## 3 Discussion and Results Evaluation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Algorithm** & **Parameters** & **Description** & **First Level** & **Second Level** & **Third Level** & **Fourth Level** & **Fifth Level** \\ \hline \multirow{3}{*}{MOWA} & Pop size & The number of first flows & 10 & 20 & 30 & 40 & 50 \\  & M\({}_{0}\) & The initial mass & 50 & 60 & 70 & 80 & 90 \\  & V\({}_{0}\) & The initial speed & 20 & 30 & 40 & 50 & 60 \\ \hline \multirow{3}{*}{MOSA} & Inner loop & The number of iterations in the inner loop & 10 & 20 & 30 & 40 & 50 \\  & alpha & Temperature reduction rate & 0.95 & 0.96 & 0.97 & 0.98 & 0.99 \\  & Pop size & Population size & 10 & 15 & 20 & 30 & 40 \\ \hline \multirow{3}{*}{NSGA-II} & Pop size & The initial population size & 60 & 80 & 100 & 120 & 140 \\  & P\({}_{\text{c}}\) & Crossover rate & 0.75 & 0.80 & 0.85 & 0.90 & 0.95 \\ \cline{1-1}  & P\({}_{\text{m}}\) & Mutation rate & 0.05 & 0.07 & 0.09 & 0.12 & 0.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Controllable parameters and their levels. The number of required experiments for the factors above equals \(\ 3^{5}=243\). However, regarding time and cost, this kind of experiment is not affordable. Accordingly, we get help from fractional iteration plans. In this problem, the freedom degree is set to 1 for the total average and 4 for each five level factors. Therefore, the total of freedom degrees equals \(1+(4\times 3)=13\). Thus, we have to select an array with at least 13 rows, and the L25 orthogonal array meets this requirement. The designed array structure and experiment results for NSGA-II, MOSA, and MOWFA are presented in Table 5. MID is considered a response variable. Each experiment is repeated three times and MID values are considered a basis for experimental results. Figure 2 demonstrates how the S/N criterion values are changed for different algorithm levels. The levels in which the S/N criterion has reached its maximum are optimum levels. It represents the MOWFA algorithm, and the best level of population size is its third level. Therefore, the appropriate population size for MOWFA is 30. The optimum levels of two other factors of MOWFA are also evaluated in the domain and for the M0 factor, the third, and for V0 the fourth levels are chosen. Figure 3 demonstrates the related results to the MOSA algorithm. The best level of population size is placed within the evaluated domain and is its third level. Therefore, the appropriate population size for MOWFA is 30. Thus, the appropriate population size for MOSA is 20. The optimum level of two other factors is also evaluated in the domain and for both factors i.e., for the inner loop and alpha, the third level is chosen. Figure 4 shows the related results to the NSGA-II algorithm. The best level of population size is placed within the evaluated domain and is its third level. Therefore, the appropriate population size for NSGA-II is 100. The optimum levels of two other factors of NSGA-II are also evaluated in the domain and for both Process Pmute factors the second levels are chosen. These real values are presented in Table 5.  
Now, we use small problems to evaluate algorithm efficiency to find a globally optimum solution. All of the examples are optimized using GAMS software and the obtained solutions from GAMS are compared with the obtained solutions of the proposed algorithms. To do that, at first we produce 10 random samples with 2 suppliers, 3 factories, and 3 vehicles and compare the obtained MID from GAMS and the obtained MID from the mentioned algorithms. All of the obtained results from GAMS are limited to 2000 s. If we don't reach the global optimum solution in the proposed time, the software stops, and the local optimum solution with its related GAP is presented. Regarding the obtained results, it can be seen that NSGAII's distance from the globally optimum solution is 2.174928, MOSA's, 2.254297, and MOWFA's, 2.805116 percent.