# Performance Analysis of Partitioned Step Particle Swarm Optimization in Function Evaluation
## 3 Data and Results
### Benchmark Functions
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline  & **PSPSO** & **PSCO** & **CPSO** & **WFCSO** & **APSO** & **SFPSO** & **PSO** & **PSSO** & **CPSO** & **CFSO** & **WFCSO** & **APSO** & **SofSO** & **PSO** \\ \hline \multirow{4}{*}{\(H\)} & **mean** & \(0.0\times 10^{4}\) & \(56\times\) & \(67\times 10^{2}\) & \(7.0\times 10^{4}\) & \(35\times 10^{6}\) & \(14\times\) & \(3.3\times 10^{6}\) & **mean** & \(13.0\times 10^{4}\) & \(0.0\times 10^{6}\) & \(1.9\times 10^{1}\) & \(1.8\times 10^{4}\) & \(2.8\times 10^{4}\) & \(1.9\times 10^{2}\) & \(1.8\times 10^{2}\) & \(1.8\times 10^{2}\) \\  & **std** & \(0.0\times 10^{4}\) & \(0.0\times 10^{2}\) & \(2.5\times 10^{2}\) & \(2.2\times 10^{4}\) & \(1.8\times 10^{4}\) & \(0.0\times 10^{2}\) & \(1.8\times 10^{4}\) & **std** & \(3.3\times 10^{4}\) & \(0.0\times 10^{6}\) & \(6.8\times 10^{4}\) & \(7.2\times 10^{4}\) & \(2.5\times 10^{4}\) & \(2.0\times 10^{4}\) \\  & **time** & 2.997 & **5.746** & 2.84 & 3.264 & 1.805 & 2.423 & 1.778 & **time** & 4.741 & 10.487 & 5.996 & 5.933 & 3.07 & **4.845** & 3.837 \\ \hline \multirow{4}{*}{\(H\)} & **mean** & \(5.0\times 10^{4}\) & \(2.5\times 10^{4}\) & \(1.7\times 10^{4}\) & \(89\times 10^{4}\) & \(4.6\times 10^{4}\) & \(15.5\times 10^{4}\) & \(11.5\times 10^{4}\) & **mean** & \(2.2\times 10^{4}\) & \(3.6\times 10^{4}\) & \(5.5\times 10^{4}\) & \(4.3\times 10^{4}\) & \(5.3\times 10^{4}\) & \(6.4\times 10^{4}\) & \(6.4\times 10^{4}\) \\  & **std** & \(16.2\times 10^{4}\) & \(3.5\times 10^{4}\) & \(2.5\times 10^{4}\) & \(72.3\times 10^{4}\) & \(5.5\times 10^{4}\) & \(7.2\times 10^{4}\) & \(72.5\times 10^{4}\) & **time** & \(6.2\times 10^{4}\) & \(3.6\times 10^{4}\) & \(1.8\times 10^{4}\) & \(4.7\times 10^{4}\) & \(8.7\times 10^{4}\) & \(7.6\times 10^{4}\) & \(7.6\times 10^{4}\) \\  & **time** & 2.666 & **5.966** & 3.082 & 1.957 & 2.262 & 2.068 & **time** & \(6.6\times 10^{4}\) & \(6.2\times 10^{4}\) & \(6.8\times 10^{4}\) & **time** & \(6.8\times 10^{4}\) & \(6.0\times 10^{4}\) & \(6.3\times 10^{4}\) & \(6.0\times 10^{4}\) & \(6.4\times 10^{4}\) \\ \hline \multirow{4}{*}{\(H\)} & **mean** & \(0.00\times 10^{4}\) & \(0.0\times 10^{4}\) & \(3.3\times 10^{4}\) & \(4.9\times 10^{4}\) & \(3.3\times 10^{4}\) & \(10.0\times 10^{4}\) & \(3.3\times 10^{4}\) & \(10.0\times 10^{4}\) & \(3.3\times 10^{4}\) & **time** & \(0.00\times 10^{4}\) & \(6.9\times 10^{4}\) & \(2.3\times 10^{4}\) & \(7.1\times 10^{4}\) & \(7.6\times 10^{4}\) & \(8.7\times 10^{4}\) & \(3.2\times 10^{4}\) \\  & **std** & \(0.0\times 10^{4}\) & \(0.0\times 10^{4}\) & \(18.7\times 10^{4}\) & \(3.2\times 10^{4}\) & \(1.8\times 10^{4}\) & \(1.8\times 1 Figure 4a shows the average ranking of the algorithms with increasing dimension, where PSPSO almost remained first in rank in function evaluation with a slightly improved performance. It can be noted that both the APSO and PSPSO, both with downward slope, had better performance when the dimension was increased. This can also mean the other way around, that the other algorithms' performance worsened, especially for the CPSO with an increased average ranking (upward slope). Figure 4b shows the average computational time of every variant with increasing dimension. It also shows that the computational times of PSPSO, CPSO, WICPSO, ScPSO, and PSO were not that far from each other, even in the increase in dimension. On the other hand, PSOCO was found to be always more than twice the computational time of the other variants. The computational time PSO variants are magnified in Figure 4c, and the effect in the increase in dimension is seen linear for all but with different slopes. The proposed PSPSO had the lowest slope followed by APSO, PSO, ScPSO, WICPSO, CPSO, and PSOCO. Although the average computational time for PSPSO was the lowest, its overall ranking for computational time