# XOR Binary Gravitational Search Algorithm with Repository: Industry 4.0 Applications
## 5 Simulation Results
### Benchmark Optimization Problem
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Function** & **n** & **d** & **Proposed** & **BGSA** & **IBPSO** & **BPSO** & **BGWO** & **BDA** \\
**Number** & & & & [16] & [17] & [15] & [18] & [19] \\ \hline \(f_{1}\left(X\right)\) & 1 & 1 & 3.64E-10 & 6.55E-10 & 0.003499 & 2.98E-07 & 0.079185 & **9.09E-11** \\ \hline \(f_{1}\left(X\right)\) & 1 & 2 & **7.28E-10** & 0.000421 & 0.110086 & 0.004851 & 3.173297 & 8.66E-08 \\ \hline \(f_{1}\left(X\right)\) & 1 & 5 & **1.82E-09** & 0.01808 & 3.837217 & 3.492558 & 54.25284 & 0.025257 \\ \hline \(f_{1}\left(X\right)\) & 1 & 10 & **1.24E-07** & 1.640722 & 23.62139 & 43.34931 & 212.2319 & 0.892732 \\ \hline \(f_{2}\left(X\right)\) & 2 & 1 & 3.64E-10 & 3.64E-10 & 8.62E-05 & 2.73E-07 & 0.153546 & **9.09E-11** \\ \hline \(f_{2}\left(X\right)\) & 2 & 2 & **2.65E-19** & 2.81E-18 & 0.000454 & 2.5E-07 & 0.358629 & 2.25E-16 \\ \hline \(f_{2}\left(X\right)\) & 2 & 5 & **7.65E-46** & 7.08E-34 & 7.45E-05 & 7.57E-05 & 2.79E-05 & 1E-22 \\ \hline \(f_{2}\left(X\right)\) & 2 & 10 & **8.3E-82** & 2.57E-56 & 12.26801 & 1274.831 & 2.09E-11 & 5.44E-22 \\ \hline \(f_{3}\left(X\right)\) & 3 & 1 & \(-\)**1** & \(-\)9.9999 & \(-\)0.99705 & \(-\)**1** & \(-\)0.98737 & \(-\)**1** \\ \hline \(f_{3}\left(X\right)\) & 3 & 2 & \(-\)0.99488 & \(-\)0.99375 & \(-\)0.98506 & \(-\)0.99787 & \(-\)0.94229 & \(-\)**0.99901** \\ \hline \(f_{3}\left(X\right)\) & 3 & 5 & \(-\)0.95717 & \(-\)0.96513 & \(-\)0.90313 & \(-\)0.91313 & \(-\)0.74288 & \(-\)**0.96923** \\ \hline \(f_{3}\left(X\right)\) & 3 & 10 & \(-\)**0.90475** & \(-\)0.89211 & \(-\)0.64083 & \(-\)0.5024 & \(-\)0.51453 & \(-\)0.88339 \\ \hline \(f_{4}\left(X\right)\) & 4 & 1 & \(-\)**19.4256** & \(-\)19.4253 & \(-\)3.94361 & \(-\)3.9453 & \(-\)18.4693 & \(-\)3.9453 \\ \hline \(f_{4}\left(X\right)\) & 4 & 2 & \(-\)**38.8511** & \(-\)38.8511 & \(-\)7.8514 & \(-\)7.8897 & \(-\)31.8297 & \(-\)7.89018 \\ \hline \(f_{4}\left(X\right)\) & 4 & 5 & \(-\)**97.1278** & \(-\)97.1165 & \(-\)19.0216 & \(-\)19.1181 & \(-\)55.8132 & \(-\)19.6948 \\ \hline \(f_{4}\left(X\right)\) & 4 & 10 & \(-\)**194.255** & \(-\)193.588 & \(-\)35.5675 & \(-\)31.5541 & \(-\)79.5703 & \(-\)39.2195 \\ \hline \(f_{5}\left(X\right)\) & 5 & 1 & 3.64E-10 & 3.64E-10 & 7.76E-05 & 3.32E-07 & 0.372345 & **9.09E-11** \\ \hline \(f_{5}\left(X\right)\) & 5 & 2 & **3.64E-10** & 0.006168 & 0.140178 & 0.002341 & 1.452548 & 1.08E-09 \\ \hline \(f_{5}\left(X\right)\) & 5 & 5 & **3.64E-10** & 0.13037 & 9.419671 & 4.551582 & 2659.276 & 0.002952 \\ \hline \(f_{5}\left(X\right)\) & 5 & 10 & **3.64E-10** & 17.81345 & \(-\)293.123 & 2334.993 & 1.06E+08 & 4.71886 \\ \hline \(f_{6}\left(X\right)\) & 6 & 1 & \(-\)**78.3323** & \(-\)78.1186 & \(-\)77.5076 & \(-\)**78.3323** & \(-\)67.8744 & \(-\)**78.3323** \\ \hline \(f_{6}\left(X\right)\) & 6 & 2 & \(-\)156.094 & \(-\)147.94 & \(-\)151.238 & \(-\)156.496 & \(-\)116.85 & \(-\)**156.659** \\ \hline \(f_{6}\left(X\right)\) & 6 & 5 & \(-\)338.666 & \(-\)327.884 & \(-\)314.902 & \(-\)322.303 & 984.8181 & \(-\)**369.827** \\ \hline \(f_{6}\left(X\right)\) & 6 & 10 & \(-\)641.095 & \(-\)630.392 & \(-\)431.271 & \(-\)400.089 & 21937.59 & \(-\)**645.258** \\ \hline \(f_{7}\left(X\right)\) & 7 & 1 & \(-\)**0.99419** & \(-\)0.97691 & \(-\)0.88143 & \(-\)0.98787 & \(-\)0.88543 & \(-\)0.98792 \\ \hline \(f_{7}\left(X\right)\) & 7 & 2 & \(-\)1.95034 & \(-\)1.95069 & \(-\)1.68317 & \(-\)1.89381 & \(-\)1.66732 & \(-\)**1.95806** \\ \hline \(f_{7}\left(X\right)\) & 7 & 5 & \(-\)4.66631 & \(-\)**4.67197** & \(-\)3.45559 & \(-\)2.81238 & \(-\)3.45303 & \(-\)4.40256 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimization results using various optimization algorithms for the minimization of several benchmark optimization problems.