f_{9}(x)=\frac{1}{4000}\sum_{i=1}^{n}x_{i}^{2}-\prod_{i=1}^{n}\cos\left(\frac{ x_{i}}{\sqrt{i}}\right)+1\) & 30 & \([-600,600]\) & 0 \\ \(f_{10}(x)=\left[\frac{1}{500}+\sum_{j=1}^{25}\frac{1}{j+\sum_{i=1}^{2}\left(x _{i}-a_{ij}\right)^{6}}\right]^{-1}\) & 2 & \([-65.536,65.536]\) & 1 \\ \(f_{11}(x)=\sum_{i=1}^{11}\biggl{[}a_{i}-\frac{x_{1}\bigl{(}b_{i}^{2}+b_{i}x_{ 2}\bigr{)}}{b_{i}^{2}+b_{1}x_{3}+x_{4}}\biggr{]}^{2}\) & 4 & \([-5,5]\) & 0.0003075 \\ \(f_{12}(x)=-\sum_{i=1}^{5}\left[(x-a_{i})(x-a_{i})^{T}+c_{i}\right]^{-1}\) & 4 & \([0,10]\) & \(-10.1532\) \\ \hline \end{tabular}
\end{table}
Table 1: Twelve benchmark functions in CEC2005.  
We can see from Table 2 and Figure 5 that DBO1, DBO2, and DBO3 have improved their optimization searching accuracy on most test functions compared to DBO, while TSDBO has improved on 11 test functions compared to DBO and 1 is comparable to DBO. Compared with DBO, DBO1, DBO2, and DBO3 have all three evaluation metrics improved to a large extent, where DBO2 and DBO3 are better than DBO1. This is due to the fact that DBO1 improves the quality of distribution of the initial populations across the search space by using only the improved Tent chaotic mapping, which raises the algorithm's solution accuracy. The algorithm's global optimal search  
the significant improvement in the optimal convergence value and average convergence accuracy on the 12 test functions when compared to DBO and DBO2. In contrast to DBO, DBO3 finds theoretically optimal values in the F1 and F3 functions. This is because the algorithm can now leap out of the local optimum when it enters it thanks to the introduction of the third approach, thereby improving algorithm performance. In comparison to DBO, TSDBO has substantially superior evaluation metrics, which integrates the three improved strategies, are improved compared with DBO, and the average convergence accuracy reaches the best value in F1, F3, F7, and F9 without negative optimization, which indicates that the integration of the three strategies is effective.