# Somersault Foraging and Elite Opposition-Based Learning Dung Beetle Optimization Algorithm
## 4 Experiments and Result Analysis
### Comparison with Classical Intelligent Optimization Algorithms  
To thoroughly assess the capability of the SFEDBO algorithm, this paper compares it to five classical optimization algorithms, including DBO [20], GWO [18], PSO [14], WOA [15], SCA [36], and RSO [17]. The parameters of the algorithms are all sourced from references [17; 20]. The outcomes are presented in Table 3.  
High-dimensional unimodal functions (F1-F7), characterized by having a single global optimal solution, are primarily used to evaluate the local search capabilities of algorithms. On these functions, the DBO algorithm shows better performance than other classic algorithms, ranking second on F1-F7. However, the capability of the SFEDBO algorithm is further enhanced based on the DBO algorithm, significantly outperforming other algorithms on F1-F7. This fully demonstrates the necessity of the adaptive strategy and tumbling foraging strategy. As the adaptive strategy dynamically shifts the focus of the population towards local exploration during later iterations, the algorithm's local search ability is significantly strengthened. Furthermore, the incorporation of the somersault foraging strategy augments the algorithm's local exploration capability. An analysis of the standard deviations of each algorithm on F1-F7 indicates that the SFEDBO algorithm attains the lowest standard deviation across all seven functions, illustrating that the superiority of the SFEDBO algorithm is not attributed to the randomness of the optimization process. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Function Number** & **DBO (s)** & **SFEDBO (s)** & **Difference (s)** & **Rate of Increase** \\ \hline F1 & 0.16524 & 0.17246 & 0.00721 & 4.37\% \\ F2 & 0.16784 & 0.18427 & 0.01642 & 9.79\% \\ F3 & 0.42334 & 0.43019 & 0.00686 & 1.62\% \\ F4 & 0.16138 & 0.16375 & 0.00237 & 1.47\% \\ F5 & 0.20266 & 0.20652 & 0.00386 & 1.91\% \\ F6 & 0.16431 & 0.16687 & 0.00257 & 1.54\% \\ F7 & 0.26792 & 0.27602 & 0.00811 & 2.94\% \\ F8 & 0.20861 & 0.21059 & 0.00198 & 0.95\% \\ F9 & 0.15905 & 0.17751 & 0.01846 & 11.61\% \\ F10 & 0.15768 & 0.18041 & 0.02273 & 14.41\% \\ F11 & 0.18596 & 0.21256 & 0.02659 & 14.30\% \\ F12 & 0.48543 & 0.48229 & \(-\)0.00314 & \(-\)0.65\% \\ F13 & 0.49889 & 0.50524 & 0.00634 & 1.27\% \\ F14 & 0.81044 & 0.84861 & 0.03817 & 4.71\% \\ F15 & 0.15712 & 0.15637 & \(-\)0.00074 & \(-\)0.47\% \\ F16 & 0.13202 & 0.13920 & 0.00718 & 5.44\% \\ F17 & 0.13973 & 0.14397 & 0.00424 & 3.04\% \\ F18 & 0.12605 & 0.14802 & 0.02197 & 17.43\% \\ F19 & 0.14560 & 0.16668 & 0.02108 & 14.48\% \\ F20 & 0.14759 & 0.15653 & 0.00894 & 6.05\% \\ F21 & 0.15494 & 0.17838 & 0.02344 & 15.13\% \\ F22 & 0.18023 & 0.18286 & 0.00263 & 1.46\% \\ F23 & 0.19007 & 0.20345 & 0.01338 & 7.04\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The computational time results of the SFEDBO algorithm and the DBO algorithm on the 23 benchmark test functions. High-dimensional multimodal functions (F8-F13) possess numerous local optimum solutions and a single global optimum solution, posing a challenge to algorithms' global search capability and their proficiency in escaping local optima. The SFEDBO algorithm still has a significant advantage on F8-F13, ranking first in optimization results on such functions. This is credited to the introduction of the OBL strategy and somersault foraging strategy. The OBL strategy generates more diverse populations, effectively enhancing the global exploration capability of the algorithm. And when the population reaches a local optimum, the somersault foraging strategy is applied to the optimal individual, enabling the population to escape the local optimum, greatly improving the algorithm's ability to escape local optima. Analysis of the standard deviations on F8-F13 shows that, except for F8 where the SFEDBO algorithm's standard deviation is inferior to GWO and PSO, the SFEDBO algorithm demonstrates a performance that surpasses the other algorithms by more than one order of magnitude on the remaining functions.