# A Spring Search Algorithm Applied to Engineering Optimization Problems
## 7 Experimental Results and Discussion
### Algorithms Used for Comparison
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Algorithms**} & \multicolumn{6}{c}{**Optimum Variables**} & \multicolumn{1}{c}{**Opt. Cost**} \\ \hline  & \(D_{\text{m}}\) & \(D_{\text{b}}\) & \(Z\) & \(f_{t}\) & \(f_{o}\) & \(KDmin\) & \(KDmax\) & \(\epsilon\) & \(e\) & \(\zeta\) & **Opt. Cost** \\ \hline \(SSA\) & 125 & 21.41890 & 10.94113 & 0.515 & 0.515 & 0.4 & 0.7 & 0.3 & 0.02 & 0.6 & 85,067.983 \\ EPO & 125 & 21.41890 & 10.93268 & 0.515 & 0.4 & 0.7 & 0.3 & 0.02 & 0.6 & 85,054.323 \\ SHO & 125.6199 & 21.35129 & 10.98781 & 0.515 & 0.515 & 0.5 & 0.68807 & 0.300151 & 0.03254 & 0.62701 & 84,807.111 \\ \(GOA\) & 125 & 20.75388 & 11.17342 & 0.515 & 0.515000 & 0.5 & 0.61503 & 0.300000 & 0.05161 & 0.60000 & 81,691.202 \\ GWO & 125.6002 & 21.32250 & 10.97338 & 0.515 & 0.515000 & 0.5 & 0.68782 & 0.301348 & 0.03617 & 0.61061 & 84,491.266 \\ TLBO & 125 & 21.14834 & 10.96928 & 0.515 & 0.515 & 0.5 & 0.7 & 0.3 & 0.02778 & 0.62912 & 83,431.117 \\ \(SA\) & 125 & 20.85417 & 11.14989 & 0.515 & 0.517746 & 0.5 & 0.61827 & 0.304068 & 0.02000 & 0.624638 & 82,794.941 \\ \(PSO\) & 125 & 20.77562 & 11.01247 & 0.515 & 0.515000 & 0.5 & 0.61397 & 0.300000 & 0.05004 & 0.610001 & 82,773.982 \\ \(GA\) & 125 & 20.87123 & 11.16697 & 0.515 & 0.516000 & 0.5 & 0.61951 & 0.301128 & 0.05024 & 0.614531 & 81,569.527 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Statistical results for welded beam design problem. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Algorithms**} & \multicolumn{3}{c}{**Optimum Variables**} & \multicolumn{1}{c}{**Optum Cost**} \\ \cline{2-6}  & \(d\) & \(D\) & \(p\) & \\ \hline \(SSA\) & 0.051087 & 0.342908 & 12.0898 & 0.012656987 \\ \(EPO\) & 0.051144 & 0.343751 & 12.0955 & 0.012674000 \\ \(SHO\) & 0.050178 & 0.341541 & 12.07349 & 0.012678321 \\ \(GOA\) & 0.05000 & 0.310414 & 15.0000 & 0.013192580 \\ \(GWO\) & 0.05000 & 0.315956 & 14.22623 & 0.012816930 \\ \(TLBO\) & 0.050780 & 0.334779 & 12.72269 & 0.012709667 \\ \(GSA\) & 0.05000 & 0.317312 & 14.22867 & 0.012873881 \\ \(PSO\) & 0.05010 & 0.310111 & 14.0000 & 0.013036251 \\ \(GA\) & 0.05025 & 0.316351 & 15.23960 & 0.012776352 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Comparison results for tension/compression spring design problem. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Algorithms**} & \multicolumn{3}{c}{**Optimum Variables**} & \multicolumn{1}{c}{**Optum Cost**} \\ \cline{2-6}  & \(D\) & \(D\) & \(Z\) & \(f_{t}\) & \(f_{o}\) & \(KDmin\) & \(KDmax\) & \(\epsilon\) & \(e\) & \(\zeta\) \\ \hline \(SSA\) & 125 & 21.41890 & 10.94113 & 0.515 & 0.515 & 0.4 & 0.7 & 0.3 & 0.02 & 0.6 & 85,067.983 \\ \(EPO\) & 125 & 21.41732 & 10.93268 & 0.515 & 0.515 & 0.4 & 0.7 & 0.3 & 0.02 & 0.6 & 85,054.323 \\ \(SHO\) & 125.6199 & 21.35129 & 10.98781 & 0.515 & 0.515 & 0.5 & 0.68807 & 0.300151 & 0.03254 & 0.62701 & 84,807.111 \\ \(GOA\) & 125 & 20.75388 & 11.17342 & 0.515 & 0.515000 & 0.5 & 0.61503 & 0.300000 & 0.05161 & 0.60000 & 81,691.202 \\ \(GWO\) & 125 & 6002 & 21.32250 & 10.97338 & 0.515 & 0.515000 & 0.5 & 0.68782 & 0.301348 & 0.03617 & 0.61061 & 84,491.266 \\ \(TLBO\) & 125 & 21.14834 & 10.96928 & 0.515 & 0.515 & 0.5 & 0.7 & 0.3 & 0.02778 & 0.62912 & 83,431.117 \\ \(GSA\) & 125 & 20.85417 & 11.14989 & 0.515 & 0.517746 & 0.5 & 0.61827 & 0.304068 & 0.02000 & 0.624638 & 82,794.941 \\ \(PSO\) & 125 & 20.77562 & 11.01247 & 0.515 & 0.515000 & 0.5 & 0.61397 & 0.300000 & 0.05004 & 0.610001 & 82,773.982 \\ \(GA\) & 125 & 20.87123 & 11.16697 & 0.515 & 0.516000 & 0.5 & 0.61951 & 0.301128 & 0.05024 & 0.614531 & 81,569.527 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Statistical results for tension/compression spring design problem. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Algorithms**} & \multicolumn{6}{c}{**Optimum Variables**} & \multicolumn{1}{c}{**Optum Cost**} \\ \cline{2-6}  & \(D\) & \(D\) & \(Z\) & \(f_{t}\) & \(f_{o}\) & \(KDmin\) & \(KDmax\) & \(\epsilon\) & \(e\) & \(\zeta\) & **Opt.