# An Efficient and Fast Hybrid GWO-JAYA Algorithm for Design Optimization
## 3 Test Problems and Optimization Results
### Optimal Crashworthiness Design of a Vehicle Subject to Side Impact
In fact, the present algorithm converged to the very low structural weight of 21.38340 kg while the optimized weights obtained with the other algorithms ranged between 21.39473 kg  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline
**Algorithms** & **x\({}_{1}\) (mm)** & **x\({}_{2}\) (mm)** & **x\({}_{3}\) (mm)** & **x\({}_{4}\) (mm)** & **x\({}_{5}\) (mm)** & **x\({}_{6}\) (mm)** & **x\({}_{7}\) (mm)** & **x\({}_{8}\)** & **x\({}_{9}\) (mm)** & **x\({}_{11}\) (mm)** & **Structural** \\  & & & & & & & & & & & & & **Weight (kg)** \\ \hline FHGWJA * & 0.50000 & 1.21204 & 0.50000 & 0.77908 & 0.50000 & 1.49004 & 0.50000 & 0.345 & 0.345 & \(-\)28.9781 & 0.00010 & 21.38340 \\ Present & & & & & & & & & & & & & \\ Standard & & & & & & & & & & & & & \\ GWO * & & & & & & & & & & & & & \\ Standard & & & & & & & & & & & & & \\ JAYA * & 0.50000 & 1.22573 & 0.50000 & 1.20711 & 0.50000 & 1.49194 & 0.50000 & 0.345 & 0.345 & 0.00000 & 0.00000 & 23.19115 \\ \hline IGWO [69]\({}^{\blacktriangle}\) & 0.50000 & 0.88641 & 0.50000 & 1.25781 & 0.64809 & 0.91372 & 0.50000 & 1.00000 & 0.52483 & 1.94790 & 15.3719 & 21.39473 \\ Chaotic GW \({}^{\blacktriangle}\) & 0.84525 & 0.50000 & 0.50000 & 1.36186 & 0.83852 & 0.86445 & 0.57679 & 0.94066 & 0.24622 & 4.55062 & 12.3084 & 21.46164 \\ CSO \({}^{\blacktriangle}\) & 0.78544 & 0.56882 & 0.50000 & 1.34514 & 0.82107 & 0.86975 & 0.74586 & 0.89302 & 0.39281 & 0.89510 & 1.17997 & 22.00444 \\ TSA \({}^{\blacktriangle}\) & 0.50315 & 0.89471 & 0.50000 & 1.40533 & 0.86396 & 0.84245 & 0.99580 & 0.86533 & 0.06579 & 0.12364 & 2.06338 & 22.70296 \\ \hline ASGWO [70]\({}^{\blacktriangle}\) & 0.50004 & 1.13454 & 0.50009 & 1.27905 & 0.50020 & 1.49996 & 0.50005 & 0.34496 & 0.33248 & \(-\)16.33322 & \(-\)2.14912 & 22.87188 \\ \hline SMO [47]\({}^{**}\) & 0.5000 & 1.11634 & 0.5000 & 1.30224 & 0.5000 & 1.50000 & 0.5000 & 0.345 & \(-\)19.566 & 0.000001 & 22.84298 \\ LIACO ** & 0.5000 & 1.11593 & 0.5000 & 1.30293 & 0.5000 & 1.50000 & 0.5000 & 0.192 & 0.345 & \(-\)19.640 & \(-\)0.000003 & 22.84299 \\ KH ** & 0.5000 & 1.14747 & 0.5000 & 1.26118 & 0.5000 & 1.5000 & 0.5000 & 0.345 & \(-\)13.9989 & -0.8984 & 22.88596 \\ Best ABC ** & 0.5000 & 1.30539 & 0.5000 & 1.10312 & 0.5000 & 0.50000 & 0.5000 & 0.345 & 0.14213 & 20.3306 & 22.88605 \\ HHO ** & 0.5000 & 1.15627 & 0.5000 & 1.27133 & 0.5000 & 1.47770 & 0.5000 & 0.345 & 0.192 & \(-\)14.592 & \(-\)2.4898 & 22.98537 \\ CLPSO ** & 0.5061 & 1.17379 & 0.5013 & 1.24706 & 0.5037 & 1.49560 & 0.5000 & 0.345 & \(-\)5.9585 & 3.3627 & 23.06244 \\ WOA ** & 0.5000 & 1.09276 & 0.5000 & 1.41233 & 0.5000 & 1.45497 & 0.5000 & 0.345 & 0.192 & \(-\)24.038 & \(-\)3.1789 & 23.12717 \\ \hline \multicolumn{10}{c}{\({}^{\blacktriangle}\)Optimized weight: 21.3905 \(\pm\) 0.007125 kg for FHGWJA; \(22.9318\pm\) 0.1423 kg for the standard GWO; \(23.2067\pm\) 0.02431 kg for standard JAYA; computational cost: \(30.019\pm\) 343 extremal analyses for FHGWJA 5; \(50.000\) for standard GWO; \(7560\pm\) 998 for standard JAYA; the best optimizer and computational cost were \(1367\) structural analyses. \({}^{\blacktriangle}\) Computational cost: 30,000 structural analyses, determined as the product between the population size \(N_{\text{POP}}=30\) and the limit number of iterations \(N_{\text{lemma}}=1000\). No statistical information on optimized weight and computational cost were given in [69]. \({}^{\blacktriangle}\) Computational cost: 15,000 structural analyses, determined as the product between the population size \(N_{\text{POP}}=30\) and the limit number of iterations \(N_{\text{lemma}}=500\). No statistical information on optimized weight and computational cost were given in [70]. \({}^{**}\) computational cost: 30,000 structural analyses, determined as the product between the population size \(N_{\text{POP}}  
(IGWO used in [69]) and 23.12717 kg (WOA used in [70]). The chaotic GWO (used in [69]) ranked 3 rd overall, finding a very close structural weight to those of FHGWJA and IGWO: 21.46164 kg vs. 21.38340 and 21.39473 kg, respectively.