# Improvement of Dung Beetle Optimization Algorithm Application to Robot Path Planning
## 4 Results of the Experiment and Discussion
### Comparison with Other Algorithms
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Function** & **Index** & **SSA** & **TSDBO** & **GODBO** & **MSADBO** & **MSDBO** & **IWOA** & **SAGWO** & **TSDBO** \\ \hline \multirow{3}{*}{F1} & Best & \(1.34\times 10^{-8}\) & \(1.43\times 10^{-180}\) & 0 & 0 & \(2.89\times 10^{-201}\) & \(5.92\times 10^{-279}\) & \(2.35\times 10^{-225}\) & **0** \\  & Mean & \(2.24\times 10^{-8}\) & \(3.56\times 10^{-114}\) & \(2.34\times 10^{-164}\) & 0 & \(3.02\times 10^{-165}\) & \(1.85\times 10^{-111}\) & \(1.34\times 10^{-214}\) & **0** \\  & Std & \(6.79\times 10^{-9}\) & \(1.95\times 10^{-113}\) & 0 & 0 & 0 & \(1.01\times 10^{-110}\) & 0 & **0** \\ \hline \multirow{3}{*}{F2} & Best & \(2.60\times 10^{-2}\) & \(1.19\times 10^{-81}\) & \(8.42\times 10^{-28}\) & \(2.71\times 10^{-206}\) & \(2.64\times 10^{-232}\) & \(1.32\times 10^{-84}\) & \(2.01\times 10^{-128}\) & **6.30 \(\times\) 10\({}^{-279}\)** \\  & Mean & \(8.12\times 10^{-1}\) & \(4.47\times 10^{-64}\) & \(5.43\times 10^{-13}\) & \(2.97\times 10^{-171}\) & \(2.85\times 10^{-186}\) & \(5.95\times 10^{-61}\) & \(1.04\times 10^{-107}\) & **1.40 \(\times\) 10\({}^{-146}\)** \\  & Std & \(7.24\times 10^{-1}\) & \(2.43\times 10^{-46}\) & \(1.71\times 10^{-12}\) & 0 & 0 & \(3.21\times 10^{-60}\) & \(5.43\times 10^{-107}\) & **0** \\ \hline \multirow{3}{*}{F3} & Best & \(9.76\times 10^{-1}\) & \(2.78\times 10^{-6}\) & \(1.13\times 10^{-21}\) & \(2.45\times 10^{-173}\) & \(2.63\times 10^{-162}\) & \(3.44\times 10^{-148}\) & \(1.75\times 10^{-28}\) & **0** \\  & Mean & \(5.47\times 10^{-2}\) & \(14.88\times 10^{-14}\) & \(5.84\times 10^{-11}\) & \(8.81\times 10^{-111}\) & \(7.89\times 10^{-122}\) & \(5.00\times 10^{-27}\) & \(5.21\times 10^{-108}\) & **0** \\  & Std & \(4.56\times 10^{2}\) & \(7.28\times 10^{-46}\) & \(3.69\times 10^{-10}\) & \(4.83\times 10^{-10}\) & \(5.62\times 10^{-102}\) & \(3.12\times 10^{-86}\) & 0 & **0** \\ \hline \multirow{3}{*}{F4} & Best & \(2.60\times 10^{-2}\) & \(4.19\times 10^{-2}\) & \(5.85\times 10^{-9}\) & \(9.06\times 10^{-29}\) & \(8.54\times 10^{-26}\) & \(7.02\times 10^{-25}\) & \(2.98\times 10^{-15}\) & **2.30 \(\times\) 10\({}^{-286}\)** \\  & Mean & \(6.59\times 10^{-2}\) & \(3.74\times 10^{-14}\) & \(2.31\times 10^{-10}\) & \(3.24\times 10^{-181}\) & \(6.78\times 10^{-201}\) & \(6.14\times 10^{-28}\) & \(2.12\times 10^{-107}\) & **9.50 \(\times\) 10\({}^{-286}\)** \\  & Std & \(2.51\times 10^{-1}\) & \(1.62\times 10^{-13}\) & \(1.23\times 10^{-9}\) & 0 & \(9.97\times 10^{-145}\) & \(3.36\times 10^{-6}\) & \(1.19\times 10^{-106}\) & **0** \\ \hline \multirow{3}{*}{F5} & Best & \(2.42\times 10^{2}\) & \(2.50\times 10^{1}\) & \(2.50\times 10^{1}\) & \(2.48\times 10^{10}\) & \(2.46\times 10^{1}\) & \(2.44\times 10^{1}\) & \(3.94\times 10^{1}\) & **6.99 \(\times\) 10\({}^{-2}\)** \\  & Mean & \(1.44\times 10^{2}\) & \(2.58\times 10^{1}\) & \(2.56\times 10^{1}\) & \(2.55\times 10^{1}\) & \(2.57\times 10^{1}\) & \(2.50\times 10^{1}\) & \(2.35\times 10^{10}\) & \(2.34\times 10^{1}\) \\  & St1. Comparison between TSDBO and SSA: SSA is highly adaptive and can find optimal solutions on 12 test functions. However, the optimal solution found by SSA has a big gap compared with TSDBO, and the average value is much larger than TSDBO. And the standard deviation of SSA is larger than that of TSDBO, which is an indicator to reflect the stability of the algorithm, and a too-large standard deviation indicates that the deviation between the data is relatively large. The combined performance of the two algorithms indicates that TSDBO also has a good adaptive performance. 2. Comparison between TSDBO and IDBO: IDBO finds the optimal value in the F7 and F9 functions, but analyzing the data shows that IDBO improves the performance of the algorithm, but it is easy to fall into the local optimum, and it cannot be compared with TSDBO. 3. Comparison between TSDBO and GODBO: The performance of GODBO on the 12 test functions is average, even negative optimization occurs on some functions, and there is no competitive advantage compared with TSDBO. 4.