# 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} \hline  & & **PSO** & **DWPSO** & **TVAC** & **TrigAC-PSO** & **FSVAC** \\ \hline \multirow{6}{*}{Pr.18} & Mean & 820 & 820 & 820 & 820 & 820 \\  & St.Dev & 0 & 0 & 0 & 0 & 0 \\  & Min & 820 & 820 & 820 & 820 & 820 \\  & Max & 820 & 820 & 820 & 820 & 820 \\  & cv\% & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{6}{*}{Pr.19} & Mean & 190.8 & 190.7 & 190.9333 & 190.56667 & 190 \\  & St.Dev & 0.924755326 & 0.952311 & 0.98026 & 0.81720 & 0 \\  & Min & 190 & 190 & 190 & 190 & 190 \\  & Max & 192 & 192 & 192 & 192 & 190 \\  & cv\% & 0.484672603 & 0.499377 & 0.513407 & 0.4288264 & 0 \\ \hline \multirow{6}{*}{Pr.20} & Mean & 83 & 83 & 83.3 & 83.2 & 83.1 \\  & St.Dev & 0 & 0 & 0.91538 & 0.761124 & 0.54772 \\  & Min & 83 & 83 & 83 & 83 \\  & Max & 83 & 83 & 86 & 86 & 86 \\  & cv\% & 0 & 0 & 1.098902 & 0.914813 & 0.659113 \\ \hline \multirow{6}{*}{Pr.21} & Mean & 3484.5 & 3536.467 & 3468.2 & 3460 & 3536.1 \\  & St.Dev & 58.99371679 & 71.42864 & 34.7804 & 0 & 63.5839 \\  & Min & 3460 & 3460 & 3460 & 3460 & 3460 \\  & Max & 3745 & 3646 & 3645 & 3460 & 3644 \\  & cv\% & 1.693032481 & 2.019774 & 1.00284 & 0 & 1.798138 \\ \hline \multirow{6}{*}{Pr.22} & Mean & 928.3 & 910 & 913.6 & 910 & 910 \\  & St.Dev & 28.61534433 & 0 & 14.8686 & 0 & 0 \\  & Min & 910 & 910 & 910 & 910 & 910 \\  & Max & 990 & 910 & 990 & 910 & 910 \\  & cv\% & 3.08255352 & 0 & 1.627476 & 0 & 0 \\ \hline \multirow{6}{*}{Pr.23} & Mean & 1679.1 & 1671.133 & 1670.733 & 1671 & 1671.367 \\  & St.Dev & 14.23291474 & 1.136642 & 0.58329 & 2.34888 & 2.02541 \\  & Min & 1670 & 1670 & 1670 & 1670 & 1670 \\  & Max & 1724 & 1675 & 1672 & 1679 & 1678 \\  & cv\% & 0.847651405 & 0.068016 & 0.034912 & 0.1405674 & 0.121183 \\ \hline \multirow{6}{*}{Pr.24} & Mean & 2403.966667 & 2366.4 & 2372.8 & 2361.5667 & 2333.833 \\  & St.Dev & 44.98005944 & 20.99627 & 31.0332 & 18.34287 & 117.1320 \\  & Min & 2280 & 2317 & 2320 & 2322 & 2292 \\  & Max & 4295 & 2430 & 2424 & 2390 & 2420 \\  & cv\% & 1.871076669 & 1.229559 & 1.307874 & 0.7767247 & 1.47626 \\ \hline \multirow{6}{*}{Pr.25} & Mean & 2468.766667 & 2460 & 2460 & 2460 & 2460 \\  & St.Dev & 24.21695521 & 0 & 0 & 0 & 0 \\  & Min & 2460 & 2460 & 2460 & 2460 & 2460 \\  & Max & 2563 & 2460 & 2460 & 2460 & 2460 \\  & cv\% & 0.98093335 & 0 & 0 & 0 & 0 \\ \hline \multirow{6}{*}{Pr.26} & Mean & 292.6 & 291 & 291 & 291 & 291 \\  & St.Dev & 2.485821865 & 0 & 0 & 0 & 0 \\  & Min & 291 & 291 & 291 & 291 & 291 \\  & Max & 299 & 291 & 291 & 291 & 291 \\  & cv\% & 0.84956318 & 0 & 0 & 0 & 0 \\ \hline \multirow{6}{*}{Pr.27} & Mean & 4574.233333 & 4639.967 & 4666.433 & 4535 & 4634.9 \\  & St.Dev & 73.42821187 & 60.22915 & 29.96973 & 18.34910 & 67.4073 \\  & Min & 4525 & 4525 & 4529 & 4525 & 4525 \\  & Max & 4753 & 4675 & 4677 & 4585 & 4675 \\  & cv\% & 1.605257243 & 1.298051 & 0.642241 & 0.0406109 & 1.454343 \\ \hline \multirow{6}{*}{Pr.28} & Mean & 941.7 & 953.3667 & 953.0667 & 947.26667 & 947.9667 \\  & St.Dev & 22.49314072 & 19.7404 & 13.35957 & 17.26454 & 13.60396 \\ \cline{1-1}  & Min & 920 & 920 & 920 & 920 & 920 \\ \cline{1-1}  & Max & 974 & 992 & 960 & 960 & 968 \\ \cline{1-1}  & cv\% & 2.38856756 & 2.063638 & 1.401746 & 1.8225639 & 1.435068 \\ \hline \multirow{6}{*}{Pr.29} & Mean & 809 & 809 & 809 & 809 & 809 \\ \cline{1-1}  & St.Dev & 0 & 0 & 0 & 0 & 0 \\ \cline{1-1}  & Min & 809 & 809 & 809 & 809 & 809 \\ \cline{1-1}  & Max & 809 & 809 & 809 & 809 & 809 \\ \cline{1-1}  & cv\% & 0 & 0 & 0 & 0 & 0 \\ \hline \end{tabular}
\end{table} 
Table 7: _Cont._The above results urged us to continue the research for an even greater number of particles, in order to study the behavior of new variations in a multi-solution environment. More specifically, the aforementioned variations were also tested on the set of 40 and 50 particles. In this case, 10 independent runs were carried out for each test instance, reducing the chances of finding the optimal solution from the 30 independent runs that we have already performed. Selecting more particles revealed significant results.