# A Hybrid JADE-Sine Cosine Approach for Advanced Metaheuristic Optimization
## 5 Results and Discussion  
As shown in Tables 3-5, JADESCA demonstrates superior performance across all five functions (F1-F5) when compared to 25 optimization algorithms over CEC2022. It consistently achieves the best mean values, ranking first in all cases. For F1, F2, F3, F4, and F5, JADESCA not only provides the lowest mean performance values but also exhibits exceptional stability, as evidenced by its low standard deviation (Std) and standard error of the mean (SEM). Specifically, in F1, JADESCA shares the top rank with a few others but still stands out due to its minimal Std and SEM. In other functions, JADESCA maintains its leading position with significant margins over other algorithms, particularly outperforming those like SPBO, SSOA, and AO, which show much higher mean values and lower ranks. The zero Std and SEM in F5 further highlight JADESCA's consistency. a leading optimizer. In contrast, algorithms such as FLO, SPBO, and SSOA show higher mean values and rank lower, indicating lower efficiency and more fluctuating performance compared to JADESCA. Moreover, the CEC2022 benchmark functions encompass a variety of unimodal, multimodal, hybrid, and composition functions. Analyzing JADESCA's behavior regarding  
\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline \hline
**Function** & **Statistics** & **SDE** & **HHO** & **SCSO** & **OMA** & **CPO** & **ROA** & **COA** & **CMAES** \\ \hline F1 & Mean & 3.00E+02 & 3.05E+02 & 1.36E+03 & 3.00E+02 & 2.67E+03  
its exploration and exploitation capabilities within the context of these functions reveals the following:  
Unimodal functions, like the shifted and rotated Zakharov function (F1), typically feature a single global minimum. In these functions, exploitation is critical, as the main challenge is refining the solution to converge on the global optimum. JADESCA's performance on F1, where it ranks first, indicates its strong exploitation capabilities, effectively narrowing down on the optimal solution with high precision and minimal deviation. Multimodal functions (F2 to F5): Multimodal functions, such as the shifted and rotated [PERSON]'s function (F2), [PERSON]'s f6 function (F3), non-continuous [PERSON]'s function (F4), and Levy function (F5), contain multiple local optima, making exploration essential to avoid premature convergence to suboptimal solutions. JADESCA's strong performance across these functions demonstrates its ability to balance exploration and exploitation effectively. It navigates the complex landscapes of these multimodal functions, finding and exploiting the global optimum while avoiding local traps. This balance is reflected in its consistent top rankings and low variability in performance. Hybrid functions (F6 to F8): Hybrid functions, such as hybrid function 1 (F6), 2 (F7), and 3 (F8), combine elements from different types of functions, often blending multimodal and unimodal characteristics. These functions challenge both the exploratory and exploitative abilities of an optimizer. JADESCA's top performance in these functions suggests that it is highly adaptable, effectively shifting between exploration and exploitation as needed. It can explore the diverse landscapes introduced by the hybrid nature of these functions and then exploit the best solutions efficiently. Composition functions (F9 to F12): Composition functions, like composition function 1 (F9) through function 4 (F12), are some of the most challenging, as they integrate multiple sub-functions with varying characteristics into a single problem. These functions require an optimizer to be adept at both exploration (to handle the diverse landscapes created by sub-functions) and exploitation (to fine-tune solutions within promising regions). JADESCA's strong and consistent performance on these composition functions indicates that it handles this complexity well, balancing broad exploration across different subspaces with targeted exploitation within the most promising areas. This is critical for achieving optimal or near-optimal solutions on such demanding benchmarks.