## 5 Comparative Results and Analysis  
### Test case 1  
The first case considered the test data of a four-unit system with one available power-only unit, two CHP units, and one available heat-only unit. The test data for this case is taken from the articles [7; 8; 9; 11; 13; 27; 32; 37]. All the optimization techniques were tested for the power and heat demands of 200 MW and 115 MWth, respectively. Table 2 shows the comparative results of FA [7], MADS-DACE [8], TVAC-PSO [9], CSO [10], EMA [11], IGA-NCM [13], SFS [27], ETLBOPSO [37], and GWO [45] for the load demand of 200 MW and heat demand of 115 MWth. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Ref. No.**} & \multirow{2}{*}{**Optimization Techniques**} & \multirow{2}{*}{**Constraints**} & \multirow{2}{*}{**Taken Case Study for Optimization**} & \multirow{2}{*}{**Advantages and Disadvantages**} \\  & & & & & & & & \\ \hline \multirow{3}{*}{[44] 2014} & Teaching–learning-based optimization & \multirow{3}{*}{Valve-point loading} & \multirow{3}{*}{7, 24, and 48 units} & For multiobjective problems, this approach effectively enhances the overall performance of the solutions. \\  & & & & & & & \\ \hline \multirow{3}{*}{[45] 2016} & \multirow{3}{*}{Grey wolf optimization} & Ramp rate, valve point, and spinning reserve & \multirow{3}{*}{4, 7, 11, and 24 units} & The recommended method works more consistently and with higher-quality solutions. \\ \hline \multirow{3}{*}{[46] 2013} & \multirow{3}{*}{Fuzzy logic} & Ramp-rate limits & \multirow{3}{*}{7 units} & This technique has the potential to solve a larger, multi-objective problem. \\  & & & & & & \\ \hline \multirow{3}{*}{[47] 2005} & \multirow{3}{*}{IGA-MU} & Change fuels and valve point & \multirow{3}{*}{4-, 7-unit system} & This approach has a straightforward idea that makes it easier to use and more successful. \\  & & & & & & \\ \hline \multirow{3}{*}{[48] 2020} & \multirow{3}{*}{Cuckoo optimization} & Power generation and heat limits & \multirow{3}{*}{4 units} & Enhances the exploration on the search space \\  & & & & & & & \\ \hline \multirow{3}{*}{[49] 2015} & Coded genetic algorithm & Valve point and transmission losses & \multirow{3}{*}{4, 5, 7, and 24 units} & Effective for small and large test data \\  & & & & & & & \\ \hline \multirow{3}{*}{[50] 2019} & MPHS & \multirow{3}{*}{ETLBOPSO [37], and GWO [45] for the load demand of 200 MW and heat demand of 115 MWth.} & \multirow{3}{*}{Toinprove the efficiency and simulation solution, Gaussian random variables were used.} \\  & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Results of Generating Units**} & \multirow{2}{*}{**FA [7]**} & \
\begin{tabular}{c} **MADS–DACE** \\ [8] \\ \end{tabular} & \multirow{2}{*}{**TVAC-PSO [9]**} & \multirow{2}{*}{**CSO**} & **EMA** &
\begin{tabular}{c} **IGA-** \\ [10] \\ \end{tabular} & \multirow{2}{*}{**NCM**} & \multirow{2}{*}{**SFS**} & **ETLBOI** & **GWO** \\  & & & & & & & & \\ \hline P1 (MW) & 0.0014 & 0 & 0 & 0 & 0 & 0 & 0.8473 & 0 \\ \hline P2 (MW) & 159.99 & 160 & 160 & 160 & 160 & 160 & 160 & 159.338 & 160 \\ \hline P3 (MW) & 40 & 40 & 40 & 40 & 40 & 40 & 40 & 39.8150 & 40 \\ \hline H2 (MWh) & 40 & 40 & 40 & 40 & 40 & 40 & 40 & 40 & 40 \\ \hline H3 (MWh) & 75 & 75 & 75 & 75 & 75 & 75 & 75 & 75 & 75 \\ \hline H4 (MWh) & 0.0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.18 & 0 \\ \hline Total cost (S) & 9257.1 & 9257.07 & 9257.07 & 9257.07 & 9257.07 & 9257.07 & 9257.07 & 9178.9934 & 9257.07 \\ \hline CPU time (s) & 1.25 & 3.27 & 1.78 & 1.18 & 0.9846 & 1.44 & 3.78 & 1.59 & 2.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results obtained for the four generating units with two co-generation units and one heat unit for the load demand of 200 MW and 115 MWth.