Research Article
Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems
Table 22
MBO using sequential merge sort algorithm.
| ID | OPT | Optimum | Execution time | Cycle | Time cycle | MBO | AVG | SD | RPD% | BET | AVG | ST | BC | AVG | SD | BTC | AVG | SD |
| B1 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 158 | 251 | 171.6413 | 4 | 7 | 2.4350 | 17 | 53 | 34.2198 | B2 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 157 | 263 | 84.9052 | 1 | 3 | 1.1575 | 4 | 31 | 23.2120 | B3 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 209 | 47.3905 | 2 | 4 | 1.4984 | 9 | 24 | 10.2378 | B4 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 155 | 160 | 4.7848 | 2 | 4 | 1.9449 | 8 | 20 | 8.5007 | B5 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 155 | 160 | 4.4053 | 2 | 4 | 2.0723 | 8 | 20 | 9.2034 | B6 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 165 | 172 | 5.9968 | 2 | 8 | 5.4244 | 10 | 40 | 25.3084 | B7 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 158 | 165 | 10.2942 | 2 | 5 | 2.6567 | 9 | 24 | 10.9301 | B8 | 4 | 4 | 4.1935 | 0.6011 | 0.00 | 154 | 226 | 63.7678 | 3 | 10 | 8.5001 | 13 | 59 | 55.3723 | B9 | 3 | 3 | 3.1935 | 0.4016 | 0.00 | 152 | 157 | 3.4802 | 2 | 5 | 2.5686 | 8 | 24 | 10.5719 | B10 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 152 | 183 | 41.7133 | 2 | 4 | 1.5422 | 8 | 21 | 10.5715 | B11 | 4 | 4 | 4.1613 | 0.3739 | 0.00 | 155 | 233 | 66.3620 | 2 | 11 | 9.9109 | 9 | 73 | 63.6411 | B12 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 153 | 235 | 86.2169 | 2 | 4 | 1.6643 | 11 | 29 | 18.5750 | B13 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 161 | 30.0537 | 3 | 6 | 3.6577 | 12 | 27 | 14.8101 | B14 | 3 | 3 | 3.3548 | 0.4864 | 0.00 | 152 | 159 | 26.0370 | 2 | 6 | 3.7006 | 8 | 26 | 15.6561 | B15 | 1 | 1 | 1.6452 | 0.9504 | 0.00 | 152 | 155 | 2.6176 | 2 | 5 | 2.3505 | 8 | 22 | 9.6363 | B16 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 155 | 182 | 48.3518 | 3 | 8 | 3.5493 | 12 | 43 | 25.2893 | B17 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 174 | 35.1554 | 2 | 5 | 2.1717 | 8 | 26 | 9.4585 | B18 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 177 | 41.1985 | 2 | 4 | 1.8275 | 8 | 21 | 8.6059 | B19 | 13 | 13 | 13.0968 | 0.5388 | 0.00 | 153 | 218 | 62.5518 | 1 | 6 | 4.0377 | 4 | 39 | 26.7267 | B20 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 155 | 225 | 138.3519 | 3 | 7 | 4.5423 | 13 | 41 | 21.4062 | B21 | 9 | 9 | 9.1935 | 0.4016 | 0.00 | 153 | 172 | 43.6026 | 2 | 9 | 5.2990 | 8 | 41 | 26.7630 | B22 | 6 | 6 | 6.1290 | 0.3408 | 0.00 | 152 | 155 | 2.0494 | 1 | 5 | 3.1326 | 4 | 23 | 12.9070 | B23 | 6 | 6 | 6.1290 | 0.3408 | 0.00 | 152 | 153 | 2.0489 | 2 | 7 | 4.8491 | 8 | 31 | 19.7735 | B24 | 5 | 5 | 5.2581 | 0.5755 | 0.00 | 152 | 153 | 1.6409 | 2 | 6 | 2.4012 | 8 | 24 | 9.6949 | B25 | 4 | 4 | 4.1290 | 0.3408 | 0.00 | 152 | 154 | 6.0300 | 3 | 6 | 5.4158 | 12 | 27 | 22.1520 | B26 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 154 | 157 | 2.3372 | 2 | 8 | 6.0393 | 8 | 37 | 24.7760 | B27 | 3 | 3 | 3.0323 | 0.1796 | 0.00 | 152 | 154 | 2.2017 | 2 | 7 | 4.8524 | 8 | 30 | 19.3886 | B28 | 3 | 3 | 3.2903 | 0.5884 | 0.00 | 152 | 155 | 4.7996 | 1 | 5 | 3.2670 | 4 | 24 | 13.9205 | B29 | 3 | 3 | 3.0968 | 0.3005 | 0.00 | 152 | 156 | 7.3660 | 3 | 5 | 2.0447 | 12 | 23 | 8.2142 | B30 | 2 | 2 | 2.4516 | 0.5680 | 0.00 | 152 | 153 | 1.7289 | 2 | 7 | 6.5031 | 8 | 28 | 26.3895 | B31 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 153 | 157 | 2.7615 | 4 | 8 | 3.2156 | 19 | 37 | 13.2221 | B32 | 4 | 4 | 4.2903 | 0.9016 | 0.00 | 152 | 155 | 4.1960 | 3 | 7 | 3.7805 | 13 | 31 | 15.0563 | B33 | 4 | 4 | 4.1290 | 0.4995 | 0.00 | 152 | 154 | 3.7868 | 2 | 6 | 3.0154 | 8 | 26 | 12.7931 | B34 | 4 | 4 | 4.3226 | 0.7478 | 0.00 | 152 | 153 | 1.2835 | 2 | 6 | 4.2925 | 8 | 27 | 17.1088 | B35 | 4 | 4 | 4.7097 | 0.9727 | 0.00 | 152 | 153 | 1.6468 | 1 | 5 | 2.0723 | 4 | 21 | 8.5183 | B36 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 158 | 3.8763 | 3 | 9 | 4.9110 | 13 | 39 | 19.3956 | B37 | 10 | 10 | 10.3226 | 0.7478 | 0.00 | 152 | 155 | 2.5387 | 2 | 6 | 5.4497 | 9 | 28 | 22.2304 | B38 | 8 | 8 | 8.0968 | 0.3005 | 0.00 | 152 | 154 | 3.3601 | 2 | 8 | 5.6323 | 8 | 34 | 22.8731 | B39 | 5 | 5 | 5.1935 | 1.0776 | 0.00 | 152 | 166 | 20.9165 | 2 | 6 | 3.5493 | 8 | 27 | 15.7638 | B40 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 152 | 162 | 16.8069 | 2 | 4 | 1.8357 | 8 | 19 | 7.9044 | B41 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 155 | 158 | 2.9064 | 1 | 10 | 5.2974 | 4 | 42 | 22.2617 | B42 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 198 | 70.2758 | 1 | 4 | 2.0718 | 8 | 24 | 17.2073 | B43 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 154 | 1.7221 | 1 | 4 | 2.2818 | 4 | 19 | 9.3681 | B44 | 5 | 5 | 5.9677 | 1.4256 | 0.00 | 152 | 154 | 3.8616 | 2 | 5 | 2.5264 | 8 | 24 | 10.1847 | B45 | 5 | 5 | 6.1935 | 1.5366 | 0.00 | 152 | 153 | 1.3536 | 2 | 6 | 4.6467 | 8 | 26 | 19.1860 | B46 | 8 | 8 | 8.0645 | 0.2497 | 0.00 | 154 | 158 | 3.4348 | 3 | 10 | 6.7563 | 12 | 42 | 27.9592 | B47 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 152 | 155 | 4.1228 | 2 | 5 | 2.9256 | 8 | 22 | 13.0905 | B48 | 5 | 5 | 5.4839 | 2.0145 | 0.00 | 152 | 153 | 1.3897 | 2 | 5 | 2.8931 | 8 | 22 | 11.7203 | B49 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 152 | 152 | 1.1704 | 3 | 6 | 3.1819 | 12 | 26 | 12.7969 | B50 | 5 | 5 | 5.3226 | 0.7478 | 0.00 | 152 | 153 | 1.4473 | 2 | 6 | 3.4529 | 8 | 26 | 14.0041 | B51 | 27 | 27 | 28.1613 | 0.9694 | 0.00 | 154 | 159 | 4.7774 | 5 | 21 | 9.0993 | 21 | 92 | 39.5406 | B52 | 18 | 18 | 18.9355 | 1.0307 | 0.00 | 154 | 156 | 2.2785 | 2 | 19 | 9.3341 | 8 | 80 | 38.7324 | B53 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 155 | 1.5889 | 4 | 10 | 2.8815 | 16 | 42 | 12.1075 | B54 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 154 | 1.6277 | 3 | 7 | 2.4596 | 12 | 32 | 10.2627 | B55 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 158 | 4.4897 | 4 | 11 | 5.5967 | 16 | 48 | 22.6364 | B56 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 153 | 155 | 1.9233 | 4 | 10 | 3.4112 | 16 | 44 | 13.9193 | B57 | 6 | 6 | 6.0968 | 0.3962 | 0.00 | 153 | 154 | 1.3552 | 6 | 12 | 5.2644 | 24 | 52 | 21.4015 | B58 | 6 | 6 | 6.0645 | 0.3592 | 0.00 | 152 | 155 | 4.0377 | 3 | 9 | 3.7643 | 14 | 38 | 14.9752 | B59 | 9 | 9 | 9.1290 | 0.3408 | 0.00 | 154 | 158 | 2.6825 | 5 | 15 | 6.7165 | 21 | 64 | 28.5839 | B60 | 4 | 4 | 4.3871 | 1.2021 | 0.00 | 152 | 156 | 2.3145 | 6 | 13 | 5.7136 | 24 | 56 | 23.8186 | B61 | 4 | 4 | 4.1290 | 0.3408 | 0.00 | 152 | 155 | 2.0394 | 4 | 13 | 6.7101 | 16 | 54 | 27.4017 | B62 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 155 | 4.1824 | 4 | 9 | 3.4273 | 18 | 40 | 13.6191 | B63 | 27 | 27 | 27.2581 | 0.5143 | 0.00 | 155 | 165 | 11.2005 | 4 | 21 | 11.4243 | 16 | 90 | 48.4598 | B64 | 18 | 18 | 18.3871 | 0.9549 | 0.00 | 155 | 167 | 14.2569 | 7 | 19 | 9.3371 | 28 | 86 | 39.7379 | B65 | 14 | 14 | 14.0645 | 0.2497 | 0.00 | 153 | 161 | 9.3472 | 6 | 15 | 7.5537 | 25 | 65 | 31.4611 | B66 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 247 | 97.6943 | 6 | 11 | 3.3020 | 24 | 81 | 67.8854 | B67 | 11 | 11 | 11.0323 | 0.1796 | 0.00 | 156 | 209 | 33.3034 | 4 | 14 | 7.7241 | 19 | 77 | 43.7733 | B68 | 8 | 8 | 8.8065 | 2.3154 | 0.00 | 156 | 179 | 30.7013 | 2 | 13 | 7.7239 | 9 | 63 | 40.9466 | B69 | 8 | 8 | 8.5161 | 0.6256 | 0.00 | 154 | 190 | 35.2266 | 5 | 12 | 5.7914 | 20 | 64 | 35.7448 | B70 | 6 | 6 | 6.4839 | 0.6256 | 0.00 | 152 | 167 | 16.6121 | 5 | 12 | 5.6220 | 22 | 57 | 26.9089 | B71 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 155 | 176 | 15.3473 | 6 | 11 | 5.4370 | 29 | 54 | 24.4164 | B72 | 4 | 4 | 4.2258 | 0.5603 | 0.00 | 155 | 168 | 21.0614 | 6 | 12 | 4.0783 | 28 | 55 | 23.1119 | B73 | 4 | 4 | 4.4516 | 0.6752 | 0.00 | 152 | 173 | 15.2415 | 4 | 11 | 6.4611 | 16 | 52 | 28.1919 | B74 | 3 | 3 | 3.3226 | 0.4752 | 0.00 | 153 | 166 | 14.9468 | 4 | 13 | 8.6221 | 20 | 60 | 35.3722 | B75 | 11 | 11 | 11.6774 | 0.9794 | 0.00 | 156 | 169 | 8.4222 | 4 | 17 | 10.5949 | 17 | 77 | 47.6167 | B76 | 5 | 5 | 5.2581 | 0.6816 | 0.00 | 154 | 167 | 23.7204 | 3 | 12 | 5.0513 | 14 | 56 | 26.0949 | B77 | 5 | 5 | 5.3871 | 0.8032 | 0.00 | 165 | 174 | 8.3753 | 6 | 14 | 8.1313 | 27 | 66 | 37.9381 | B78 | 4 | 4 | 4.9355 | 1.2093 | 0.00 | 163 | 176 | 12.2235 | 5 | 13 | 4.7399 | 22 | 60 | 25.3983 | B79 | 14 | 14 | 14.0323 | 0.1796 | 0.00 | 156 | 181 | 28.4157 | 5 | 10 | 3.2965 | 25 | 47 | 16.9919 | B80 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 171 | 190 | 20.4805 | 3 | 10 | 4.6704 | 17 | 53 | 23.3860 | B81 | 11 | 11 | 11.3871 | 0.8032 | 0.00 | 159 | 186 | 24.6086 | 7 | 14 | 7.1159 | 34 | 70 | 35.5031 | B82 | 10 | 10 | 10.3548 | 0.6607 | 0.00 | 153 | 169 | 25.0386 | 4 | 12 | 6.0875 | 16 | 55 | 29.4125 | B83 | 12 | 12 | 12.2258 | 1.2572 | 0.00 | 154 | 167 | 8.4371 | 4 | 12 | 6.3860 | 18 | 57 | 29.6714 | B84 | 12 | 12 | 12.0000 | 0.0000 | 0.00 | 155 | 165 | 13.7350 | 6 | 11 | 3.8852 | 31 | 52 | 17.8962 | B85 | 8 | 8 | 8.9355 | 1.4361 | 0.00 | 153 | 170 | 23.4146 | 4 | 14 | 7.3518 | 17 | 64 | 33.0030 | B86 | 8 | 8 | 8.1613 | 0.5829 | 0.00 | 156 | 177 | 15.4220 | 3 | 10 | 3.7814 | 13 | 47 | 18.0706 | B87 | 10 | 10 | 10.4839 | 1.0605 | 0.00 | 156 | 184 | 20.5574 | 4 | 18 | 9.4481 | 19 | 89 | 50.8878 | B88 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 155 | 194 | 109.8234 | 4 | 9 | 3.1995 | 20 | 61 | 96.8101 | B89 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 153 | 159 | 8.7550 | 4 | 10 | 3.7275 | 17 | 42 | 15.4842 | B90 | 5 | 5 | 5.2903 | 0.9016 | 0.00 | 152 | 156 | 2.2509 | 4 | 11 | 5.6435 | 17 | 49 | 22.9895 |
| ā | ā | AVG | 8.1025 | 0.4576 | 0.00 | 153 | 171 | 21.1539 | 3 | 9 | 4.7263 | 13 | 43 | 23.8747 |
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