## 4 Results and Discussion
### Statistical Analysis Using \(t\)-Test  
Tables 4-13 contain the outcomes of a paired \(t\)-test that was carried out to assess whether there are substantial changes between the makespan and cost obtained from the proposed algorithm--HWACO--and other algorithms, namely, QANA, MTF-BPSO, ACO, MIN-MIN, and FCFS, using comparable stopping standards for all task instances. The satisfactory \(p\)-value must be less than alpha \(\alpha<0.5\). As shown in the tables below, almost all of the datasets had \(p\)-values that were less than this alpha value, which shows a substantial enhancement in the proposed HWACO algorithm compared to the other algorithms used for comparison. Thus, it can be inferred that the HWACO outperforms other task scheduling algorithm in terms of makespan and cost. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Makespan** & **Task Size** & **HWACO** & **QANA** & **Improvement** & \(t\)**-Test Value** & \(p\)**-Value** \\ \hline \multirow{4}{*}{Onset rate 10} & 100 & 13.78 & 15.01 & 8.194536975 & 3.4534 & \(7.430\times 10^{-3}\) \\ \cline{2-7}  & 200 & 25.9 & 27.23 & 4.884318766 & 2.4533 & \(4.405\times 10^{-2}\) \\ \cline{2-7}  & 300 & 36.56 & 38.31 & 4.567997912 & 3.3093 & \(6.351\times 10^{-2}\) \\ \cline{2-7}  & 400 & 50.4 & 52.3 & 3.632887189 & 2.4534 & \(9.984\times 10^{-2}\) \\ \hline \multirow{4}{*}{Onset rate 40} & 100 & 16.98 & 17.01 & 0.176366843 & 1.9093 & \(1.308\times 10^{-2}\) \\ \cline{2-7}  & 200 & 30.76 & 32.26 & 4.649721017 & 2.4532 & \(4.304\times 10^{-4}\) \\ \cline{2-7}  & 300 & 45.13 & 46.12 & 2.146574154 & 2.0984 & \(6.094\times 10^{-2}\) \\ \cline{2-7}  & 400 & 60.8 & 62.3 & 2.407704655 & 2.3221 & \(5.534\times 10^{-3}\) \\ \hline \end{tabular}
\end{table} 
Table 4: \(t\)-Test for makespan between HWACO and QANA. Figure 7: The task cost values of 400. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Makespan** & **Task Size** & **HWACO** & **ACO** & **Improvement** & \(t\)**-Test Value** & \(p\)**-Value** \\ \hline \multirow{4}{*}{Onset rate 10} & 100 & 13.78 & 18.9 & 27.08994709 & 5.4535 & \(5.563\times 10^{-4}\) \\ \cline{2-6}  & 200 & 25.9 & 34.61 & 25.16613695 & 5.2434 & \(8.456\times 10^{-3}\) \\ \cline{2-6}  & 300 & 36.56 & 50.31 & 27.33055059 & 4.9305 & \(2.344\times 10^{-4}\) \\ \cline{2-6}  & 400 & 50.4 & 66 & 23.63636364 & 5.8497 & \(1.084\times 10^{-2}\) \\ \hline \multirow{4}{*}{Onset rate 40} & 100 & 16.98 & 22.68 & 25.13227513 & 4.2433 & \(9.083\times 10^{-3}\) \\ \cline{2-6}  & 200 & 30.76 & 41.53 & 25.93306044 & 4.9085 & \(4.304\times 10^{-5}\) \\ \cline{2-6}  & 300 & 45.13 & 60.37 & 25.24432665 & 5.2324 & \(7.305\times 10^{-4}\) \\ \cline{2-6}  & 400 & 60.8 & 79.2 & 23.232323 & 3.5345 & \(3.405\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: \(t\)-Test for makespan between HWACO and ACO. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Makespan** & **Task Size** & **HWACO** & **MIN-MIN** & **Improvement** & \(t\)**-Test Value** & \(p\)**-Value** \\ \hline \multirow{4}{*}{Onset rate 10} & 100 & 13.78 & 15.73 & 12.39669421 & 3.5673 & \(6.451\times 10^{-3}\) \\ \cline{2-6}  & 200 & 25.9 & 29.05 & 10.84337349 & 3.2324 & \(4.454\times 10^{-3}\) \\ \cline{2-6}  & 300 & 36.56 & 40.02 & 8.645677161 & 2.9038 & \(3.408\times 10^{-2}\) \\ \cline{2-6}  & 400 & 50.4 & 53.1 & 5.084745763 & 3.0485 & \(2.532\times 10^{-2}\) \\ \hline \multirow{4}{*}{Onset rate 40} & 100 & 16.98 & 18.786 & 9.613541999 & 3.8058 & \(5.403\times 10^{-3}\) \\ \cline{2-6}  & 200 & 30.76 & 34.86 & 11.76133104 & 4.0835 & \(6.358\times 10^{-3}\) \\ \cline{2-6}  & 300 & 45.13 & 48.02 & 6.018325698 & 2.0805 & \(4.456\times 10^{-2}\) \\ \cline{2-6}  & 400 & 60.8 & 63.98 & 4.97030322 & 4.3034 & \(9.308\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: \(t\)-Test for makespan between HWACO and MIN-MIN.