# An Improved Artificial Ecosystem Algorithm for Economic Dispatch with Combined Heat and Power Units
## 4 Simulation Results
### Implementation for Case 4  
The suggested MAEA and basic AEA are employed to solve the ED with CHPUs to minimise fuel expenditures, taking into consideration the power losses. Table 9 illustrates the optimal settings of the POUs, CHPUs, and HOUs. According to this data, the suggested MAEA achieves remarkable results by having the lowest fuel costs of 118,134.96 USD/h. The basic AEA, on the other hand, attains fuel costs of 118,793.85 USD/h.  
In addition, Figure 13 displays the obtained costs for all simulated runs of the proposed MAEA and the basic AEA of Case 4. 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 0.55% to 3.87%.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Costs (USD/h)** & **AEO** & **Proposed MAEA** & **Improvement \%** \\ \hline Minimum & 118,881.4473 & 116,897.8879 & 1.668518838 \\ \hline Mean & 120,045.6955 & 118,004.3493 & 1.70047432 \\ \hline Maximum & 124,396.4722 & 119,424.0332 & 3.997250827 \\ \hline Standard Deviation & 1106.34051 & 597.0478043 & 46.03399236 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Robustness metrics of the proposed MAEA and the basic AEA of Case 3.  
Figure 10: Obtained costs for all simulated runs of the proposed MAEA and the basic AEA of Case 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Optimizer** & **Best Costs (USD/h)** & **Mean Costs (USD/h)** & **Worst Costs (USD/h)** \\ \hline Proposed MAEA & 116,897.8879 & 118,004.3493 & 119,424.0332 \\ \hline AEO & 118,881.4473 & 120,045.6955 & 124,396.4722 \\ \hline GSA [15] & 119,775.9 & - & - \\ \hline MRFO [47] & 117,336.9 & 117,875.4 & 118,217.5 \\ \hline CPSO [41] & 120,918.9 & - & - \\ \hline TVAC-PSO [41] & 118,962.5 & - & - \\ \hline MVO [47] & 117,657.9 & 118,724 & 119,249.3 \\ \hline SSA [47] & 120,174.1 & 121,110.2 & 122,636.8 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparative Results for Case 3 for the 48-Unit System.  
Figure 11: Convergence rates of the proposed MAEA and the basic AEA of Case 3.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Outputs** & **AEA** & \
\begin{tabular}{c} **Proposed** \\ **MAEA** \\ \end{tabular} & **Outputs** & **AEA** &
\begin{tabular}{c} **Proposed** \\ **MAEA** \\ \end{tabular} \\ \hline Pg 1 & 538.5587406 & 628.6477795 & Pg 32 & 38.76118435 & 63.12739336 \\ \hline Pg 2 & 224.500532 & 299.3039097 & Pg 33 & 88.66870343 & 146.019954 \\ \hline Pg 3 & 224.4082699 & 224.4413162 & Pg 34 & 42.77532917 & 50.56025758 \\ \hline Pg 4 & 159.7326419 & 110.1098241 & Pg 35 & 139.9313947 & 111.1809533 \\ \hline Pg 5 & 109.8653469 & 109.9778609 & Pg 36 & 64.33155077 & 41.38648745 \\ \hline Pg 6 & 110.0410418 & 109.9393484 & Pg 37 & 17.10618711 & 21.37570912 \\ \hline \hline \end{tabular}
\end{table}
Table 9: Optimal operational settings and related costs of the proposed MAEA and the basic AEA of Case 4.  
Figure 12: Percentage difference for the best, worst run, and the average of all runs of the MAEA and AEA of Case 3.