# 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  
In all simulations we executed WOA-AEFS in 100 independent runs. In each run we initialized a random population of a size \(N\) by using the Equation (32). For the purpose of experiments, we implemented our own pseudo-random number generator, and for each run we used a different seed. The WOA-AEFS algorithm is implemented using Java SE Development Kit 11 technology and the Intellij environment. We first compared WOA-AEFS performance with original WOA metaheuristics. Both algorithms were tested for same benchmark instances (F1-F23) and under the same experimental conditions. Results for the WOA were taken from [22]. We note that we have also implemented basic WOA in Java and obtained the same results as reported in [22]. The WOA showed in [22] was implemented in MATLAB software. We used the same performance metrics as in [22]--best values averaged over 100 independent runs (mean indicator) and the standard deviation (std). In [22], values are averaged over 30 runs. By performing a simulation with more runs, we wanted to obtain more accurate and precise results. In order to evaluate improvements over the basic WOA implementation, we first give side-by-side comparison between the WOA-AEFS and the original WOA in Table 4. For the sake of easier visualization of performance indicators, better results for every test instance and for each performance metric (mean and std) are marked bold. When improving an algorithm (metaheuristics), there should always be trade-offs. For example, for one benchmark instance, the results improve, while for some other, the results get worse. However, it is important that on average (by taking into account all benchmark instances), an improved/hybridized version overcomes the original one. Results presented in Table 4 provide valid proof of the enhancements over the original WOA, that are obtained by hybridizing WOA with ABC and FA algorithms. On average, the WOA-AEFS significantly outperforms WOA. Benchmark instances and indicators where original WOA establishes better performance than the WOA-AEFS only include the following: mean value for the F7 test, std metric for the F16 benchmark, and mean and std indicators for the F19 test. Experiments where both approaches accomplished the same results encompass mean indicator values for the F9, F15, F16, and F18 benchmark instances and std value for the F9 test. In all other cases, WOA-AEFS completely outperformed basic WOA metaheuristics. In the Table 4, we included an additional row, where we counted for each column the number of times a particular algorithm obtained better results. In 18 out of 23 benchmark instances, the WOA-AEFS for both indicators (mean and std) achieved better convergence speed and result quality compared with the original WOA. In the original WOA approach, due to the dynamic behavior of parameter \(\vec{a}\) (adaptive mechanism), the search process tends to accelerate with the iterations progress [22]. This mechanism performs well in cases, when in early iterations, the algorithm has found the promising region of the search space. However, if this was not the case, the algorithm can become stuck in some of the suboptimal regions, and the whole population (again due to the adaptive mechanism) converges to this suboptimal domain and loses diversity. As already mentioned in Section 4.2, this behavior is known as premature convergence. Premature convergence is particularly emphasized in the F8 and F21 simulations, as was also noted in [22]. The main cause of premature convergence is an inadequate exploitation-exploration trade-off especially in early iterations of algorithms' execution. By using the ABC exploration mechanism, our proposed WOA-AEFS algorithm avoids the premature convergence, as was empirically proved. In cases of F8 and F21 benchmarks, the WOA-AEFS successfully managed to avoid trapping in local optimum regions.