## 3 Materials and Methods
### Proposed Algorithm
Standard algorithms, i.e., GA and PSO, were used in the comparison as a baseline. Specialized schedulers [30; 31] were also included in the comparison. The algorithms were selected based on their relevance to the problem. The experiments were carried out on an Intel Core i3 processor equipped with 8 GB of memory running on the Ubuntu 16.04 operating system. The algorithms were evaluated in terms of makespan, energy consumption, and balancing degree. CloudSim [34] was used to simulate the algorithms. The simulation was performed with 10 VMs and three data centers. VMs with different specifications were selected for simulation. Each VM was allocated 1000 MBs of memory and MIPS from 1500 to 3000. Processing, memory, storage, and transfer costs were set to 0.017, 0.05, 0.01, and 0.01, respectively. The GA was evaluated with a crossover probability of 0.8 and a mutation probability of 0.2. PSO was executed with the value of inertia weight factor \(\omega\) of 1.2, and the learning factors were set to 2. The other algorithms were executed with the parameters specified in the respective articles. Each experiment was repeated 20 times, and the average values were selected for comparison. Table 2 shows the results of the proposed algorithm compared to those of the other algorithms. The proposed algorithm yielded better results for all parameters on all datasets. In comparison to the standard algorithms, i.e., PSO and GA, the proposed algorithm performed better and at higher rates than the specialized algorithms. In the specialized schedulers, ERES remained closest to the proposed algorithm in terms of energy consumption. In terms of makespan and load balance, FIMPSO remained close to the proposed algorithm on the majority of the datasets. For some datasets, the energy consumption of FIMPSO was better than that of ERES and was close to that of the proposed algorithm. Figures 2-6 show the percent improvement gain of the proposed algorithm over the other algorithms. For the Montage dataset, in terms of makespan, the proposed algorithm achieved percent improvement gain of 32.60, 31.36, 22.8, and 21.18 over PSO, GA, ERES, and FIMPSO, respectively. For the same dataset, the improvement gains in terms of energy consumption over the compared methods were 25.1, 24.01, 18.35, and 20.99. In terms of load balance, the percent improvement gains of the proposed algorithm over PSO, GA, ERES, and FIMPSO were 31.55, 32.75, 24.13, and 22.22, respectively. The results are shown in Figure 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Nodes** & **w-Levels** & \begin{tabular}{c} **Parallel** \\ **Tasks** \\ \end{tabular} & \
\begin{tabular}{c} **Average File Size** \\ **(MBs)** \\ \end{tabular} &
\begin{tabular}{c} **Average Execution** \\ **Time (s)** \\ \end{tabular} \\ \hline Montage & 100 & 9 & 62 & 18.05 & 10.19 \\ Sipht & 100 & 7 & 51 & 22.34 & 173.34 \\ LIGO & 100 & 8 & 24 & 28.8 & 209.78 \\ CyberShake & 100 & 5 & 48 & 999.41 & 21.82 \\ Epigenomics & 100 & 8 & 24 & 4033.59 & 1277.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Datasets used for the experiments. Figure 1: Structures of the workflows used for the experiments: (**a**) Sipht, (**b**) CyberShake, (**c**) Epigenomics, (**d**) LIGO, and (**e**) Montage. In the case of the Sight dataset, the percent improvement gains in terms of makespan over PSO, GA, ERES, and FIMPSO were 22.41, 20.09, 12.15, and 13.21, respectively. In terms of energy consumption, the improvement gains of the proposed algorithm were 19.51, 19.14, 11.55, and 11.10 over PSO, GA, ERES, and FIMPSO. In terms of load balance, the proposed algorithm achieved percent improvement gains of 22.05, 21.28, 13.58, and 12.63 over the other algorithms. Figure 3 shows the results of the percent improvement gains of the proposed algorithm over the other algorithms.