# Resource Scheduling in Cloud Computing Based on a Hybridized Whale Optimization Algorithm
## 5 Practical Simulations, Analysis, and Discussion
### Tests with Standard Benchmark Functions
#### 5.1.3 Comparative Analysis and Discussion
However, by using the ABC exploration, some good solutions could be wasted and our WOA-AEFS compensates this by utilizing dynamic parameter \(\mathit{eir}\) and the very efficient FA's search equation (please refer to Section 4.3). Moreover, WOA-AEFS still employs adaptive shrinking mechanism (parameter \(\bar{a}\)) of the original WOA and the search process is accelerating with the increase of iterations. Convergence speed graphs of WOA and WOA-AEFS for F8 and F21 benchmark instances are given in Figure 1. \begin{table}
\begin{tabular}{c c c c c} \hline
**ID** & \multicolumn{2}{c}{**WOA**} & \multicolumn{2}{c}{**WOA-AEFS**} \\  & \(\mathit{Mean}\) & \(\mathit{Standard}\) _Deviation (std)_ & \(\mathit{Mean}\) & \(\mathit{Standard}\) _Deviation (std)_ \\ \hline F1 & \(1.41\times 10^{-30}\) & \(4.9\times 10^{-30}\) & \(\mathbf{2.55\times 10^{-31}}\) & \(\mathbf{8.75\times 10^{-32}}\) \\ F2 & \(1.06\times 10^{-21}\) & \(2.39\times 10^{-21}\) & \(\mathbf{3.97\times 10^{-23}}\) & \(\mathbf{2.99\times 10^{-23}}\) \\ F3 & \(5.39\times 10^{-7}\) & \(2.93\times 10^{-6}\) & \(\mathbf{6.72\times 10^{-10}}\) & \(\mathbf{5.04\times 10^{-10}}\) \\ F4 & \(0.072581\) & \(0.39747\) & \(\mathbf{0}\) & \(\mathbf{0}\) \\ F5 & \(27.865580\) & \(0.763626\) & \(\mathbf{3.29}\) & \(\mathbf{0.012500}\) \\ F6 & \(3.116266\) & \(0.532429\) & \(\mathbf{1.5\times 10^{-19}}\) & \(\mathbf{7.59\times 10^{-20}}\) \\ F7 & \(\mathbf{0.001425}\) & \(0.001149\) & \(0.001452\) & \(\mathbf{0.000851}\) \\ F8 & \(-5080.76\) & \(695.7968\) & \(-\mathbf{13239.3}\) & \(\mathbf{48.3}\) \\ F9 & \(0\) & \(0\) & \(0\) & \(0\) \\ F10 & \(7.4043\) & \(9.897572\) & \(\mathbf{0.013}\) & \(\mathbf{0.0051}\) \\ F11 & \(0.000289\) & \(0.001586\) & \(\mathbf{0}\) & \(\mathbf{0}\) \\ F12 & \(0.339676\) & \(0.214864\) & \(\mathbf{9.29\times 10^{-15}}\) & \(\mathbf{2.02\times 10^{-15}}\) \\ F13 & \(1.889015\) & \(0.266088\) & \(\mathbf{7.56\times 10^{-14}}\) & \(\mathbf{2.09\times 10^{-14}}\) \\ F14 & \(2.11973\) & \(2.498594\) & \(\mathbf{0.998023}\) & \(\mathbf{1.99\times 10^{-16}}\) \\ F15 & \(0.000572\) & \(0.000324\) & \(\mathbf{0.000322}\) & \(0.000324\) \\ F16 & \(-1.03163\) & \(\mathbf{4.2\times 10^{-7}}\) & \(-1.03163\) & \(2.87\times 10^{-6}\) \\ F17 & \(0.397914\) & \(2.7\times 10^{-5}\) & \(\mathbf{0.397887}\) & \(\mathbf{1.83\times 10^{-10}}\) \\ F18 & \(3\) & \(4.22\times 10^{-15}\) & \(3\) & \(\mathbf{2.35\times 10^{-15}}\) \\ F19 & \(-\mathbf{3.85616}\) & \(\mathbf{0.002706}\) & \(-3.85529\) & \(0.003812\) \\ F20 & \(-2.98105\) & \(0.376653\) & \(-\mathbf{3.31952}\) & \(\mathbf{0.025821}\) \\ F21 & \(-7.04918\) & \(3.629551\) & \(-\mathbf{10.1532}\) & \(\mathbf{3.02\times 10^{-12}}\) \\ F22 & \(-8.181780\) & \(3.829202\) & \(-\mathbf{8.925003}\) & \(\mathbf{3.352013}\) \\ F23 & \(-9.34238\) & \(2.414737\) & \(-\mathbf{10.5364}\) & \(\mathbf{3.5\times 10^{-13}}\) \\ \hline \(\mathit{Better}\) & \(2\) & \(2\) & \(18\) & \(18\) \\ \hline \end{tabular}
\end{table} 
Table 4: Comparative analysis—WOA-AEFS vs. WOA for unconstrained benchmarks. Figure 1: Convergence speed graphs: F8 benchmark (a) –F21 benchmark (b). From the Figure 1, some interesting conclusions about the algorithms' behavior can be drawn. First, it should be noted that the both algorithms accelerate with the increase of iteration number due to the shrinking behavior mechanism. Secondly, it can be concluded that the WOA-AEFS after approximately 300 and 400 iterations obtains the value that the basic WOA generates after 500 iterations, when observing F8 and F21 benchmarks, respectively. Also, it can be noticed that the basic WOA in the F21 simulation gets stuck somewhere between the 80 th and 120 th, and between the 200 th and 220 th iterations. At the other side, the WOA-AEFS shows non-volatile convergence during the whole execution.