# An Improved Artificial Ecosystem Algorithm for Economic Dispatch with Combined Heat and Power Units
## 4 Simulation Results
### Implementation for Case 1  
The suggested MAEA and basic AEA are employed to solve the ED with CHPUs in order to minimize fuel expenditures without accounting for losses. Table 1 depicts the optimal operating parameters of the POUs, CHPUs, and HOUs depending upon the suggested MAEA and the essential AEA in this instance. According to this data, the suggested MAEA achieves remarkable results by having the lowest fuel costs of 10,092.18 USD/h. To obtain these circumstances, the proposed MAEA sets the operational settings to 44.76, 98.56, 112.68, 209.82, 94.19, and 40 MW for the power outputs and 27.18, 74.99, and 47.82 MWth for the heat units. The basic AEA, on the other hand, attains fuel costs of 10,092.41 USD/h.  
In addition, Figure 4 displays the obtained costs for all simulated runs of the proposed MAEA and the basic AEA of Case 1. 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 0.0023% to 0.89%.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Outputs** & **AEA** & **Proposed MAEA** \\ \hline \multirow{4}{*}{Power-only units} & Pg 1 & 44.70016 & 44.75768 \\ \cline{2-4}  & Pg 2 & 98.56597 & 98.56182 \\ \cline{2-4}  & Pg 3 & 112.681 & 112.6768 \\ \cline{2-4}  & Pg 4 & 209.8095 & 209.8153 \\ \hline \multirow{2}{*}{CHP 1} & Pg 5 & 94.24102 & 94.18733 \\ \cline{2-4}  & Hg 5 & 26.88296 & 27.18475 \\ \hline \multirow{2}{*}{CHP 2} & Pg 6 & 40.00238 & 40.00106 \\ \cline{2-4}  & Hg 6 & 74.95064 & 74.99904 \\ \hline Heat-only unit & Hg 7 & 48.1664 & 47.81621 \\ \hline \multicolumn{2}{c}{Costs (USD/h)} & 10,092.41375 & 10,092.18153 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Optimal operational settings and related costs of the proposed MAEA and the basic AEA of Case 1.  
Based on that outcome in Figure 4, Table 2 records the robustness metrics of the proposed MAEA and the basic AEA of Case 1 in terms of the minimum, mean, maximum, and standard deviation. 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 0.0023, 0.145, 0.892, and 97.31%, respectively.  
In addition, Figure 5 displays the convergence rates of the proposed MAEA and the basic AEA related to the best run, worst run, and the average of all simulated runs. As demonstrated, the suggested MAEA has superior convergence features in its evolution in terms of lowering fuel expenditures throughout the duration of iterations. Despite achieving lower fitness values in the first 130 iterations, the AEA remained in a local optimal zone, particularly for its best run. The difference between the best run, worst run, and the average of all runs of the MAEA and AEA of Case 1 is shown in Figure 6, confirming the considerable improvement of the proposed MAEA after about 47%, 7%, and 20% of the total number of iterations for the average, best, and worst situations.