## 2 Chimp Optimization Algorithm
### Mathematical Model: Chimp Optimization
In order to further compare the convergence of various algorithms in the optimization process, we drew the optimized iteration curves of the 13 algorithm processes. The convergence curves of functions F1-F13 are shown in Figure 4, which shows that SDChOA performs well in most of the following aspects. ### SDChOA Convergence Analysis

To reflect the dynamic convergence characteristics of SDChOA, as shown in Figure 4, both ChOA and IChOA were used to solve the single-peaked function when F1-F4. Its search accuracy is at least 100 orders of magnitude and 30 orders of magnitude higher than the standard ChOA, respectively. This is attributed to the adaptive location update and dynamic weighting strategy that produce a more optimal solution to guide the population to find the global optimal solution stably, improving the convergence accuracy of the algorithm. At the same time, the \"attacker\" individuals lead the population to a larger prey search range to find the optimal solution, which helps the algorithm to jump out of the local optimum while maintaining the population diversity, and the nonlinear adjustment of the convergence factor based on the logarithmic function balances the local and global exploration capabilities. Specifically, SDChOA outperforms other comparative algorithms in search performance at the beginning of the iterations and exploration performance at the end of the iterations, with higher solution accuracy and faster convergence speed under the same number of iterations. This indicates that SDChOA can fully guarantee exploration ability without losing population diversity and stability of prey search while ensuring exploration ability. ### Comparison of SDChOA, Swarm Intelligence Algorithms, and Improved Algorithms

To further verify its effectiveness, SDChOA was compared with PSO, SSA, GWO [16; 24; 25; 26], ChOA, and IChOA, citing experimental data from the literature and reproducing experiments from the literature [23; 27]. To reflect the fairness of the comparison, the same experimental parameter settings as in the literature (population size of 30, maximum iteration number of 1000) are used. The optimization results of each algorithm for different types of benchmark test functions are listed, where the single-peak and multi-peak function search dimensions are set to 30/50/100, respectively. Each algorithm is run 30 times independently, and its optimal value, mean and standard deviation are recorded. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Function** & **Algorithm** & \multicolumn{2}{c}{**30 dim**} & \multicolumn{2}{c}{**50 dim**} & \multicolumn{2}{c}{**50 dim**} & \multicolumn{2}{c}{**100 dim**} \\ \hline  & SSA & 9.1421 \(\times\) 10\({}^{-4}\) & -3.005 \(\



Figure 4: The convergence curves of SDChOA with other comparative algorithms. Also, in all cases, SDChOA outperforms the original ChOA and its improved versions, including the newly proposed IchOA, which indicates that the proposed improvements can improve the performance of ChOA and make it competitive with other comparative algorithms. To further compare the convergence of various algorithms in the optimization process, we plotted the iteration curves of the optimization process for 13 algorithms. The convergence curves of functions F1-F13 are shown in Figure 4, which indicates that SDChOA performs well for most of the functions. ChOA focuses on global search in the early and middle stages and converges slowly [28]. With time, SDChOA converges quickly and eventually converges to good results. Compared with the original ChOA, SDChOA accelerates the convergence speed and proves that the proposed nonlinear control parameter strategy is effective [29; 30; 31]. In summary, the proposed improvement strategy has an obvious optimization effect on the standard ChOA, and the SDChOA that incorporates the three strategies shows certain advantages in both the accuracy and stability of the optimization search.