## 4 Proposed Load Scheduling Model
### Artificial Hummingbird Optimization Algorithm
The pairwise comparison of criteria values of ACLPS versus ToU for various users' data set is tabulated in Table 8. According to Table 8, the ACLPS pricing scheme offers progress relative to ToU with the minimum cost, inconvenience, and peak of power values for the first and all-users data set. The ACLPS pricing scheme offers reduction as compared to the ToU in terms of the cost, inconvenience, and peak around 91%, 11%, and 46% for the first user, respectively. Meanwhile, they are 68%, 10%, and 12% for the all-users data set. In the second and fifth users' data set, the ACLPS pricing scheme offers an enhancement in terms of cost as compared to the ToU with reduction around 91% and 92%, respectively. The ACLPS and ToU pricing schemes for the second, third, fourth, and fifth users realize the same peak of power values around 2510 W, 2510 W, 2110 W, and 2110 W, respectively. The inconvenience values obtained based on ACLPS for the second and fifth users were \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**User** & **Pricing Schemes** & \(\mathbf{w_{1}}\) & \(\mathbf{w_{2}}\) & \(\mathbf{w_{3}}\) \\ \hline \multirow{2}{*}{1} & ToU & 0.341 & 0.346 & 0.313 \\  & ACLPS & 0.576 & 0.149 & 0.275 \\ \hline \multirow{2}{*}{2} & ToU & 0.359 & 0.346 & 0.295 \\  & ACLPS & 0.703 & 0.025 & 0.272 \\ \hline \multirow{3}{*}{3} & ToU & 0.169 & 0.533 & 0.298 \\  & ACLPS & 0.372 & 0.311 & 0.317 \\ \hline \multirow{3}{*}{4} & ToU & 0.293 & 0.295 & 0.412 \\  & ACLPS & 0.631 & 0.001 & 0.368 \\ \hline \multirow{3}{*}{5} & ToU & 0.01 & 0.845 & 0.145 \\  & ACLPS & 0.641 & 0.12 & 0.24 \\ \hline \multirow{3}{*}{All} & ToU & 0.307 & 0.308 & 0.384 \\  & ACLPS & 0.67 & 0.042 & 0.288 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The weights of various criteria for different pricing schemes and data sets. greater than those values achieved by the ToU pricing scheme. Finally, as compared to the ToU, the third and fourth users with the ACLPS have realized a cost reduction around 91% and 93%, respectively. Meanwhile, the inconvenience is decreased and increased around 5% and 7.5% for the third and fourth users, respectively. Figures 2-7 depict different comparisons of load management prior to and after using the MAHA-MEREC-VIKOR to optimize the user load management of ToU and ACLPS regarding different users, with the non-cooperative (individual work) mode as mentioned above. These peak loads of different users' profile for both ToU and ACLPS demonstrate the superiority of the proposed model as compared to the original or the user preferred operation time. For the first user as mentioned in Figure 2, the peak load for the ToU \begin{table}
\begin{tabular}{l l l l} \hline \hline
**User** & **Pricing Schemes** & **Acceptable Advantage** & **Acceptable Stability** \\ \hline \multirow{2}{*}{1} & ToU & ✓ & ✓ \\  & ACLPS & \(\times\) & - \\ \hline \multirow{2}{*}{2} & ToU & \(\times\) & - \\  & ACLPS & \(\times\) & - \\ \hline \multirow{2}{*}{3} & ToU & \(\times\) & - \\  & ACLPS & \(\times\) & - \\ \hline \multirow{2}{*}{4} & ToU & ✓ & ✓ \\  & ACLPS & \(\times\) & - \\ \hline \multirow{2}{*}{5} & ToU & ✓ & ✓ \\  & ACLPS & \(\times\) & - \\ \hline \multirow{2}{*}{All} & ToU & ✓ & ✓ \\  & ACLPS & \(\times\) & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Acceptable advantage and acceptable stability of VIKOR model regarding pricing plans and various users.