# Resource Scheduling in Cloud Computing Based on a Hybridized Whale Optimization Algorithm
## 5 Practical Simulations, Analysis, and Discussion
### Tests with Standard Benchmark Functions
#### 5.1.1 Benchmark Problems Definitions  
To test the robustness, solutions' quality and convergence of the WOA-AEFS, we utilized a set of 23 classical unconstrained benchmarks. The original WOA has also been tested on the same benchmark instances, as it was presented in [22].  
For the sake of easier readability, and according to the practice from modern computer science literature [91], we divided benchmark sets into two groups: unimodal and multimodal. From the group of multimodal benchmarks, a special group of fixed-dimension multimodal functions can be extrapolated. The basic difference between multimodal and fixed-dimension multimodal functions is the ability to define a desired number of decision variables. When using fixed-dimension multimodal benchmarks in experiments, the number of decision variables can not be tuned.  
For each function (unimodal and multimodal), a unique identifier (ID) is given. In Table 1 characteristics of unimodal benchmarks that were utilized in simulations, are shown. Mathematical formulation of these functions can be found in [22].  
Characteristics of multimodal benchmarks, that were employed in experiments, are given in Table 2. Functions in the Table 2 with IDs F8-F13 are classical multimodal benchmarks, while the functions with IDs from the range F14-F23 belong to the group of fixed-dimension multimodal tests.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ID** & **Name of the Benchmark** & **Separability** & **Convexity** & **Scalability** \\ \hline F1 & Sphere & Separable & Convex & Scalable \\ F2 & [PERSON]’s Problem 2.22 & Non-separable & Convex & Scalable \\ F3 & [PERSON]’s Problem 1.2 & Separable & Convex & Scalable \\ F4 & [PERSON]’s Problem 2.21 & Separable & Convex & Scalable \\ F5 & Generalized Rosenbrock’s Function & Non-separable & Non-convex & Scalable \\ F6 & Step 2 Function & Separable & Convex & Scalable \\ F7 & Quartic Function with Noise & Separable & Non-convex & Scalable \\ \hline \hline \end{tabular}
\end{table}
Table 1: Characteristics of unimodal benchmark functions  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ID** & **Name of the Benchmark** & **Separability** & **Convexity** & **Scalability** \\ \hline F8 & Generalized Schwefel’s Problem 2.26 & Separable & Convex & Scalable \\ F9 & Generalized Rastrigin’s Function & Non-separable & Convex & Scalable \\ F10 & Ackley’s Function & Non-separable & Non-convex & Scalable \\ F11 & Generalized Griewank Function & Non-separable & Non-convex & Scalable \\ F12 & Generalized Penalized Functions & Non-separable & Non-convex & Scalable \\ F13 & Generalized Penalized Functions & Non-separable & Non-convex & Scalable \\ F14 & Shekel’s Foxholes Function & Non-separable & Non-convex & Scalable \\ \hline \hline \end{tabular}
\end{table}
Table 2: Characteristics of multimodal benchmark functions.  
In simulations with benchmarks F1-F13 we utilized 30 dimensions (\(D=30\)), as in [22]. For more information regarding the dimension size of fixed-dimension multimodal tests (F14-F23), please refer to [22].