# Applying Particle Swarm Optimization Variations to Solve the Transportation Problem Effectively
## 4 The Basic PSO for Solving the TP
\begin{table}
\begin{tabular}{l l l l l l l l} \hline  & & **PSO** & **DWPSO** & **TVAC** & **TrigAC-PSO** & **FSVAC** \\ \hline  & Mean & 393.9 & 390 & 390 & 390 & 390 & 390 \\  & Var & 8.2253 & 0 & 0 & 0 & 0 & 0 \\
**Pr.07** & Min & 390 & 390 & 390 & 390 & 390 \\  & Max & 410 & 390 & 390 & 390 & 390 \\  & cv\% & 2.08817 & 0 & 0 & 0 & 0 \\ \hline  & Mean & 1659.4 & 1595.4 & 1611.5 & 1586.3 & 1623.8 \\  & Var & 74.99363 & 23.41035 & 53.60193 & 18.53555 & 32.25179 \\
**Pr.08** & Min & 1580 & 1580 & 1571 & 1580 & 1580 \\  & Max & 1802 & 1650 & 1717 & 1639 & 1671 \\  & cv\% & 4.519322 & 1.467365 & 3.326213 & 1.168477 & 1.986192 \\ \hline  & Mean & 52.4 & 50.2 & 50.5 & 49.7 & 50.4 \\  & Var & 1.57721 & 1.619328 & 1.509231 & 1.251666 & 1.074968 \\
**Pr.09** & Min & 50 & 49 & 49 & 49 & 49 \\  & Max & 55 & 53 & 53 & 53 & 52 \\  & cv\% & 3.010728 & 3.225725 & 2.988576 & 2.518442 & 2.132872 \\ \hline  & Mean & 421.7 & 417 & 417.2 & 414.3 & 414.7 \\  & Var & 11.72888 & 9.092121 & 6.924995 & 5.945119 & 6.848357 \\
**Pr.10** & Min & 410 & 410 & 410 & 410 & 410 \\  & Max & 434 & 430 & 430 & 425 & 430 \\  & cv\% & 2.781333 & 2.180365 & 1.659874 & 1.434979 & 1.6514 \\ \hline  & Mean & 3273.9 & 2894 & 2852.8 & 2850.2 & 3016.8 \\  & Var & 557.6408 & 121.5237 & 4.391912 & 0.421637 & 255.7915 \\
**Pr.11** & Min & 2851 & 2850 & 2850 & 2850 & 2850 \\  & Max & 4360 & 3237 & 2864 & 2851 & 3513 \\  & cv\% & 17.03292 & 4.199159 & 0.153951 & 0.014793 & 8.478901 \\ \hline  & Mean & 190.9 & 185.2 & 183.7 & 183.9 & 183 \\  & Var & 7.218035 & 4.289522 & 1.251666 & 1.449138 & 0 \\
**Pr.12** & Min & 183 & 183 & 183 & 183 & 183 \\  & Max & 203 & 196 & 186 & 186 & 183 \\  & cv\% & 3.781054 & 2.316157 & 0.681364 & 0.788003 & 0 \\ \hline  & Mean & 807.4 & 799 & 799 & 799 & 799 \\  & Var & 13.52528 & 0 & 0 & 0 & 0 \\
**Pr.13** & Min & 799 & 799 & 799 & 799 & 799 \\  & Max & 827 & 799 & 799 & 799 & 799 \\  & cv\% & 1.675165 & 0 & 0 & 0 & 0 \\ \hline  & Mean & 300.9 & 284.6 & 280 & 276.9 & 281.8 \\  & Var & 15.16905 & 10.25454 & 8.628119 & 6.707376 & 9.29516 \\
**Pr.14** & Min & 290 & 273 & 273 & 273 & 273 \\  & Max & 330 & 302 & 290 & 291 & 292 \\  & cv\% & 5.041225 & 3.603141 & 3.081471 & 2.422331 & 3.298495 \\ \hline  & Mean & 1160.4 & 1160 & 1160 & 1160 & 1160 \\  & Var & 0.843274 & 0 & 0 & 0 & 0 \\
**Pr.15** & Min & 1160 & 1160 & 1160 & 1160 & 1160 \\  & Max & 1162 & 1160 & 1160 & 1160 & 1160 \\  & cv\% & 0.072671 & 0 & 0 & 0 & 0 \\ \hline  & Mean & 215.2 & 200 & 201.6 & 200 & 200 \\  & Var & 8.243516 & 0 & 4.718757 & 0 & 0 \\
**Pr.16** & Min & 200 & 200 & 200 & 200 & 200 \\  & Max & 221 & 200 & 215 & 200 & 200 \\  & cv\% & 3.83063 & 0 & 2.340653 & 0 & 0 \\ \hline  & Mean & 244.7 & 240 & 240 & 240 & 240 \\  & Var & 6.236986 & 0 & 0 & 0 & 0 \\
**Pr.17** & Min & 240 & 240 & 240 & 240 & 240 \\  & Max & 256 & 240 & 240 & 240 & 240 \\  & cv\% & 2.54883 & 0 & 0 & 0 & 0 \\ \hline  & Mean & 820 & 820 & 820 & 820 & 820 \\  & Var & 0 & 0 & 0 & 0 & 0 \\
**Pr.18** & Min & 820 & 820 & 820 & 820 & 820 \\  & Max & 820 & 820 & 820 & 820 & 820 \\  & cv\% & 0 & 0 & 0 & 0 & 0 \\ \hline  & Mean & 191.4 & 190.2 & 190.7 & 190.1 & 190.1 \\  & Var & 0.843274 & 0.632456 & 0.948683 & 0.316228 & 0 \\
**Pr.19** & Min & 190 & 190 & 190 & 190 & 190 \\  & Max & 192 & 192 & 192 & 191 & 190 \\  & cv\% & 0.440582 & 0.332521 & 0.497474 & 0.166348 & 0 \\ \hline  & Mean & 83.3 & 83.3 & 83 & 83 & 83 \\  & Var & 0.948683 & 0.948683 & 0 & 0 & 0 \\
**Pr.20** & Min & 83 & 83 & 83 & 83 & 83 \\  & Max & 86 & 86 & 83 & 83 & 83 \\  & cv\% & 1.138876 & 1.138876 & 0 & 0 & 0 \\ \hline \end{tabular}
\end{table} 
Table 9: _Cont._The following table (Table 10) and Figure 5 present the accuracy for the 50 particles. The accuracy for each PSO variation is as follows: Classic PSO, 52.5%; DWPSO, 74.3%; TVAC, 76.56%; TrigAC-PSO, 86.88%; and FSVAC, 82.19%. The two new variations range at the highest levels. These are particularly promising results, demonstrating that the increase in the particle's number leads to an increase in the PSO variation's accuracy, especially in the case of TrigAC-PSO and FSVAC.