Research Article
Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems
Table 25
MBO using parallel merge sort algorithm with 8 threads.
| 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 | 153 | 175 | 52.9600 | 2 | 7 | 3.4650 | 10 | 40 | 24.1691 | B2 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 155 | 4.2538 | 1 | 4 | 1.3663 | 4 | 17 | 6.3123 | B3 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 154 | 2.2737 | 2 | 4 | 1.2675 | 8 | 16 | 4.9966 | B4 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 154 | 2.1875 | 3 | 5 | 1.6669 | 12 | 22 | 6.6451 | B5 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 154 | 3.5484 | 1 | 5 | 4.6460 | 4 | 22 | 19.1976 | B6 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 159 | 6.9589 | 3 | 9 | 5.6927 | 12 | 41 | 23.3150 | B7 | 6 | 6 | 6.0323 | 0.1796 | 0.00 | 152 | 155 | 2.6567 | 2 | 5 | 3.3376 | 8 | 24 | 13.6479 | B8 | 4 | 4 | 4.2581 | 0.6816 | 0.00 | 152 | 154 | 2.2500 | 2 | 10 | 7.8339 | 8 | 43 | 31.7022 | B9 | 3 | 3 | 3.0645 | 0.2497 | 0.00 | 152 | 154 | 2.8853 | 1 | 6 | 4.2480 | 4 | 26 | 17.5545 | B10 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 152 | 155 | 4.3342 | 2 | 4 | 2.2017 | 8 | 19 | 9.0625 | B11 | 4 | 4 | 4.1613 | 0.3739 | 0.00 | 154 | 158 | 4.0725 | 3 | 11 | 6.8310 | 12 | 46 | 28.0720 | B12 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 154 | 2.2041 | 1 | 4 | 1.7487 | 4 | 18 | 7.3882 | B13 | 4 | 4 | 4.0645 | 0.3592 | 0.00 | 152 | 157 | 8.3824 | 2 | 6 | 4.0825 | 8 | 24 | 16.4007 | B14 | 3 | 3 | 3.4516 | 0.5059 | 0.00 | 152 | 156 | 10.8955 | 2 | 5 | 2.0848 | 8 | 21 | 8.3643 | B15 | 1 | 1 | 1.2903 | 0.7829 | 0.00 | 152 | 153 | 1.8322 | 2 | 5 | 2.4110 | 8 | 23 | 9.8292 | B16 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 155 | 160 | 4.5349 | 2 | 7 | 3.6044 | 10 | 32 | 14.9542 | B17 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 155 | 2.2423 | 2 | 4 | 1.6145 | 8 | 20 | 6.7850 | B18 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 154 | 3.8763 | 1 | 5 | 2.1553 | 4 | 22 | 9.3721 | B19 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 153 | 1.4796 | 2 | 7 | 6.3034 | 8 | 28 | 25.4949 | B20 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 153 | 1.4803 | 2 | 8 | 5.1278 | 8 | 33 | 20.5847 | B21 | 9 | 9 | 9.1613 | 0.3739 | 0.00 | 154 | 158 | 2.8485 | 2 | 12 | 10.3146 | 8 | 52 | 42.6586 | B22 | 6 | 6 | 6.2581 | 0.6308 | 0.00 | 152 | 155 | 3.1380 | 2 | 6 | 2.8459 | 8 | 25 | 11.7755 | B23 | 6 | 6 | 6.1935 | 0.5428 | 0.00 | 152 | 153 | 2.0198 | 2 | 10 | 7.3810 | 8 | 43 | 30.1207 | B24 | 5 | 5 | 5.2581 | 0.5755 | 0.00 | 152 | 154 | 1.9355 | 1 | 7 | 3.5024 | 4 | 28 | 14.1402 | B25 | 4 | 4 | 4.2581 | 0.5143 | 0.00 | 152 | 153 | 2.0562 | 2 | 6 | 3.2132 | 8 | 26 | 12.9135 | B26 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 154 | 158 | 4.3165 | 2 | 9 | 6.1518 | 8 | 39 | 26.6302 | B27 | 3 | 3 | 3.0645 | 0.2497 | 0.00 | 152 | 155 | 2.3085 | 2 | 7 | 3.3033 | 8 | 30 | 13.5624 | B28 | 3 | 3 | 3.2581 | 0.5755 | 0.00 | 152 | 153 | 1.9680 | 2 | 5 | 3.0261 | 8 | 24 | 13.0409 | B29 | 3 | 3 | 3.2258 | 0.4250 | 0.00 | 152 | 154 | 2.4705 | 2 | 4 | 1.8228 | 8 | 18 | 7.6122 | B30 | 2 | 2 | 2.5484 | 0.6239 | 0.00 | 152 | 154 | 3.7018 | 2 | 7 | 5.7358 | 8 | 28 | 23.3637 | B31 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 158 | 3.0953 | 2 | 10 | 6.2340 | 8 | 42 | 25.8763 | B32 | 4 | 4 | 4.3871 | 1.2826 | 0.00 | 152 | 155 | 2.7875 | 2 | 8 | 5.7081 | 8 | 36 | 23.1095 | B33 | 4 | 4 | 4.1935 | 0.6011 | 0.00 | 152 | 154 | 3.7125 | 2 | 5 | 3.5753 | 8 | 21 | 15.1291 | B34 | 4 | 4 | 4.1290 | 0.4995 | 0.00 | 152 | 153 | 1.5268 | 2 | 5 | 4.2205 | 8 | 23 | 16.8363 | B35 | 4 | 4 | 4.6452 | 0.9504 | 0.00 | 152 | 152 | 1.0984 | 1 | 5 | 2.2177 | 4 | 21 | 8.8371 | B36 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 158 | 3.6041 | 4 | 9 | 4.6647 | 16 | 39 | 19.2969 | B37 | 10 | 10 | 10.3871 | 0.8032 | 0.00 | 152 | 155 | 4.3569 | 1 | 6 | 2.7689 | 4 | 24 | 11.4273 | B38 | 8 | 8 | 8.2258 | 0.4973 | 0.00 | 152 | 154 | 2.2026 | 2 | 9 | 7.5453 | 8 | 40 | 30.0411 | B39 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 152 | 154 | 2.2327 | 2 | 5 | 2.9759 | 9 | 22 | 11.9398 | B40 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 152 | 153 | 1.9989 | 2 | 5 | 2.7552 | 8 | 22 | 11.5980 | B41 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 159 | 4.8193 | 3 | 10 | 5.9482 | 14 | 45 | 24.6265 | B42 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 154 | 2.3692 | 2 | 4 | 2.3592 | 8 | 20 | 9.9095 | B43 | 8 | 8 | 8.0645 | 0.3592 | 0.00 | 152 | 154 | 1.8526 | 1 | 5 | 2.9563 | 4 | 21 | 12.2532 | B44 | 5 | 5 | 6.3548 | 1.5176 | 0.00 | 152 | 153 | 1.1538 | 2 | 5 | 2.9494 | 8 | 24 | 11.9644 | B45 | 5 | 5 | 6.1613 | 1.4854 | 0.00 | 152 | 153 | 1.5443 | 2 | 5 | 2.6917 | 8 | 23 | 10.8397 | B46 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 155 | 159 | 4.2805 | 2 | 9 | 6.9125 | 8 | 41 | 28.3549 | B47 | 5 | 5 | 5.0968 | 0.5388 | 0.00 | 152 | 154 | 2.0294 | 2 | 5 | 2.0811 | 8 | 21 | 8.4729 | B48 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 152 | 154 | 1.6428 | 2 | 4 | 2.2647 | 8 | 20 | 9.1640 | B49 | 5 | 5 | 5.2581 | 0.6816 | 0.00 | 151 | 153 | 3.5342 | 2 | 5 | 2.6482 | 8 | 21 | 10.6357 | B50 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 152 | 153 | 3.1826 | 2 | 5 | 2.8493 | 8 | 22 | 11.5451 | B51 | 27 | 27 | 27.9355 | 0.8139 | 0.00 | 154 | 161 | 3.4660 | 10 | 26 | 8.4370 | 41 | 111 | 35.6271 | B52 | 18 | 18 | 18.9355 | 1.0626 | 0.00 | 154 | 157 | 3.3758 | 8 | 24 | 9.0310 | 32 | 102 | 36.6151 | B53 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 155 | 1.8334 | 6 | 11 | 4.6911 | 24 | 45 | 19.0585 | B54 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 154 | 3.7637 | 3 | 8 | 2.6941 | 12 | 35 | 11.1208 | B55 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 158 | 3.2984 | 3 | 11 | 5.1034 | 13 | 49 | 21.0208 | B56 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 153 | 156 | 3.0093 | 4 | 11 | 3.8401 | 16 | 48 | 15.2743 | B57 | 6 | 6 | 6.1290 | 0.4275 | 0.00 | 153 | 155 | 2.8387 | 4 | 11 | 5.4081 | 16 | 46 | 22.2407 | B58 | 6 | 6 | 6.0645 | 0.2497 | 0.00 | 152 | 155 | 4.2566 | 3 | 10 | 3.8702 | 12 | 43 | 15.8509 | B59 | 9 | 9 | 9.0323 | 0.1796 | 0.00 | 155 | 158 | 3.0526 | 5 | 14 | 6.9780 | 22 | 60 | 29.3752 | B60 | 4 | 4 | 4.3871 | 1.2021 | 0.00 | 153 | 156 | 2.1687 | 5 | 14 | 7.0227 | 21 | 59 | 29.2113 | B61 | 4 | 4 | 4.1613 | 0.4544 | 0.00 | 153 | 156 | 4.8604 | 3 | 12 | 6.3903 | 12 | 52 | 27.7761 | B62 | 4 | 4 | 4.0323 | 0.1796 | 0.00 | 152 | 154 | 2.3678 | 4 | 10 | 4.8644 | 17 | 45 | 20.3279 | B63 | 27 | 27 | 27.1935 | 0.4016 | 0.00 | 156 | 162 | 4.4719 | 4 | 15 | 7.7450 | 16 | 66 | 32.7914 | B64 | 18 | 18 | 18.0968 | 0.3005 | 0.00 | 154 | 157 | 2.4722 | 5 | 19 | 8.3824 | 23 | 81 | 35.1227 | B65 | 14 | 14 | 14.0323 | 0.1796 | 0.00 | 153 | 156 | 4.1228 | 6 | 15 | 8.5828 | 24 | 65 | 35.2348 | B66 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 155 | 2.5179 | 7 | 9 | 2.7072 | 28 | 41 | 11.3806 | B67 | 11 | 11 | 11.1290 | 0.3408 | 0.00 | 154 | 159 | 4.6810 | 4 | 12 | 6.4386 | 17 | 52 | 27.4067 | B68 | 8 | 8 | 8.2258 | 0.9205 | 0.00 | 154 | 157 | 3.4830 | 3 | 14 | 9.5942 | 12 | 61 | 40.0795 | B69 | 8 | 8 | 8.6129 | 0.7154 | 0.00 | 153 | 156 | 4.5924 | 4 | 11 | 5.9648 | 16 | 48 | 24.0260 | B70 | 6 | 6 | 6.3548 | 0.7549 | 0.00 | 152 | 159 | 9.1831 | 3 | 14 | 6.6604 | 12 | 60 | 29.2535 | B71 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 154 | 160 | 5.0885 | 6 | 14 | 6.2436 | 28 | 60 | 26.1248 | B72 | 4 | 4 | 4.2581 | 0.5143 | 0.00 | 153 | 156 | 2.0956 | 3 | 11 | 5.6317 | 13 | 49 | 23.2173 | B73 | 4 | 4 | 4.3548 | 0.6607 | 0.00 | 152 | 155 | 4.3015 | 3 | 12 | 7.6978 | 12 | 51 | 31.3144 | B74 | 3 | 3 | 3.4839 | 0.5699 | 0.00 | 152 | 154 | 2.1038 | 3 | 11 | 6.2472 | 12 | 45 | 25.2912 | B75 | 11 | 11 | 11.7419 | 0.9298 | 0.00 | 154 | 160 | 4.5345 | 3 | 17 | 8.7525 | 13 | 72 | 37.3021 | B76 | 5 | 5 | 5.0645 | 0.3592 | 0.00 | 153 | 156 | 2.3192 | 4 | 12 | 6.1097 | 19 | 53 | 25.0673 | B77 | 5 | 5 | 5.5161 | 0.8896 | 0.00 | 152 | 155 | 4.3891 | 3 | 12 | 7.1977 | 12 | 52 | 29.2321 | B78 | 4 | 4 | 4.6774 | 1.1072 | 0.00 | 152 | 155 | 2.3908 | 4 | 15 | 6.2862 | 17 | 62 | 25.6253 | B79 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 155 | 159 | 3.0324 | 6 | 10 | 4.4923 | 24 | 43 | 18.5246 | B80 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 157 | 3.3665 | 4 | 11 | 3.6697 | 16 | 46 | 15.4853 | B81 | 11 | 11 | 11.3871 | 0.8032 | 0.00 | 152 | 156 | 4.2659 | 3 | 14 | 8.3982 | 12 | 61 | 34.5279 | B82 | 10 | 10 | 10.6774 | 0.7911 | 0.00 | 153 | 155 | 1.8613 | 5 | 12 | 5.4156 | 21 | 53 | 22.2498 | B83 | 12 | 12 | 12.1935 | 0.7492 | 0.00 | 154 | 160 | 4.3436 | 2 | 11 | 5.9686 | 8 | 50 | 25.0351 | B84 | 12 | 12 | 12.1290 | 0.4995 | 0.00 | 153 | 156 | 2.6567 | 6 | 13 | 6.1890 | 25 | 55 | 25.4035 | B85 | 8 | 8 | 9.5806 | 1.8934 | 0.00 | 153 | 156 | 3.8652 | 3 | 13 | 6.6922 | 13 | 55 | 27.3698 | B86 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 155 | 2.2504 | 4 | 10 | 4.1195 | 16 | 43 | 17.4584 | B87 | 10 | 10 | 10.4839 | 0.9263 | 0.00 | 155 | 159 | 3.6559 | 4 | 18 | 8.6221 | 16 | 79 | 36.8990 | B88 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 156 | 2.8530 | 4 | 10 | 3.8077 | 16 | 41 | 15.5335 | B89 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 156 | 4.3232 | 3 | 9 | 3.6948 | 12 | 39 | 15.6479 | B90 | 5 | 5 | 5.3871 | 1.0223 | 0.00 | 152 | 155 | 3.4501 | 3 | 11 | 4.1108 | 13 | 45 | 16.8234 |
| ā | ā | AVG | 8.1029 | 0.4293 | 0.00 | 152 | 155 | 3.8451 | 2 | 9 | 4.8785 | 12 | 40 | 20.2717 |
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