# An Improved Artificial Ecosystem Algorithm for Economic Dispatch with Combined Heat and Power Units
## 4 Simulation Results
### Implementation for Case 2  
The suggested MAEA and basic AEA are employed to solve the ED with CHPUs in order to minimize fuel expenditures, taking into consideration the power losses. Table 3 illustrates the optimal operating parameters of the POUs, CHPUs, and HOUs depending upon the suggested MAEA and the essential AEA in this instance. The suggested MAEA achieves remarkable results by having the lowest fuel costs of 10,095.02 USD/h. To obtain these circumstances, the proposed MAEA sets the operational settings to 45.17, 98.54, 112.69, 209.82, 94.6, and 40 MW for the power outputs and 24.73, 75, and 50.27 MWth for the heat units. The basic AEA, on the other hand, attains fuel costs of 10,092.18 USD/h. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Costs (USD/h)** & **AEO** & **Proposed MAEA** & **Improvement \%** \\ \hline Minimum & 10,092.41 & 10,092.18 & 0.002301 \\ \hline Mean & 10,108.01 & 10,093.32 & 0.145364 \\ \hline Maximum & 10,186.05 & 10,095.17 & 0.892249 \\ \hline Standard Deviation & 27.37743 & 0.734646 & 97.3166 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Robustness metrics of the proposed MAEA and the basic AEA of Case 1. Figure 4: Obtained costs for all simulated runs of the proposed MAEA and the basic AEA of Case 1. In addition, Figure 7 displays the obtained costs for all simulated runs of the proposed MAEA and the basic AEA of Case 2. As shown, the superior performance of the proposed MAEA is declared over the basic AEA in all simulated runs. The improvement percentage ranges from the very small value of 0.0009% to 0.73%. Based on the outcome in Figure 7, Table 4 records the robustness metrics of the proposed MAEA and the basic AEA of Case 2. As shown, superior resilience performance related to the proposed MAEA is declared over the basic AEA. The proposed MAEA acquires the lowest minimum, mean, maximum, and standard deviation of 10,092.18, 10,093.32, 10,095.17, and 0.734646 USD/h with improvements of 0.0009, 0.115, 0.73, and 96.63%, respectively. Figure 5: Convergence rates of the proposed MAEA and the basic AEA of Case 1. Figure 6: Percentage difference for the best and worst run and the average of all runs of the MAEA and AEA of Case 1. In addition, comparisons are made with the results of powerful optimization algorithms used in solving ED problems in the literature. For this purpose, Table 5 displays the comparative assessment of the AEA and the proposed MAEA with reported algorithms of TVAC-PSO [38], IGA [39], ECSA [40], PSO [41], TVAC-PSO [41], LCA [42], CPSO [43], WVO [44], WVO-PSO [44], RCGA [45], BCO [45], and DE [43; 46]. As shown, the suggested MAEA provides better-performing features compared with the others. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Costs (USD/h)** & **AEO** & **Proposed MAEA** & **Improvement \%** \\ \hline Minimum & 10,095.11736 & 10,095.02453 & 0.000919468 \\ \hline Mean & 10,107.45372 & 10,095.84203 & 0.114882388 \\ \hline Maximum & 10,172.61916 & 10,097.86343 & 0.734872038 \\ \hline Standard Deviation & 23.09259359 & 0.777264037 & 96.63414144 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Robustness metrics of the proposed MAEA and the basic AEA of Case 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Outputs** & **AEA** & **Proposed MAEA** \\ \hline \multirow{4}{*}{Power-only units} & Pg 1 & 45.17078 & 45.17078 \\ \cline{2-4}  & Pg 2 & 98.53982 & 98.53982 \\ \cline{2-4}  & Pg 3 & 112.6899 & 112.6899 \\ \cline{2-4}  & Pg 4 & 209.8158 & 209.8158 \\ \hline \multirow{2}{*}{CHP 1} & Pg 5 & 94.59907 & 94.59907 \\ \cline{2-4}  & Hg 5 & 24.72766 & 24.72766 \\ \hline \multirow{2}{*}{CHP 2} & Pg 6 & 40 & 40 \\ \cline{2-4}  & Hg 6 & 75.00086 & 75.00086 \\ \hline Heat-only unit & Hg 7 & 50.27148 & 50.27148 \\ \hline \multicolumn{2}{c}{Costs (USD/h)} & 10,095.12 & 10,095.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimal operational settings and related costs of the proposed MAEA and the basic AEA of Case 2. Figure 7: Obtained costs for all simulated runs of the proposed MAEA and the basic AEA of Case 2.