## 5 Comparative Results and Analysis
### Test case 1
#### Test case 2  
In this case study, a non-convex system with seven generating units was investigated, and the testing performances of several optimization strategies were compared. Seven units consisting of four power-only units, two CHP units, and one heat-only unit made-up this system [6; 9; 11; 10; 20; 25; 34; 39]. Optimization results yielded power and heat demands of 600 MW and 150 MWth, respectively. For this case, the comparative performances of AIS [6], TVAC-PSO [9], CSO [10], EMA [11], IGA-NCM [13], HTS [34], GSO [39], GWO [45], and RCGA-I [49] are shown in Table 3. CSO [10], HTS [34], and RCGA-I [49] reported the lowest generation cost compared to other techniques, whereas EMA [11] reported the least amount of computation time. The AIS [6] techniques reported large generation costs and long computation times compared to the other algorithms. Figure 3 shows the total costs obtained by different optimization techniques for a load demand of 600 MW and a heat demand of 150 MWth. Out of all the techniques, CSO [10] gave the best results, whereas AIS [6] gave the worst results for this case study. Figure 3: Total costs for load demand of 600 MW and heat demand of 150 MWth. Figure 2: Total costs for load demand of 200 MW and heat demand of 115 MWth. _Test Case 3_  
In this case, comparative results are shown in Table 4 for a large test data set consisting of twenty-four units (thirteen power-only units, six CHP units, and five heat-only units) [10; 11; 12; 13; 17; 18; 22; 26; 34; 37]. All the algorithms were tested for power and heat demands of 2350 MW and 1250 MWth, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Output** & **CSO** & **EMA** & **WOA** & **IGA-** & **HOOA** & **HBJSA** & **HTS** & **ETLBOI-** & **TLBO** \\  & **[10]** & **[11]** & **[12]** & **[13]** & **[17]** & **[18]** & **[34]** & **PSO** [37] & **[44]** \\ \hline P1 & 448.7 & 628.31 & 628.3185 & 628.318 & 538.5587 & 448.818 & 539.5724 & 458.4 & 628.324 \\ \hline P2 & 225.2 & 299.18 & 299.1993 & 299.198 & 300.2175 & 299.2188 & 298.9487 & 291.93 & 298.7686 \\ \hline P3 & 299.2 & 299.16 & 299.1993 & 29.1665 & 301.08255 & 300.7211 & 297.9085 & 228.1 & 298.9086 \\ \hline P4 & 109.86 & 109.86 & 109.8665 & 109.867 & 159.777 & 60.10963 & 110.082 & 93.74 & 110.1919 \\ \hline P5 & 109.86 & 109.8665 & 109.8665 & 109.866 & 63.2173 & 159.7451 & 110.2645 & 180 & 110.0846 \\ \hline P6 & 159.73 & 109.865 & 109.8665 & 60 & 60.6889 & 159.7769 & 110.2381 & 124.06 & 110.1379 \\ \hline P7 & 159.73 & 60 & 109.8665 & 109.866 & 160.20652 & 159.7718 & 110.2745 & 115.92 & 110.1045 \\ \hline P8 & 159.73 & 109.86 & 60.00003 & 109.823 & 111.5383 & 60 & 110.2452 & 116.68 & 110.2444 \\ \hline P9 & 109.86 & 109.856 & 109.8665 & 109.852 & 11.25395 & 159.751 & 110.1592 & 180 & 110.1992 \\ \hline P10 & 40 & 40 & 40.00003 & 40.0001 & 40 & 77.41183 & 77.3992 & 65.38 & 77.4989 \\ \hline P11 & 77.399 & 77.019 & 76.9485 & 77.0316 & 40.00025 & 40.00109 & 77.8364 & 40 & 77.7367 \\ \hline P12 & 92.399 & 55 & 55.00003 & 55.0098 & 55.657936 & 55.00862 & 55.0023 & 79.44 & 55.1036 \\ \hline P13 & 55 & 55 & 55.00003 & 55 & 55.284 & 55.6611 & 55.0109 & 89.23 & 55.1107 \\ \hline P14 & 87.554 & 81 & 81.00003 & 81.0035 & 87.944 & 85.84419 & 81.0524 & 81 & 81.0624 \\ \hline P15 & 40 & 40 & 40.00165 & 40.0003 & 41.2662 & 42.75199 & 40.0015 & 40 & 40.3515 \\ \hline P16 & 90.609 & 81 & 81.00003 & 81.0003 & 84.034 & 95.88869 & 81.003 & 81.1 & 81.262 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Competitive results for a 24-unit system for the power and heat demands of 2350 MW and 1250 MWth.