## 4 Proposed Load Scheduling Model
### Artificial Hummingbird Optimization Algorithm
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multirow{2}{*}{**Seq.**} & \multicolumn{4}{c}{**Condition**} & \multirow{2}{*}{**Compromise Solution**} \\ \cline{2-2} \cline{4-11}  & & **C1** & & **C2** & & & & & & \\ \hline
1 & \(\surd\) & \(\surd\) & \(\surd\) & \(A(1)\) is the compromise solution. & & & & & \\
2 & \(\surd\) & \(\times\) & \(A(1)\)and\(A(2)\) are the compromise solutions. & & & & & & \\
3 & \(\times\) & - & & & & & & & \\ \hline \end{tabular} \(\surd\): satisfied, \(\times\): not satisfied.

\end{table} 
Table 1: Compromise solutions according to list of satisfied conditions. \begin{table}
\begin{tabular}{c l c c c c c c c c c} \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Device Name**} & \multicolumn{6}{c}{**Power Rate (kW)**} & \multicolumn{6}{c}{**Duration (min/day)**} \\ \cline{3-11}  & & \(H_{1}\) & \(H_{2}\) & \(H_{3}\) & \(H_{4}\) & \(H_{5}\) & \(H_{1}\) & \(H_{2}\) & \(H_{3}\) & \(H_{4}\) & \(H_{5}\) \\ \hline
1 & Microwave & 0.8 & 1.5 & 0.6 & 1.2 & 0.6 & 6 & 8 & 6 & 6 & 9 \\ \hline
2 & Stove & 2.2 & 2 & 2.4 & 2 & 2 & 54 & 45 & 48 & 62 & 36 \\ \hline
3 & Electrical Water Heater & 2 & 2 & 2 & 2 & 2 & 180 & 120 & 180 & 180 & 180 \\ \hline
4 & Dishwasher Machine & 2 & 2.4 & 2.2 & 2 & 2 & 60 & 60 & 60 & 60 \\ \hline
5 & Clothes Dryer & 2 & 0.6 & 2 & 0.6 & 0.6 & 30 & 30 & 30 & 30 & 15 \\ \hline
6 & Vacuum Cleaner & 0.8 & 0.8 & 0.4 & 0.8 & 0.35 & 12 & 24 & 16 & 18 & 10 \\ \hline
7 & DVD Player & 0.025 & 0.025 & 0.025 & 0.015 & 0.015 & 120 & 180 & 120 & 120 & 120 \\ \hline \end{tabular}
\end{table} 
Table 2: Time intervals and rated consumption power users’ profile [16]. The optimal solutions of the Pareto front, which are produced by applying MAHA for the first and second users regarding both ToU and ACLPS pricing schemes, are tabulated in Appendix A (Table A1). It is worth mentioning that Table A1 includes 30 solutions related to the cost, inconvenience, and peak of power. According to Table A1, the minimum cost, inconvenience, and peak of the first and second users based on the ToU pricing scheme are (R7.618, 45 slots, 4310 W) and (R5.9438, 46 slots, and 2510 W), respectively. Meanwhile, the corresponding values based on the ACLPS pricing scheme are (R 0.6656, 40 slots, 2310 W) and (R 0.5268, 56 slots, and 2510 W). The ACLPS pricing scheme produces better results than ToU in terms of the cost, inconvenience, and peak of power for both the first and second users. Table A2 illustrates the Pareto front of triple-objective function values for the third and fourth users according to ToU and ACLPS pricing schemes. The MAHA based on the ACLPS pricing scheme produces a minimum cost and peak for the third user, around R 0.7703 and 2510 W, respectively. On the other hand, the MAHA based on the ToU pricing scheme offers R 8.8058 and 2510 W. The minimum cost and peak can be obtained by the MAHA for the fourth user's data set around R 8.5507 and 2110 W and R 0.5687 and 2110 W for ToU and ACLPS pricing schemes, respectively. According to Table A2, the ACLPS pricing scheme offers an enhancement in the cost and peak of power as compared to the ToU scheme for both the third and fourth users. In contrast, the ToU exhibits a little enhancement with inconvenience values compared to those obtained by the ACLPS pricing scheme for both the third and fourth users' data set. In general, the ACLPS is still superior to the ToU pricing scheme for the first, second, third, and fourth users. The optimal solutions produced by using the multi-objective optimization algorithm based on two different pricing schemes for the fifth user and all users combined together are tabulated in Table A3. For the fifth user case, the peak of power based on ACLPS and ToU pricing schemes is the same at 2110 W, while the cost was R 0.4970 and R 6.4792, respectively. Regarding all-users data set cases (cooperation mode), the ACLPS pricing scheme realizes advancement compared to ToU with minimum cost and peak values around R13.4078 and 4620 W, respectively.