# Applying Particle Swarm Optimization Variations to Solve the Transportation Problem Effectively
## 4 The Basic PSO for Solving the TP
The results of 50 particles are equal to or better than the results that are currently presented. Overall, TrigAC-PSO was the one that obtained the most robust results. The results of Table 11 lead to similar conclusions. In order to examine the stability for the 50 particles, it is worth comparing the CV values of the proposed variations with those of the traditional variations. Superior results are seen from TrigAC-PSO, as the CV value is \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & **PSO** & **DWPSO** & **TYAC** & **TrigAC-PSO** & **FSVAC** \\ \hline



verage** & 0.525 & 0.74375 & 0.765625 & 0.86875 & 0.821875 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Accuracy of PSO, DWPSO, TVAC, TrigAC-PSO and FSVAC for 50 particles. Figure 5: Accuracy for 50 particles. equal to 0.4%, followed by the FSVAC with 0.59%. The other values of variations ranged as follows: Classic PSO, 2.19%; DWPSO, 0.77%; and TVAC, 0.83%. \begin{table}
\begin{tabular}{l l l l l l l} \hline  & & **PSO** & **DWPSO** & **TVAC** & **TrigAC-PSO** & **FSVAC** \\ \hline \multirow{4}{*}{**Pr.01**} & Mean & 896.7 & 880 & 880 & 880 & 880 \\  & Var & 17.79544 & 0 & 0 & 0 & 0 \\  & Min & 880 & 880 & 880 & 880 & 880 \\  & Max & 929 & 880 & 880 & 880 & 880 \\  & cv\% & 1.984548 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr.02**} & Mean & 743 & 743 & 743 & 743 & 743 \\  & Var & 0 & 0 & 0 & 0 & 0 \\  & Min & 743 & 743 & 743 & 743 & 743 \\  & Max & 743 & 743 & 743 & 743 & 743 \\  & cv\% & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr.03**} & Mean & 5600 & 5600 & 5600 & 5600 & 5600 \\  & Var & 0 & 0 & 0 & 0 & 0 \\  & Min & 5600 & 5600 & 5600 & 5600 & 5600 \\  & Max & 5600 & 5600 & 5600 & 5600 & 5600 \\  & cv\% & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr.04**} & Mean & 59 & 59 & 59 & 59 & 59 \\  & Var & 0 & 0 & 0 & 0 & 0 \\  & Min & 59 & 59 & 59 & 59 & 59 \\  & Max & 59 & 59 & 59 & 59 & 59 \\  & cv\% & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr.05**} & Mean & 28 & 28 & 28 & 28 & 28 \\  & Var & 0 & 0 & 0 & 0 & 0 \\  & Min & 28 & 28 & 28 & 28 & 28 \\  & Max & 28 & 28 & 28 & 28 & 28 \\  & cv\% & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr.06**} & Mean & 438.9 & 435 & 435 & 435 & 435 \\  & Var & 6.279597 & 0 & 0 & 0 & 0 \\  & Min & 435 & 435 & 435 & 435 & 435 \\  & Max & 448 & 435 & 435 & 435 & 435 \\  & cv\% & 1.430758 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr.07**} & Mean & 392 & 390 & 390 & 390 & 390 \\  & Var & 6.324555 & 0 & 0 & 0 & 0 \\  & Min & 390 & 390 & 390 & 390 & 390 \\  & Max & 410 & 390 & 390 & 390 & 390 \\  & cv\% & 1.613407 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr.08**} & Mean & 1677.3 & 1611.7 & 1601.7 & 1585.9 & 1634.5 \\  & Var & 73.73986 & 47.30058 & 31.18778 & 7.125073 & 41.31518 \\  & Min & 1580 & 1580 & 1580 & 1580 & 1580 \\  & Max & 1794 & 1713 & 1672 & 1595 & 1705 \\  & cv\% & 4.396343 & 2.934825 & 1.947168 & 0.449276 & 2.527696 \\ \hline \multirow{4}{*}{**Pr.09**} & Mean & 52.4 & 50.3 & 50.2 & 49.4 & 50.8 \\  & Var & 0.966092 & 1.888562 & 1.549193 & 0.843274 & 2.043961 \\  & Min & 51 & 49 & 49 & 49 & 49 \\  & Max & 53 & 53 & 53 & 51 & 54 \\  & cv\% & 1.843687 & 3.754597 & 3.086043 & 1.707032 & 4.023546 \\ \hline \multirow{4}{*}{**Pr.10**} & Mean & 424.1 & 421 & 418.6 & 412.6 & 416.1 \\  & Var & 9.362455 & 8.589399 & 9.057839 & 4.2999871 & 8.292567 \\ \cline{1-1}  & Min & 410 & 410 & 410 & 410 & 410 \\ \cline{1-1}  & Max & 432 & 430 & 430 & 421 & 430 \\ \cline{1-1}  & cv\% & 2.207605 & 2.040237 & 2.163841 & 1.04214 & 1.992926 \\ \hline \multirow{4}{*}{**Pr.11**} & Mean & 3149.1 & 2870.4 & 2856.9 & 2850 & 2898.3 \\ \cline{1-1}  & Var & 611.9779 & 44.53014 & 14.0115 & 0 & 95.44405 \\ \cline{1-1}  & Min & 2850 & 2850 & 2850 & 2850 & 2850 \\ \cline{1-1}  & Max & 4429 & 2990 & 2894 & 2850 & 3091 \\ \cline{1-1}  & cv\% & 19.43342 & 1.551357 & 0.490444 & 0 & 3.293105 \\ \hline \end{tabular}
\end{table} 
Table 11: Statistical measures for 50 particles.