# Modified Migrating Birds Optimization for Energy-Aware Flexible Job Shop Scheduling Problem
## 4 Computational Results and Discussion
### Effectiveness of the Proposed MMBO
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multicolumn{6}{c}{**MMBO**} & \multicolumn{6}{c}{**VNS**} & \multicolumn{6}{c}{**IWOA**} \\ \cline{2-13}  & **Best** & **Avg.** & **ARPD** & **Time** & **Best** & **Avg.** & **ARPD** & **Time** & **Best** & **Avg.** & **ARPD** & **Time** \\ \hline RM01 & \(10\times 10\times 6\) & 9588 & 9865.5 & 2.89 & 23.8 & 9839 & 10,244.8 & 6.85 & 7.3 & 11,089 & 11,307.0 & 17.93 & 8.1 \\ RM02 & \(10\times 2\times 6\) & 22,347 & 22,970.0 & 2.79 & 66.7 & 24,096 & 25,186 & 12.70 & 10.3 & 29,258 & 30,355.6 & 35.84 & 21.4 \\ RM03 & \(10\times 3\times 6\) & 33,351 & 34,018.9 & 2.00 & 130.5 & 36,103 & 37,296.4 & 11.83 & 14.7 & 41,631 & 44,732.8 & 34.13 & 39.7 \\ RM04 & \(10\times 50\times 6\) & 57,298 & 58,542.5 & 2.17 & 30.5 & 63,475 & 64,937.2 & 13.33 & 27.6 & 80,901 & 58,493.2 & 49.21 & 91.9 \\ RM05 & \(10\times 80\times 6\) & 113,831 & 116,054.4 & 1.97 & 66.5 & 127,773 & 131,051.2 & 15.5 & 61.9 & 183,505 & 186,510.6 & 63.87 & 212.9 \\ RM06 & \(15\times 10\times 9\) & 8324 & 8598.8 & 3.30 & 30.5 & 8822 & 8985.2 & 7.94 & 8.5 & 9851 & 10,147.8 & 21.91 & 8.5 \\ RM07 & \(15\times 20\times 9\) & 18,334 & 19,149.9 & 4.45 & 84.7 & 21,097 & 21,417.8 & 16.82 & 11.4 & 23,143 & 24,873.4 & 35.67 & 23.3 \\ RM08 & \(15\times 30\times 9\) & 29,063 & 29,064.4 & 2.90 & 1507.5 & 31,382 & 32,548.0 & 11.99 & 15.6 & 40,030 & 41,550.4 & 42.97 & 41.1 \\ RM09 & \(15\times 50\times 9\) & 54,172 & 55,361.1 & **2.20** & 355.9 & 59,499 & 61,390 & 13.32 & 28.0 & 77,961 & 82,297.4 & 51.92 & 100.0 \\ RM10 & \(15\times 80\times 9\) & 103,491 & 104,707.1 & 1.18 & 820,198.4 & 211,022.6 & 16.94 & 65.6 & 1750,720.48 & 46.67 & 213.8 \\ RM11 & \(20\times 10\times 12\) & 8259 & 8497.5 & **2.40** & 37.4 & 8729 & 8939.0 & 8.23 & 7.6 & 9314 & 9851.1 & 19.29 & 8.9 \\ RM12 & \(20\times 20\times 12\) & 17,736 & 18,447.0 & **4.01** & 103.0 & 19,958 & 20,384.6 & 14.93 & 11.0 & 24,348 & 25,053.4 & 41.26 & 24.9 \\ RM13 & \(20\times 30\times 12\) & 27,732 & 28,833.5 & 3.97 & 194.9 & 30,359 & 31,759.2 & 14.52 & 15.6 & 38,457 & 40,512.4 & 46.09 & 43.1 \\ RM14 & \(20\times 20\times 12\) & 52,213 & 53,833.0 & 2.43 & 426.4 & 58,905 & 99,957.1 & 14.83 & 31.2 & 81,699 & 85,436.0 & 63.63 & 105.7 \\ RM15 & \(20\times 80\times 12\) & 98,071 & 100,441.3 & **2.42** & 944.4 & 110,985 & 113,107.0 & 15.33 & 67.4 & 155,883 & 168,369.8 & 71.68 & 237.1 \\ RM16 & \(25\times 10\times 15\) & 7704 & 7828.3 & 1.61 & 42.4 & 8117 & 8359.0 & 8.50 & 8.0 & 8976 & 9318.2 & 20.95 & 9.6 \\ RM17 & \(25\times 20\times 15\) & 16,694.3 & **2.07** & 114.3 & 18,304.1 & 19.13 & 15.10 & 12.4 & 23,126 & 23,744.42 & 42.86 & 25.8 \\ RM18 & \(25\times 30\times 15\) & 25,708 & 26,074.5 & **1.43** & 203.6 & 29,204 & 29,598.0 & 15.13 & 16.6 & 37,902 & 38,599.6 & 50.15 & 47.2 \\ RM19 & \(25\times 50\times 15\) & 49,020 & **50,020.3** & **2.04** & 436.2 & 55,360 & 56,950.6 & 16.18 & 31.3 & 76,848 & 80,789.4 & 64.81 & 106.6 \\ RM20 & \(25\times 80\times 15\) & **96,029** & **97,181.2** & **1.20** & 1099.2 & 107,528 & 111,204.6 & 15.80 & 71.7 & 161,517 & 170,567.4 & 77.62 & 258.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison results of different algorithms. To test whether the differences from the algorithms in Table 4 are significant or not, an analysis of variance (ANOVA) is conducted in Table 5, where all the algorithms are viewed as the factors. The results demonstrate that there is a statistically significant difference between the compared algorithms since the \(p\) value is smaller than 0.05.