# An Enhanced Crowned Porcupine Optimization Algorithm Based on Multiple Improvement Strategies
## 4 Simulation Experiments
### Test Results
#### 4.2.2 Analysis of Multimodal Function (F8-F13) Test Results  
The test results on multimodal functions F8-F13 demonstrate that ICPO performs excellently on most of these functions, further validating its effectiveness in handling complex optimization problems. On function F8, ICPO (\(-1.23\)\(\times\) 10\({}^{4}\)) slightly outperforms CPO (\(-1.26\)\(\times\) 10\({}^{4}\)) and WOA (\(-1.26\)\(\times\) 10\({}^{4}\)) and significantly exceeds the performance of other algorithms. For functions F9 and F11, ICPO, along with CPO, WOA, and DBO, achieved the ideal optimal value of 0.00, while PSO fell slightly behind. On function F10, ICPO, CPO, and DBO all reached the optimal value of 4.44 \(\times\) 10\({}^{-16}\), slightly better than WOA (3.98 \(\times\) 10\({}^{-15}\)) and significantly better than PSO (5.68 \(\times\) 10\({}^{-4}\)). For functions F12 and F13, ICPO showed consistent performance with CPO (1.57 \(\times\) 10\({}^{-32}\) and 1.35 \(\times\) 10\({}^{-32}\), respectively), outperforming the other algorithms. In terms of computational efficiency, ICPO's runtime was comparable to the other algorithms on most functions and was even slightly faster in certain cases (e.g., F8, F9). This indicates that the improvements in ICPO did not introduce a significant computational burden and struck a good balance between efficiency and performance.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & \multirow{2}{*}{**Function**} & \multicolumn{6}{c}{**Comparative Algorithms**} \\ \cline{3-6}  & & **PSO** & **DBO** & **WOA** & **CPO** & **ICPO** \\ \hline \multirow{3}{*}{F18} & Best & 3.00 & 3.00 & 3.00 & 3.00 & 3.00 \\  & Median & 3.00 & 3.00 & 3.00 & 3.00 & 3.00 \\  & Time(s) & \(1.02\times 10^{-1}\) & \(4.33\times 10^{-1}\) & \(1.86\times 10^{-1}\) & \(2.23\times 10^{-1}\) & \(2.35\times 10^{-1}\) \\  & Best & \(-3.86\) & \(-3.86\) & \(-3.86\) & \(-3.86\) & \(-3.86\) \\ F19 & Median & \(-3.86\) & \(-3.86\) & \(-3.86\) & \(-3.86\) & \(-3.86\) \\  & Time(s) & \(1.81\times 10^{-1}\) & \(5.39\times 10^{-1}\) & \(2.64\times 10^{-1}\) & \(3.08\times 10^{-1}\) & \(3.23\times 10^{-1}\) \\  & Best & \(-3.32\) & \(-3.32\) & \(-3.32\) & \(-3.32\) & \(-3.32\) \\ F20 & Median & \(-3.32\) & \(-3.26\) & \(-3.20\) & \(-3.32\) & \(-3.32\) \\  & Time(s) & \(1.97\times 10^{-1}\) & \(5.41\times 10^{-1}\) & \(2.68\times 10^{-1}\) & \(3.13\times 10^{-1}\) & \(3.20\) \\  & Best & \(-1.02\times 10\) & \(-1.02\times 10\) & \(-1.02\times 10\) & \(-1.02\times 10\) & \(-1.02\times 10\) \\ F21 & Median & \(-1.02\times 10\) & \(-1.00\times 10\) & \(-1.02\times 10\) & \(-1.02\times 10\) & \(-1.02\times 10\) \\  & Time(s) & \(2.27\times 10^{-1}\) & \(5.82\times 10^{-1}\) & \(3.03\times 10^{-1}\) & \(3.48\times 10^{-1}\) & \(3.51\times 10^{-1}\) \\  & Best & \(-1.04\times 10\) & \(-1.04\times 10\) & \(-1.04\times 10\) & \(-1.04\times 10\) & \(-1.04\times 10\) \\ F22 & Median & \(-1.04\times 10\) & \(-1.04\times 10\) & \(-1.04\times 10\) & \(-1.04\times 10\) & \(-1.04\times 10\) \\  & Time(s) & \(2.73\times 10^{-1}\) & \(6.51\times 10^{-1}\) & \(3.57\times 10^{-1}\) & \(3.98\times 10^{-1}\) & \(4.15\times 10^{-1}\) \\  & Best & \(-1.05\times 10\) & \(-1.05\times 10\) & \(-1.05\times 10\) & \(-1.05\times 10\) & \(-1.05\times 10\) \\ F23 & Median & \(-9.73\) & \(-7.86\) & \(-1.05\times 10\) & \(-1.05\times 10\) & \(-1.05\times 10\) \\  & Time(s) & \(3.35\times 10^{-1}\) & \(7.16\times 10^{-1}\) & \(4.19\times 10^{-1}\) & \(4.62\times 10^{-1}\) & \(4.65\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Cont.  
ICPO's exceptional overall performance on the multimodal function tests, particularly in terms of solution quality and computational efficiency, demonstrates its capability to effectively solve a wide range of complex multimodal optimization problems.