## 4 Proposed Load Scheduling Model
### Artificial Hummingbird Optimization Algorithm
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**User** & **Pricing Schemes** & **Cost** & **Inconvenience** & **Peak of Power** \\ \hline \multirow{2}{*}{1} & ToU & 7.6185 & 45 & 4310 \\  & ACLPS & 0.6656 & 40 & 2310 \\ \hline \multirow{2}{*}{2} & ToU & 5.9438 & 46 & 2510 \\  & ACLPS & 0.5268 & 56 & 2510 \\ \hline \multirow{2}{*}{3} & ToU & 8.8058 & 37 & 2510 \\  & ACLPS & 0.7703 & 35 & 2510 \\ \hline \multirow{2}{*}{4} & ToU & 8.5507 & 53 & 2110 \\  & ACLPS & 0.5687 & 57 & 2110 \\ \hline \multirow{2}{*}{5} & ToU & 6.4792 & 31 & 2110 \\  & ACLPS & 0.4970 & 116 & 2110 \\ \hline \multirow{2}{*}{All} & ToU & 41.6497 & 358 & 5220 \\  & ACLPS & 13.4078 & 321 & 4620 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Compromise solutions for various users’ cases and pricing schemes based on VIKOR method. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**User** & **Cost** & **Inconvenience** & **Peak of Power** \\ \hline \multirow{2}{*}{1} & \(\downarrow\) 91 & \(\downarrow\) 11 & \(\downarrow\) 46 \\  & 2 & \(\downarrow\) 91 & \(\uparrow\) 22 & - \\  & 3 & \(\downarrow\) 91 & \(\downarrow\) 05 & - \\  & 4 & \(\downarrow\) 93 & \(\uparrow\) 7.5 & - \\  & 5 & \(\downarrow\) 92 & \(\uparrow\)274 & - \\  & All & \(\downarrow\) 68 & \(\downarrow\) 10 & \(\downarrow\) 12 \\ \hline \end{tabular}
\end{table} 
Table 8: Percentage comparison of criteria values of ACLPS versus ToU for different users. pricing rate is reduced from 5220 (before scheduling) to 4310 W (after scheduling), which is about 17% reduction. Furthermore, based on ACLPS, more peak reduction is gained and is around 55% (2310 W). For cost saving of the first user, the energy cost before scheduling is about R11.419 while after implementing an optimal scheduling, the cost reduces to R7.612 (about 33%) and R0.665 (about 94%) for ToU and ALCPS, respectively. ACLPS offers high-cost reduction compared to ToU, since ACLPS provides a lower-consumption user profile with higher cost reduction, whereas a high-energy-consumption user receives lower cost reduction. For the second user, the energy consumption is presented in Figure 3; the peak consumption for optimal energy consumption for both ToU and ACLPS is about 2510 W, while before scheduling, it is 4935 W (about 49% reduction). The cost saving of the second user is about 43% (from R10.453 to R5.9438) and 94% (from R10.453 to R 0.5268) for ToU and ACLPS, respectively. The energy consumption for the third, fourth, and fifth users for both pricing schemes are shown in Figures 4-6, and the peak energy saving is 43%, 56%, and 38%, respectively. Moreover, the cost saving for the third, fourth, and fifth users based on ToU are 24%, 38%, and 38%, respectively. Based on ACLPS, the cost saving for the same users above are 93%, 95%, and 95%, respectively. Figure 4: Power consumption without and with scheduling for ToU and ACLPS for third user. Figure 5: Power consumption without and with scheduling for ToU and ACLPS for fourth user. Figure 6: Power consumption without and with scheduling for ToU and ACLPS for fifth user. The synchronized multi-user cooperative load scheduling (SMUCLS) makes all users work together for optimal load scheduling. The results of the five users are presented in Figure 7; the peak consumption based on ToU is reduced from 14,525 to 5220 W for about 64% saving, while the cost saving is 40% (reduced from R70.233 to 41.649). For the ACLPS pricing rate, the peak energy consumption is reduced to 4620 W for around 68% peak saving while the cost saving becomes about 81% (R13.407). ACLPS based on the proposed scheduling method (MAHA-MEREC-VIKOR) provides superior cost and peak reduction while maintaining the user's preferences. Accordingly, both the utility company and users get benefited from the proposed scheduling method. ## 6 Validating the Proposed Load Scheduling Optimization Problem

Seeking to highlight the significance of the proposed scheduling approach, a comparison is formulated with the contribution in [16].