# 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 \hline  & & **PSO** & **DWPSO** & **TVAC** & **TrigAC-PSO** & **FSVAC** \\ \hline \multirow{4}{*}{**Pr24**} & Mean & 2423.4 & 2354.5 & 2336.8 & 2347 & 2355 \\  & Var & 13.35165 & 31.64824 & 37.90573 & 26.48689 & 28.5151 \\  & Min & 2401 & 2288 & 2280 & 2307 & 2309 \\  & Max & 2446 & 2390 & 2404 & 2388 & 2395 \\  & cv\% & 0.550947 & 1.34416 & 1.622121 & 1.128543 & 1.210832 \\ \hline \multirow{4}{*}{**Pr25**} & Mean & 2460 & 2460 & 2460 & 2460 & 2460 \\  & Var & 0 & 0 & 0 & 0 & 0 \\  & Min & 2460 & 2460 & 2460 & 2460 & 2460 \\  & cv\% & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr26**} & Mean & 292.2 & 291 & 291 & 291 & 291 \\  & Var & 1.932184 & 0 & 0 & 0 & 0 \\  & Min & 291 & 291 & 291 & 291 & 291 \\  & Max & 295 & 291 & 291 & 291 & 291 \\  & cv\% & 0.661254 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr27**} & Mean & 4585.8 & 4549.3 & 4552.3 & 4532 & 4595.2 \\  & Var & 69.97904 & 45.93486 & 42.05829 & 16.57307 & 75.36843 \\  & Min & 4525 & 4525 & 4525 & 4525 & 4525 \\  & Max & 4675 & 4675 & 4668 & 4577 & 4675 \\  & cv\% & 1.525994 & 1.009713 & 0.923891 & 0.36569 & 1.640156 \\ \hline \multirow{4}{*}{**Pr28**} & Mean & 957.3 & 928 & 929.9 & 923.3 & 923.6 \\  & Var & 21.11242 & 12.6558 & 17.85404 & 8.420214 & 9.070097 \\  & Min & 920 & 920 & 920 & 920 & 920 \\  & Max & 990 & 960 & 967 & 947 & 949 \\  & cv\% & 2.206647 & 1.321722 & 1.919995 & 0.911969 & 0.982037 \\ \hline \multirow{4}{*}{**Pr29**} & Mean & 809 & 809 & 809 & 809 & 809 \\  & Var & 0 & 0 & 0 & 0 & 0 \\  & Min & 809 & 809 & 809 & 809 & 809 \\  & Max & 809 & 809 & 809 & 809 & 809 \\  & cv\% & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr30**} & Mean & 417 & 417 & 417 & 417 & 417 \\  & Var & 0 & 0 & 0 & 0 & 0 \\  & Min & 417 & 417 & 417 & 417 & 417 \\  & cv\% & 0 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr31**} & Mean & 3470.4 & 3458 & 3458 & 3458 & 3458 \\  & Var & 18.42221 & 0 & 0 & 0 & 0 \\ \cline{1-1}  & Min & 3458 & 3458 & 3458 & 3458 & 3458 \\ \cline{1-1}  & Max & 3508 & 3458 & 3458 & 3458 & 3458 \\ \cline{1-1}  & cv\% & 0.530838 & 0 & 0 & 0 & 0 \\ \hline \multirow{4}{*}{**Pr32**} & Mean & 118.1 & 122.3 & 123.7 & 114.1 & 112.6 \\ \cline{1-1}  & Var & 5.384133 & 6.498718 & 8.590046 & 3.784471 & 3.306559 \\ \cline{1-1}  & Min & 112 & 1142 & 109 & 109 & 109 \\ \cline{1-1}  & Max & 127 & 129 & 129 & 120 & 119 \\ \cline{1-1}  & cv\% & 4.558961 & 5.313751 & 6.944257 & 3.316802 & 2.936553 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: _Cont._acceleration parameters. It was evidently proven that the solution quality is inseparably linked with the selection of proper values for controlling the algorithm parameters. In order to see the effectiveness and stability of the proposed variations, we compared their results with those of other PSO variations for the same instances. Remarkably, the punctuality of one of our variations rose to 88%, and it was finally established as the ideal option compared to all other variations for the solution of TP. It can be easily observed that this PSO variationis simple compared to other variations with complex structures. It was a challenge to achieve better results by creating and running simple computational algorithms, proving that keeping a balance between human and artificial intelligence is the key to the success of computational intelligence. A more comprehensive analysis may be needed in order to examine the TP to a greater extent. Moreover, the proposed PSO variations could be applied to more complex networks such as the Sioux Fall network [27] in order to demonstrate the algorithm's good performance and independence of the network's size. Except for this, some other real constraints can be proposed in order to find the optimal solution for the TP with PSO algorithm variations not only in balanced instances but also in more realistic unbalanced instances in the future. Moreover, combining the proposed PSO variations with other meta-heuristic methods to solve the TP will be an interesting challenge. Conceptualization, C.A. and G.N.B. ; methodology, C.A.