# Modified Migrating Birds Optimization for Energy-Aware Flexible Job Shop Scheduling Problem
## 4 Computational Results and Discussion
### Effectiveness of the Improvement Strategy  
In this paper, three improvement strategies are adopted to enhance the performance of the proposed algorithm, such as population initialization method, aging-based re-initialization mechanism and local search strategy. Here, we first test the effectiveness of the three improvement strategies. In Table 2, the first column shows the names of different instances, other columns report the computational data. 'MMBO' is our proposed algorithm. 'MBO1' is the algorithm where the random rule is only used to generate the initial population. 'MBO2' represents the algorithm where the aging-based re-initialization mechanism is excluded from the MMBO. 'MBO3' is the algorithm where the local search strategy is excluded from the MMBO. In the table, 'Best' represents the best value in the ten runs. 'Avg.' denotes the average result in the ten runs. The average relative percent deviation (ARPD) is measured by Equation (18). \[ARPD=\sum_{n\
eq 1}^{NR}\frac{100\times(Alg_{ur}-Min)}{Min}/NR \tag{18}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(J_{i}\) & _nop_ & \(w\) & _nwk_ & \(P_{ijkl}\) & \(E_{ijkl}\) & \(SE_{k}\) & \(T\!U_{I}\) &  
where 'Min' is the minimum value obtained by all compared algorithms. 'Time' is the average time (in seconds) of the ten runs. For each instance, boldface represents the best value obtained by all compared algorithms. \begin{table} \begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{\(m\times n\times w\)} & \multicolumn{5}{c}{**MMBO**} & \multicolumn{5}{c}{**MBO1**} \\ \cline{3-10}  & & **Best** & **Avg.** & **ARPD** & **Time** & **Best** & **Avg.** & **ARPD** & **Time** \\ \hline RM01 & \(10\times 10\times 6\) & 9588 & 9865.5 & 3.53 & 23.8 & 9696 & 10,089.8 & 5.89 & 24.0 \\ RM02 & \(10\times 20\times 6\) & **22,347** & **22,970.0** & **2.79** & 66.7 & 24,080 & 24,336.4 & 8.90 & 64.3 \\ RM03 & \(10\times 30\times 6\) & 33,351 & 34,018.9 & 2.88 & 130.5 & 34,999 & 35,830.6 & 8.36 & 121.5 \\ RM04 & \(10\times 50\times 6\) & 57,298 & 58,542.5 & 2.48 & 303.5 & 62,475 & 63,914.8 & 11.89 & 279.2 \\ RM05 & \(10\times 80\times 6\) & **113,813** & **116,054.4** & **1.97** & 667.5 & 126,105 & 129,280.6 & 13.59 & 658.6 \\ RM06 & \(15\times 10\times 9\) & **8324** & **8598.8** & **3.30** & 30.5 & 8421 & 8708.4 & 4.62 & 29.0 \\ RM07 & \(15\times 20\times 9\) & **18,334** & **19,149.9** & **4.45** & 84.7 & 19,437 & 19,767.8 & 7.82 & 72.5 \\ RM08 & \(15\times 30\times 9\) & 29,063 & 29,906.4 & 2.98 & 150.7 & 30,338 & 31,387.4 & 8.08 & 130.6 \\ RM09 & \(15\times 50\times 9\) & 54,172 & 55,361.1 & 2.51 & 355.9 & 58,186 & 58,710.6 & 8.71 & 300.1 \\ RM10 & \(15\times 80\times 9\) & **103,491** & **104,707.1** & **1.18** & 820.9 & 115,624 & 117,196.6 & 13.24 & 729.4 \\ RM11 & \(20\times 10\times 12\) & **8259** & 8457.5 & 2.40 & 37.4 & 8370 & 8493.4 & 2.84 & 30.0 \\ RM12 & \(20\times 20\times 12\) & **17,736** & 18,447.0 & 4.01 & 103.0 & 18,863 & 19106.0 & 7.72 & 78.0 \\ RM13 & \(20\times 30\times 12\) & **27,732** & 28,833.5 & 3.97 & 194.9 & 28,961 & 29,667.2 & 6.98 & 146.5 \\ RM14 & \(20\times 50\times 12\) & **52,213** & **53,483.0** & **2.43** & 426.4 & 54,483 & 55,211.8 & 5.74 & 344.6 \\ RM15 & \(20\times 80\times 12\) & **98,071** & 100,441.3 & 2.42 & 944.4 & 107,788 & 110,569.8 & 12.74 & 758.8 \\ RM16 & \(25\times 10\times 15\) & 7704 & 7828.3 & 2.12 & 42.4 & **7666** & **7782.4** & **1.52** & 32.7 \\ RM17 & \(25\times 20\times 15\) & **16,621** & **16,964.3** & **2.07** & 114.3 & 16,888 & 17,551.4 & 5.60 & 90.3 \\ RM18 & \(25\times 30\times 15\) & 25,708 & 26,074.5 & 2.83 & 203.6 & 26,442 & 26,712.8 & 5.35 & 162.1 \\ RM19 & \(25\times 50\times 15\) & 49,020 & 50,020.3 & 2.89 & 436.2 & 50,874 & 52,262.4 & 7.50 & 374.5 \\ RM20 & \(25\times 80\times 15\) & **96,029** & **97,181.2** & **1.20** & 1099.2 & 105,785 & 106,591.2 & 11.00 & 823.2 \\ \hline \hline \end{tabular}