## 4 Case Study and Proof of Concept
### Test System 1
Each fitness function is minimized seriatim using the proposed CSAOA for both the load profiles, and their minimal values obtained are recorded and displayed in Table 3. The results obtained in Table 6 point toward the following inferences:  
1. The minimum generation cost is found to be USD 296,744 using CSAOA, which is further reduced to USD 293,098 when DSM integrated load demand is accounted for. 2. The minimum emission is 54 tons and 31 tons without and with DSM, respectively. 3. When ECED is assessed to find a trade-off solution between least cost and pollutants (using \(\mu\) = 0.5), the solution set is found to be (USD 32,4067, 134 tons) which is further improved to (USD 322,365.5, 133 tons) when DSM incorporated load demand model is considered. Figure 3: Test system 1 load demand both with and without DSM. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Without DSM** & **With DSM** \\ \hline
**Total Demand (kW)** & 7171 & 7171 \\ \hline
**Mean Demand (kW)** & 298.7 & 298.7 \\ \hline
**Peak Demand (kW)** & 399 & 334.62 \\ \hline
**Reduction in Peak (\%)** & - & 16.14\% \\ \hline
**Load Factor** & 0.7489 & 0.8929 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Advantages of DSM implementation. Thereafter, the hourly contributions of the four DERs are analyzed during the minimization of ECD, EMD, and ECED (with \(\mu=0.5\)). Figure 4 above shows the hourly output of CHP1, CHP2, CHP3, and G1. The DERs (G1) with less values of cost coefficients are utilized more during ECD minimization and the DERs (CHP1) with less values of emission coefficients are utilized more during EMD minimization. When ECED is minimized giving equal weightage to both cost and emission, a balanced amount of all the DERs is utilized to deliver the power during every hour. Figure 5 represents the percentage utilization of DERs during different fitness functions, as discussed in Figure 4. Only 33% of the total capacity of CHP1 is utilized when ECD is minimized, as the cost coefficients of CHP1 are high, whereas almost 100% of the total capacity of G1 is utilized for the same, as G1 has low-cost coefficients. On the contrary, CHP1 does not emit any harmful toxic pollutants during its operation, whereas fossil-fueled G1 has high emission coefficients. Hence, when EMD is minimized, 90% of CHP1 and only 27% of G1 is utilized. CHP3 is utilized to the maximum extent for all the fitness functions, as it has both low cost and emission coefficients compared with the rest. Table 7 shows the measures of central tendencies when ECED was evaluated for 30 individual trials using CSA, AOA and CSAOA. Hits refer to the number of times the minimum value of ECED was obtained among 30 trials. Lower values of standard deviation indicate the robustness of the algorithm. Along with the integration of the demand side management (DSM) technique, as outlined in Section 2, utilizing AOA, the test system's expected load demand is adjusted. Figure 6 displays the recently reorganized load requirement of the system. DSM offers a significant advantage, resulting in a 12.46% reduction in peak load, from 225 MW to 207 MW, and an increase in the load factor from 0.8291 to 0.8996. The statistical data are additionally documented in Table 12. It is significant to note that in both the pre- and post-DSM scenarios, at the end of the day, total and average load are the same.