# Performance Analysis of Partitioned Step Particle Swarm Optimization in Function Evaluation
## 3 Data and Results  
### Variables and Parameter Setting  
Table 7 shows the results for varying \(c_{1}\) or \(c_{2}\) value from 1.00 to 2.50 (with 0.25 increments) while making the number of particles constant at 50 and varying the number of particles N (with 10 increments) while keeping the \(c_{1}\) or \(c_{2}\) value constant at 1.50. These are evaluated using all functions in Tables 2 and 3 with zero as optimal value.  
On the basis of the data in Table 7a, we can conclude that 1.50 is the most suitable constant parameter since it has the lowest mean, standard deviation, and computational time. Increasing the c value increases all the criteria values. Decreasing its value also increases the all the criteria values but not as much as increasing the c value.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & Objective & \(\min\Bigl{(}\sum_{t=1}^{T}Fuel(t)+SU(t)\Bigr{)}\) & & & & & & & & & \\  & & s.t. & & & & & & & & & & \\ \(Fuel(t)=\sum\limits_{i=1}^{ngen}UC_{i}(t)\Bigl{(}a_{i}P_{DG,i}^{2}(t)+b_{i}P_{DG, i}(t)+c_{i}\Bigr{)}\) & & & & & & & & & \\  & & & & & & & & & & & & & \\  & & & & & & & & & & & & & \\  & & & & & & & & & & & & & \\ \(LB_{i}(t)\leq P_{DG,i}(t)\leq UB_{i}(t)\) & & & & & & & & & & & \\ \(|P_{DG,i}(t)-P_{DG,i}(t-1)|\leq Rmpt_{DG,i}\) & & & & & & & & & & & \\ \(t_{ON,i}\leq MUT_{i}\) & ; & \(t_{OFF,i}\leq MDT_{i}\) & & & & & & & & & \\ \(SU_{i}(t)=\begin{cases}HSC_{i}&MDT_{i}\leq t_{OFF,i}\leq MDT_{i}+CSH_{i}\\ CSC_{i}&MDT_{i}+CSH_{i}<t_{OFF,i}\end{cases}\) & & & & & & & & & & \\ \(\sum\limits_{i=1}^{ngen}UC_{i}(t)\bigl{(}P_{max,i}(t)-P_{DG,i}(t)\bigr{)}\geq SR (t)\) & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Ten-unit unit commitment problem.  
\begin{table}
\begin{tabular}{c c c c|c c c c} \hline \hline  & & **(a) N = 50** & & & & **(b) C1 = C2 = 1.50** & \\ \hline
**C** & **Mean** & **Std Dev** & **Time (s)** & **N** & **Mean** & **Std Dev** & **Time(s)** \\ \hline
**1.00** & 65.6091 & 14.3104 & 8.773 & 30 & 1.0940 & 5.1989 & 5.303 \\
**1.25** & 30.4968 & 29.3233 & 8.020 & 40 & 0.0546 & 0.0282 & 6.353 \\
**1.50** & **0.0447** & **0.0006** & **7.625** & **50** & **0.0446** & **0.0006** & **7.591** \\
**1.75** & 2.5755 & 0.7062 & 9.687 & 60 & 0.0445 & 0.0002 & 8.868 \\
**2.00** & 13,050.09 & 15,406.5 & 10.373 & 70 & 0.0444 & \(7.16\times 10^{-6}\) & 10.131 \\
**2.25** & 5.69 \(\times 10^{29}\) & \(3.11\times 10^{30}\) & 10.358 & 80 & 0.0445 & \(1.37\times 10^{-4}\) & 11.622 \\
**2.50** & 1.07 \(\times\) 10\({}^{36}\) & \(2.64\times 10^{36}\) & 10.107 & 90 & 0.0445 & \(9.62\times 10^{-5}\) & 12.995 \\ \hline \hline \end{tabular} Note: In bold are the results for the chosen c and N parameters.  
\end{table}
Table 7: Parameter setting results using functions with zero as global minima  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline Hour & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\ Load & 700 & 750 & 850 & 950 & 1000 & 1100 & 1150 & 1200 & 1300 & 1400 & 1450 & 1500 \\ \hline Hour & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 & 21 & 22 & 23 & 24 \\ Load & 1400 & 1300 &Using 1.5 as the constant value, as seen in Table 7b, N = 50 can be selected as the number of parameters for PSPSO, since increasing N does not give appreciable change in the mean and standard deviation. Although N = 70 has the lowest mean and standard deviation, the increase in computational time is large compared to the decrease in mean and standard deviation.