## 4 Computational Experiments
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & & **Problem 1** & **Problem 2** & **Problem 3** & **Problem 4** & **Problem 5** \\ \hline \multirow{6}{*}{\(Z1\)} & & & Optimal & 1,108,835 & 1,404,026 & 1,659,658 & 1,776,098 & 1,972,490 \\  & & ACO & Best & 1,108,835 & 1,404,026 & 1,721,895 & 1,864,015 & 2,094,193 \\  & & & Gap (\%) & 0 & 0 & 0.0375 & 0.0495 & 0.0617 \\  & & & Best & 1,108,835 & 1,404,026 & 1,721,435 & 1,851,760 & 2,087,683 \\  & & & Gap (\%) & 0 & 0 & 0.0318 & 0.0426 & 0.0584 \\  & & & Best & 1,108,835 & 1,404,026 & 1,736,500 & 1,879,467 & 2,126,739 \\  & & & Gap (\%) & 0 & 0 & 0.0463 & 0.0582 & 0.0782 \\ \cline{2-8}  & & & Optimal & 2,709,941 & 3,017,161 & 3,286,451 & 3,480,057 & 3,837,795 \\  & & & Best & 2,709,941 & 3,017,161 & 3,134,946 & 3,293,178 & 3,556,101 \\  & & & Gap (\%) & 0 & 0 & 0.0461 & 0.0537 & 0.0734 \\  & & & Best & 2,709,941 & 3,017,161 & 3,175,369 & 3,315,798 & 3,625,949 \\  & & & Gap (\%) & 0 & 0 & 0.0338 & 0.0472 & 0.0552 \\  & & & Best & 1108835 & 1,404,026 & 3,481,338 & 3,709,045 & 4,177,056 \\  & & & Gap (\%) & 0 & 0 & 0.0593 & 0.0658 & 0.0884 \\ \hline \multirow{6}{*}{\(Z2\)} & & & Optimal & 15,658,380 & 16,184,285 & 16,301,772 & 16,831,979 & 1,7763,954 \\  & & ACO & Best & 15,658,380 & 16,184,285 & 15,468,751 & 15,845,625 & 16,632,390 \\  & & & Gap (\%) & 0 & 0 & 0.0511 & 0.0586 & 0.0637 \\  & & & Best & 15,658,380 & 16,184,285 & 15,511,136 & 15,862,457 & 16,678,576 \\  & & & Gap (\%) & 0 & 0 & 0.0485 & 0.0576 & 0.0611 \\  & & & Best & 1108835 & 1,404,026 & 17,260,316 & 17,885,661 & 18,979,008 \\  & & & Gap (\%) & 0 & 0 & 0.0588 & 0.0626 & 0.0684 \\ \cline{2-8}  & & & Optimal & 11,063,345 & 11,864,926 & 12,303,159 & 12,627,619 & 12,966,067 \\  & & ACO & Best & 11,063,345 & 11,864,926 & 12,754,685 & 13,199,650 & 13,642,896 \\  & & & Gap (\%) & 0 & 0 & 0.0367 & 0.0453 & 0.0522 \\  & & & Best & 11063345 & 11,864,926 & 12,744,842 & 13,168,081 & 13,609,184 \\  & & & Gap (\%) & 0 & 0 & 0.0359 & 0.0428 & 0.0496 \\  & & & & Best & 1108835 & 1,404,026 & 12,912,165 & 13,312,036 & 13,767,370 \\  & & & Gap (\%) & 0 & 0 & 0.0495 & 0.0542 & 0.0618 \\ \hline \multirow{6}{*}{\(Z3\)} & & & Optimal & 2,365,633 & 2,760,450 & 2,980,651 & 3,277,653 & 3,413,026 \\  & & ACO & Best & 2,365,633 & 11,864,926 & 2,893,020 & 3,125,898 & 3,240,668 \\  & & & Gap (\%) & 0 & 0 & 0.0294 & 0.0463 & 0.0505 \\  & & & Best & 2,365,633 & 11864926 & 2,888,251 & 3,148,513 & 3,262,853 \\  & & & Gap (\%) & 0 & 0 & 0.031 & 0.0394 & 0.044 \\  & & & Best & 1108835 & 1,404,026 & 3,098,983 & 3,462,185 & 3,612,347 \\  & & & Gap (\%) & 0 & 0 & 0.0397 & 0.0563 & 0.0584 \\ \cline{2-8}  & & & Optimal & 1,083,653 & 1,377,620 & 1,648,027 & 1,740,722 & 1,915,385 \\  & & & Best & 1,083,653 & 1,377,620 & 1,722,188 & 1,834,025 & 2,034,713 \\  & & & Gap (\%) & 0 & 0 & 0.045 & 0.0536 & 0.0623 \\  & & & Gap (\%) & 0 & 0 & 0.0318 & 0.0431 & 0.0542 \\  & & & Best & 1,108,835 & 1,404,026 & 1,733,395 & 1,844,469 & 2,046,397 \\  & & & Gap (\%) & 0 & 0 & 0.0518 & 0.0596 & 0.0684 \\ \hline \multirow{6}{*}{\(Z4\)} & & & Optimal & 0.685 & 0.693 & 0.618 & 0.635 & 0.709 \\  & & & Best & 0.685 & 0.693 & 0.581909 & 0.594932 & 0.65859 \\  & & & Gap (\%) & 0 & 0 & 0.0584 & 0.0631 & 0.0711 \\  & & & Best & 0.685 & 0.693 & 0.582156 & 0.596138 & 0.660504 \\  & & & Gap (\%) & 0 & 0 & 0.058 & 0.0612 & 0.0684 \\  & & & Best & 1,108,835 & 1,404,026 & 0.658912 & 0.682181 & 0.763735 \\  & & & Gap (\%) & 0 & 0 & 0.0662 & 0.0743 & 0.0772 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Test problem results. problems, respectively. Comparative results of the proposed meta-heuristic algorithms are represented in Figure 4a-c Figures 5a-c and 6. Figure 4: (**a**) Minimization process of the \(Z1\); (**b**) minimization process of the \(Z2\); and (**c**) minimization process of the \(Z3\). Figure 5: (**a**) Maximization process of the \(Z1\); (**b**) maximization process of the \(Z2\); and (**c**) maximization process of the \(Z3\). Figure 6: Maximization process of \(Z4\).