# Applying Particle Swarm Optimization Variations to Solve the Transportation Problem Effectively
## 4 The Basic PSO for Solving the TP
The results showed, once again, the consistent superiority of the proposed variations. Table 8 and Figure 4 shows the accuracy achieved by each variation for 40 particles. These results provide further support for the hypothesis that TrigAC-PSO and FSVAC are still more accurate than the other PSO variations, since they attained accuracy rates 88.31% and 77.5%, respectively; the DWPSO method follows with 75.94%, and TVAC with 74.38%; last but not least is the classic PSO with 51.56%, attaining a spectacular 13% increase over the 10-particle accuracy rates, but maintaining a steady performance for 15 and 20 particles. \begin{table}
\begin{tabular}{l l l l l l l} \hline  & & **PSO** & **DWPSO** & **TVAC** & **TrigAC-PSO** & **FSVAC** \\ \hline \multirow{4}{*}{Pr.30} & Mean & 419.533333 & 417 & 417 & 417 & 417 \\  & St.Dev & 7.103827688 & 0 & 0 & 0 & 0 \\ \cline{1-1}  & Min & 417 & 417 & 417 & 417 & 417 \\  & Max & 445 & 417 & 417 & 417 & 417 \\  & cv\% & 1.693268955 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{Pr.31} & Mean & 430.06667 & 3458 & 3458 & 3458 & 3458 \\  & St.Dev & 33.27620392 & 0 & 0 & 0 & 0 \\ \cline{1-1}  & Min & 3458 & 3458 & 3458 & 3458 & 3458 \\ \cline{1-1}  & Max & 3587 & 3458 & 3458 & 3458 & 3458 \\  & cv\% & 0.956194438 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{Pr.32} & Mean & 114.3 & 116.9333 & 114.4333 & 114.7 & 118.4333 \\  & St.Dev & 3.76149395 & 4.532894 & 3.549485 & 3.77057 & 4.44648 \\ \cline{1-1}  & Min & 109 & 109 & 109 & 109 & 109 \\ \cline{1-1}  & Max & 122 & 125 & 127 & 119 & 125 \\ \cline{1-1}  & cv\% & 3.290830616 & 3.876477 & 3.101794 & 3.2873372 & 3.754424 \\ \hline \end{tabular}
\end{table} 
Table 7: _Cont._ \begin{table}
\begin{tabular}{l l l l l l} \hline  & **PSO** & **DWPSO** & **TVAC** & **TrigAC-PSO** & **FSVAC** \\ \hline Pr.01 & 0.2 & 0.8 & 0.8 & 1 & 0.8 \\ Pr.02 & 1 & 1 & 1 & 1 & 1 \\ Pr.03 & 1 & 1 & 1 & 1 & 1 \\ Pr.04 & 1 & 1 & 1 & 1 & 1 \\ Pr.05 & 1 & 1 & 1 & 1 & 1 \\ Pr.06 & 0.4 & 1 & 1 & 1 & 1 \\ Pr.07 & 0.8 & 1 & 1 & 1 & 1 \\ Pr.08 & 0.2 & 0.2 & 0.3 & 0.7 & 0.1 \\ Pr.09 & 0 & 0.5 & 0.3 & 0.6 & 0.3 \\ Pr.10 & 0.2 & 0.5 & 0.2 & 0.5 & 0.6 \\ Pr.11 & 0 & 0.5 & 0.4 & 0.8 & 0.4 \\ Pr.12 & 0.2 & 0.7 & 0.7 & 0.7 & 1 \\ Pr.13 & 0.7 & 1 & 1 & 1 & 1 \\ Pr.14 & 0 & 0.3 & 0.5 & 0.7 & 0.5 \\ Pr.15 & 0.8 & 1 & 1 & 1 & 1 \\ Pr.16 & 0.2 & 1 & 0.8 & 1 & 1 \\ Pr.17 & 0.3 & 1 & 1 & 1 & 1 \\ Pr.18 & 1 & 1 & 1 & 1 & 1 \\ Pr.19 & 0.2 & 0.9 & 0.6 & 0.9 & 1 \\ Pr.20 & 1 & 0.9 & 1 & 1 & 1 \\ Pr.21 & 0.6 & 0.5 & 0.6 & 0.7 & 0.4 \\ Pr.22 & 0.7 & 1 & 1 & 1 & 1 \\ Pr.23 & 0.1 & 0.7 & 0.9 & 1 & 0.8 \\ Pr.24 & 0 & 0 & 0 & 0 & 0 \\ Pr.25 & 0.7 & 1 & 1 & 1 & 1 \\ Pr.26 & 0.8 & 1 & 1 & 1 & 1 \\ Pr.27 & 0.8 & 0.5 & 0.2 & 0.9 & 0.6 \\ Pr.28 & 0 & 0.1 & 0.4 & 0.6 & 0.3 \\ Pr.29 & 1 & 1 & 1 & 1 & 1 \\ Pr.30 & 1 & 1 & 1 & 1 & 1 \\ Pr.31 & 0.5 & 1 & 1 & 1 & 1 \\ Pr.32 & 0.1 & 0.2 & 0.1 & 0.2 & 0 \\ Average & 0.515625 & 0.759375 & 0.74375 & 0.853125 & 0.775 \\ \hline \end{tabular}
\end{table} 
Table 8: Accuracy of PSO, DWPSO, TVAC, TrigAC-PSO and FSVAC for 40 particles. In the following table (Table 9), the most important statistical measures in the case of 40 particles for 10 independent runs are represented for all PSO variations. According to the particularly low values of the Coefficient of Variation (CV), we can infer that the PSO variations are extremely stable; more precisely, the mean CV value for each PSO variation is as follows: Classic PSO, 2.14%; DWPSO, 0.93%; TVAC, 0.86%; TrigAC-PSO, 0.47%; and FSVAC, 0.81%. These values show that TrigAC-PSO, which is one of the new PSO variations presented in this work, is once again the most stable method.