# Resource Scheduling in Cloud Computing Based on a Hybridized Whale Optimization Algorithm
## 5 Practical Simulations, Analysis, and Discussion
### Tests with Standard Benchmark Functions
#### 5.1.2 The WOA-AEFS Control Parameter Adjustments  
In order to objectively evaluate performance improvements of the WOA-AEFS, that is proposed in this paper, against the original WOA, in all tests we utilized a population with 30 individuals (\(N=30\)) that have been improving over 500 iterations (\(maxIter=500\)) in each run. These settings generate a total number of 15,000 objective function evaluations (\(30\times 500=15,000\)). The same values were used in [22].  
Since the WOA-AEFS utilizes general algorithm parameters (\(N\) and \(maxIter\)), as well as WAO, ABC, and FA specific parameters, we divided the control parameters into four groups: general parameters, WOA parameters, ABC exploration and FA search parameters. Parameters adjustments, as well as the behavior of dynamic parameters are summarized in Table 3.  
It should be noted that we took values for specific FA's search parameters as in [46]. According to the discussion presented in this paper, as well as regarding our previous experience with the FA metaheuristics [40; 47; 50; 52], the best exploitation ability of the FA can be established by utilizing this set of parameters [46]. If other values would be taken, the performance of the FA search exploitation process would decrease significantly.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**ID** & **Name of the Benchmark** & **Separability** & **Convexity** & **Scalability** \\ \hline F15 & Kowalik’s Function & Non-separable & Non-convex & Scalable \\ F16 & Six-Hump Camel-Back Function & Non-separable & Non-convex & Non-scalable \\ F17 & Branin Function & Non-separable & Non-convex & Non-scalable \\ F18 & Goldstein-Price Function & Non-separable & Non-convex & Non-scalable \\ F19 & Hartman’s Family (Hartman 3 Function) & Non-separable & Non-convex & Non-scalable \\ F20 & Hartman’s Family (Hartman 6 Function) & Non-separable & Non-convex & Non-scalable \\ F21 & Shekel’s Family (Shekel 5 Function) & Non-separable & Non-convex & Scalable \\ F22 & Shekel’s Family (Shekel 7 Function) & Non-separable & Non-convex & Scalable \\ F23 & Shekel’s Family (Shekel 10 Function) & Non-separable & Non-convex & Scalable \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter Name** & **Value** \\ \hline \multicolumn{2}{c}{**WOA-AEFS general parameters**} \\ Population size (\(N\)) & 30 \\ Number of iterations per run (\(maxIter\)) & 500 \\ \hline \multicolumn{2}{c}{**WOA search parameters**} \\ Initial value of parameter \(a\) & 2.0 \\ Dynamic behavior of parameter \(a\) & according to Equation (28) \\ \hline \multicolumn{2}{c}{**ABC exploration parameters**} \\ Parameter \(limit\) & 17 (according to Equation (37)) \\ Initial value of exploration influence parameter \(eir\) & 100 \\ Dynamic behavior of parameter \(eir\) & according to Equation (33) \\ \hline \multicolumn{2}{c}{**FA search parameters**} \\ Initial value for randomization parameter \(\alpha\) & 0.5 \\ Dynamic behavior of parameter \(\alpha\) & according to Equation (36) \\ Attractivnes at \(r\)=0 \(\beta_{0}\) & 0.2 \\ Absorption coefficient \(\gamma\) & 1.0 \\ \hline \hline \end{tabular}
\end{table}
Table 3: WOA ABC exploration firefly search (WOA-AEFS) control parameters’ adjustmentsSimilarly, as in the case of the FA, the best performance of the ABC exploration could be established if the value of \(limit\) parameter depends on the \(N\) and \(maxIter\) settings [10; 39; 41; 92]. The value of the \(limit\) in our proposed approach is determined by using the following expression:  
\[limit=round(\frac{maxIter}{N}), \tag{37}\]  
where the function \(round()\) rounds its arguments to the closest integer value.