## 5 Experiments
### Experiments Results  
In this section, the optimization methods are compared against each other in terms of efficiency, capability and computational complexity using the fifteen high-dimensional benchmark functions. Although the overall performance of an optimization algorithm changes depending on setting parameters and other experimental criteria, benchmark problems can be used to indicate the efficiency of the algorithm under different levels of complexity. The statistical significance results from experiments on the selected benchmark functions are presented in Table 4. From Figure 2 to Figure 10 present only the results for the constrained benchmark functions with different surface with \(D=25\), 40 and 50. The outcome of this study may not reflect the overall efficiency of the tested algorithms under all conditions.  
All experiments are conducted using a PC with a processor running at 2.60 GHz and 16 GB RAM in MATLAB R2015b running under Windows 8.1. It should be mentioned that the results are based on 25 independent runs for functions \(f_{1}\) to \(f_{15}\), with a population size set at 40 and the maximum number of iterations fixed at 1000. In these experiments, the basic versions of the selected algorithms are considered without further modification. All methods codes are obtained from different sources, and adjusted to be harmonic with our work objectives [18; 28; 93].  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Setting Parameters** \\ \hline ABC & Food Source = 20, the limit value = 10 \\ FFA & \(\alpha=0.5\), \(\gamma=1\), \(\beta=1\) \\ CSA & \(p=0.25\), \(\gamma=1.5\), \(\alpha=0.01\) \\ BA & \(\alpha=0.9\), Population Loudness (A) = 0.25, Pulse rate \(F\in[0,\,2]\) \\ FPA & \(p=0.8\), \(\gamma=0.1\), \(\lambda=1.5\) \\ GWO & \(\alpha\in[0,\,2]\), \(C\in[0,\,3]\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Setting parameters associated with each method.  
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Alg**} & \multicolumn{6}{c}{\(f_{s}\)(D - SB)} & \multicolumn{6}{c}{\(f_{s}\)(D - SB)} \\ \hline  & **Min** & **Median** & **SD** & **NRF** & **CPU** & **Min** & **Median** & **SD** & **NRF** & **CPU** & **Min** & **Median** & **SD** & **NRF** & **CPU** \\ \hline
**BA** & 1368 & 13.94 & 4.884 & 20,000 & 0.219 & 7760 & 50200 & 4.274 \(\times\) 10\({}^{5}\) & 20,000 & 0.484 & 6.08 & 4.270 \(\times\) 10\({}^{5}\) & 20,000 & 0.248 & 4.026 & 30,000 & 0.234 \\
**CA** & 0.6466 & 5.443 & 45,599 & 20,000 & 0.325 & 14.04 & 2240 & 41.72 \(\times\) 10\({}^{5}\) & 20,000 & 1.229 & 15.881 & 25.84 & 4.257 & 20,000 & 0.279 \\
**FFA** & 11.30 \({}^{-5}\) & 0.1129 & 0.837 & 20,000 & 1.266 & 0.219 & 2002 & 2.426 \(\times\) 10\({}^{5}\) & 20,000 & 1.453 & 1.381 & 13.67 & 4.286 & 20,000 & 1.266 \\
**FFA** & 7.03 \({}^{-5}\) & 0.130 & 0.356 & 0.2000 & 0.344 & 18700 & 34500 & 2.426 \(\times\) 10\({}^{5}\) & 20,000 & 0.547 & 3009 & 2518 & 4.413 & 20,000 & 0.533 \\
**ACO** & 56.80 \({}^{-10}\) & 0.2722 & 4.0851 & 12.270 & 0.172 & 4.5 \(\times\) 10\({}^{5}\) & 0.0213 & 3.426 \(\times\) 10\({}^{5}\) & 19,956 & 0.449 & 5.50 \(\times\) 10\({}^{5}\) & 16.18 & 4.627 & 15,047 & 0.172 \\
**ONO** & 6.14 \(\times\) 10\({}^{-6}\) & 4.27 \(\times\) 10\({}^{-9}\) & 23,000 & 2.020 & 0.207 & 0 & 4.7 \(\times\) 10\({}^{5}\) & 4.1 \(\times\) 10\({}^{5}\) & 20,000 & 0.490 & 0.0 & 4.20 \(\times\) 10\({}^{5}\) & 17.175 & 20,000 & 0.281 \\ \hline \multicolumn{1}{c}{_f_s} \(\Phi\)(D - SB)} & \multicolumn{6}{c}{\(f_{s}\)(D - SB)} & \multicolumn{6}{c}{\(f_{s}\)(D - SB)} & \multicolumn{6}{c}{\(f_{s}\)(D - SB)} \\ \hline
**BA** & 11.92 & 10.71 & 4.3038 & 20,000 & 0.50 & 1.44 \(\times\) 10\({}^{-7}\) & 4.4 \(\times\) 10\({}^{-7}\) & 40.1177 & 20,000 & 0.234 & 16.77 & 16.27 & 40.576 & 20,000 & 0.25 \\
**CA** & 4.88 \({}^{-10}\)