# Performance Analysis of Partitioned Step Particle Swarm Optimization in Function Evaluation
## 3 Data and Results
### Unit Commitment Performance  
Table 11 shows the result of the UC from the PSPSO with a total UC cost of $563,934.16. The total fuel cost is $559,844.16 and the total start-up cost is $4,090. This result is the same commitment of units with the other published literatures but with discrepancies in the dispatch and/or costs. Table 12 shows the results of the PSPSO compared with algorithms in the literature, which also solved the 10-unit UC problem. Although the maximum iteration is 1000, the algorithm terminated around the 400 th iteration with an average time of 3.57 s. The best result of the PSPSO reached the minimum solution found in the literature. The average cost of the algorithm was 104.33 more than the best cost, which was a 0.018% difference. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**hour\(\backslash\)unit** & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** & **Fuel Cost** & **SU Cost** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 11: Unit Commitment schedule and costs. Figure 4: PSO variants in increasing dimension for (**a**) average rank in function evaluation, and (**b**) average computational time. (**c**) Enlargement of (**b**). Moreover, some algorithms were three times slower than the proposed PSPSO, and only one algorithm was faster than the proposed. Table 13 shows the results of the 10-unit system multiples with the termination criteria changed to maximum iteration for all algorithms. In almost all cases, the PSPSO performed the best. However, in the 20-unit and 60-unit systems, the WICPSO was able to outperform PSPSO in finding the best cost, yet PSPSO still was the best in terms of the average cost, worst cost, and computational time. The performance of WICPSO was already expected because it has already been used to solved this test system in the literature, but the fact that PSPSO almost always demonstrates the best performance in all the multiples, costs, and computational time makes PSPSO a viable and competitive algorithm in solving a unit commitment problem. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **PSO** & **CPSO** & **PSOCO** & **WICPSO** & **PSPSO** \\ \hline best & 564,112 & 564,278 & 566,485 & 563,974 & 563,934 \\ average & 564,966 & 564,892 & 569,874 & 564,623 & 564,039 \\ worst & 566,891 & 566,847 & 572,136 & 566,127 & 564,214 \\ time & 24.05 & 21.93 & 35.86 & 19.94 & 7.24 \\  & & **30-unit DUC** & & & \\ \hline best & 1,124,723 & 1,125,119 & 1,134,358 & 1,124,639 & 1,124,663 \\ average & 1,126,983 & 1,126,516 & 1,140,327 & 1,126,166 & 1,125,221 \\ worst & 1,131,985 & 1,129,734 & 1,144,489 & 1,125,843 & 1,126,375 \\ time & 46.01 & 42.26 & 65.07 & 38.14 & 27.80 \\  & & **40-unit DUC** & & & \\ \hline best & 2,249,498 & 2,250,868 & 2,273,559 & 2,246,659 & 2,245,909 \\ average & 2,254,239 & 2,255,014 & 2,282,112 & 2,249,593 & 2,248,930 \\ worst & 2,257,990 & 2,260,150 & 2,290,050 & 2,252,665 & 2,250,830 \\ time & 96.10 & 87.31 & 131.00 & 86.45 & 85.65 \\  & & **60-unit DUC** & & & \\ \hline best & 3,379,482 & 3,376,946 & 3,407,486 & 3,367,881 & 3,368,371 \\ average & 3,384,379 & 3,385,574 & 3,420,476 & 3,373,715 & 3,371,589 \\ worst & 3,392,098 & 3,392,595 & 3,430,814 & 3,379,109 & 3,375,929 \\ time & 164.85 & 152.47 & 217.43 & 176.86 & 146.83 \\  & & **80-unit DUC** & & & \\ \hline best & 4,508,627 & 4,509,984 & 4,550,595 & 4,495,549 & 4,495,053 \\ average & 4,517,806 & 4,521,129 & 4,567,651 & 4,502,553 & 4,497,875 \\ worst & 4,533,652 & 4,536,629 & 4,585,982 & 4,509,585 & 4,500,931 \\ time & 235.21 & 214.21 & 295.07 & 240.66 & 235.68 \\  & & **100-unit DUC** & & & \\ \hline best & 5,633,268 & 5,643,919 & 5,691,819 & 5,622,310 & 5,619,793 \\ average & 5,682,797 & 5,657,421 & 5,719,049 & 5,630,848 & 5,626,222 \\ worst & 5,669,649 & 5,669,151 & 5,826,662 & 5,636,712 & 5,631,809 \\ time & 318.28 & 280.12 & 368.28 & 309.69 & 319.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Benchmark unit commitment (UC) problem.