# A Hybrid JADE-Sine Cosine Approach for Advanced Metaheuristic Optimization
## 6 Application in Engineering Design
### Speed Reducer Design Problem
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Optimizer** & **Min** & **Mean** & **Max** & **Std** & **Time** & **Rank** \\ \hline JADESCA & 2994.471 & 2994.92 & 2998.949 & 1.415589 & 0.834734 & 1 \\ MFO & 2994.471 & 2998.399 & 3033.749 & 12.42062 & 0.822204 & 2 \\ DOA & 2994.471 & 3099.145 & 3363.873 & 123.884 & 1.341059 & 3 \\ RIME & 2994.731 & 2996.055 & 2997.135 & 0.77945 & 0.902076 & 4 \\ COA & 2994.965 & 2996.059 & 2997.478 & 0.733906 & 1.788052 & 5 \\ AVOA & 2995.032 & 3000.607 & 3005.723 & 3.348249 & 0.999476 & 6 \\ ZOA & 2995.666 & 3003.03 & 3008.362 & 3.981207 & 1.453907 & 7 \\ SCSO & 2996.844 & 3007.816 & 3018.212 & 5.977215 & 0.944803 & 8 \\ SHIO & 2998.583 & 3004.512 & 3011.048 & 3.713896 & 0.831343 & 9 \\ GWO & 3001.793 & 3010.462 & 3028.562 & 8.734309 & 0.914363 & 10 \\ FVIM & 3004.641 & 3009.413 & 3019.998 & 4.724602 & 0.924222 & 11 \\ HHO & 3008.729 & 3219.386 & 4025.775 & 317.9044 & 1.57597 & 12 \\ WOA & 3015.221 & 351.743 & 4316.943 & 380.4302 & 0.803014 & 13 \\ OMA & 3016.568 & 3075.234 & 3163.744 & 42.72921 & 2.175797 & 14 \\ SOA & 3017.402 & 3038.222 & 3069.537 & 15.92089 & 0.733158 & 15 \\ TTHHO & 3018.703 & 3351.402 & 4298.54 & 486.7529 & 1.825567 & 16 \\ STOA & 3024.978 & 3040.187 & 3058.421 & 11.88368 & 0.751259 & 17 \\ AO & 3048.003 & 3104.258 & 3142.244 & 32.65513 & 2.281716 & 18 \\ ROA & 3058.109 & 10411.63 & 1007316 & 317.352.9 & 2.03042 & 19 \\ Chimp & 3075.128 & 3313.287 & 3189.936 & 29.19947 & 1.418818 & 20 \\ SCA & 3076.29 & 3139.106 & 3191.778 & 33.86397 & 0.721655 & 21 \\ FLO & 3797.939 & 723258.5 & 1048408 & 496081.5 & 1.378594 & 22 \\ CPO & 4632.48 & 5752.925 & 5877.419 & 393.6845 & 1.37111 & 23 \\ SSOA & 1017738 & 1092409 & 1250257 & 67188.3 & 1.265369 & 24 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Statistical results of the speed reducer design problem. and COA, while close in performance, showed a slight increase in the best score and some variability in the design variables, indicating slightly less precision. Lower-ranked optimizers like AVOA, ZOA, and SCSO showed a noticeable increase in the best score and variability, particularly in variables 5 through 7, indicating reduced accuracy and consistency. SHIO and GWO further increased the best score, with greater deviations in the design variables, particularly in X5. Optimizers such as FVIM, HHO, and WOA showed significantly higher best scores and greater divergence in variables 5, 6, and 7, highlighting issues in convergence or global optimization. TTHHO, STOA, AO, and ROA exhibited a significant drop in performance, with best scores far from optimal and substantial variability in variables 5, 6, and 7, indicating poor adaptation to the problem's constraints. The worst performers, such as chimp, SCA, FLO, CPO, and SSOA, exhibited drastically higher best scores and highly varied, non-ideal values across almost all variables, particularly X5. These results underscore the superiority of JADESCA and MFO for this problem, while others struggle with precision, consistency, and effective optimization.