Research Article
Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems
Table 32
MBO using parallel quick sort algorithm with 16 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 | 157 | 177 | 45.0254 | 2 | 6 | 3.3999 | 12 | 34 | 19.8172 | B2 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 157 | 6.9088 | 2 | 3 | 1.0555 | 8 | 16 | 5.8123 | B3 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 157 | 6.2524 | 2 | 4 | 1.4760 | 8 | 20 | 7.8748 | B4 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 154 | 178 | 34.0738 | 2 | 4 | 1.8198 | 9 | 22 | 13.7301 | B5 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 155 | 176 | 26.4524 | 1 | 5 | 2.4065 | 4 | 25 | 11.7152 | B6 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 155 | 197 | 56.6853 | 2 | 9 | 5.5449 | 10 | 47 | 28.6512 | B7 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 152 | 203 | 48.1049 | 3 | 7 | 3.5948 | 16 | 41 | 32.0212 | B8 | 4 | 4 | 4.1935 | 0.6011 | 0.00 | 157 | 173 | 22.7143 | 2 | 9 | 7.1292 | 8 | 42 | 31.6330 | B9 | 3 | 3 | 3.0645 | 0.2497 | 0.00 | 154 | 166 | 16.3615 | 2 | 6 | 5.1249 | 9 | 27 | 21.8324 | B10 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 156 | 184 | 33.1923 | 2 | 4 | 1.4323 | 8 | 24 | 19.4711 | B11 | 4 | 4 | 4.2258 | 0.4250 | 0.00 | 163 | 232 | 56.6515 | 4 | 10 | 5.7893 | 22 | 62 | 40.3968 | B12 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 157 | 187 | 39.6154 | 2 | 5 | 1.9962 | 8 | 27 | 14.4440 | B13 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 154 | 168 | 11.7917 | 1 | 6 | 3.1890 | 4 | 28 | 13.8900 | B14 | 3 | 3 | 3.4516 | 0.5059 | 0.00 | 153 | 196 | 78.8003 | 2 | 5 | 2.7549 | 8 | 31 | 37.8248 | B15 | 1 | 1 | 1.5806 | 1.0255 | 0.00 | 152 | 175 | 23.7062 | 2 | 5 | 2.9523 | 8 | 29 | 17.7501 | B16 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 154 | 191 | 21.0426 | 3 | 8 | 3.8362 | 12 | 43 | 22.4885 | B17 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 155 | 177 | 30.7922 | 2 | 4 | 1.3190 | 8 | 22 | 5.8902 | B18 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 167 | 11.8313 | 2 | 5 | 2.6011 | 10 | 26 | 10.8408 | B19 | 13 | 13 | 13.0968 | 0.5388 | 0.00 | 154 | 170 | 17.4841 | 3 | 8 | 4.9782 | 12 | 36 | 23.2831 | B20 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 153 | 166 | 11.7813 | 1 | 6 | 4.9294 | 7 | 31 | 23.0983 | B21 | 9 | 9 | 9.0968 | 0.3005 | 0.00 | 157 | 183 | 16.9218 | 1 | 9 | 5.6618 | 5 | 46 | 26.0856 | B22 | 6 | 6 | 6.0968 | 0.3005 | 0.00 | 154 | 177 | 24.5003 | 2 | 5 | 2.2590 | 8 | 25 | 13.5459 | B23 | 6 | 6 | 6.2258 | 0.4250 | 0.00 | 154 | 165 | 14.6940 | 3 | 8 | 6.6832 | 13 | 36 | 30.1027 | B24 | 5 | 5 | 5.2903 | 0.5884 | 0.00 | 154 | 168 | 13.6450 | 3 | 6 | 4.7176 | 12 | 29 | 19.0212 | B25 | 4 | 4 | 4.3226 | 0.6525 | 0.00 | 152 | 173 | 25.1826 | 1 | 5 | 2.3233 | 4 | 24 | 11.7187 | B26 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 155 | 177 | 24.4236 | 2 | 7 | 4.0783 | 8 | 32 | 18.5792 | B27 | 3 | 3 | 3.0968 | 0.3005 | 0.00 | 153 | 165 | 10.0336 | 1 | 6 | 2.6303 | 4 | 28 | 11.0112 | B28 | 3 | 3 | 3.1613 | 0.4544 | 0.00 | 154 | 175 | 22.3457 | 1 | 6 | 3.1084 | 4 | 27 | 13.0248 | B29 | 3 | 3 | 3.0323 | 0.1796 | 0.00 | 156 | 166 | 14.2496 | 3 | 5 | 2.0457 | 12 | 23 | 9.0459 | B30 | 2 | 2 | 2.4839 | 0.6256 | 0.00 | 153 | 162 | 10.4239 | 2 | 8 | 7.0603 | 8 | 34 | 28.7763 | B31 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 163 | 175 | 10.1719 | 2 | 8 | 4.4158 | 11 | 37 | 20.2809 | B32 | 4 | 4 | 4.0968 | 0.5388 | 0.00 | 154 | 171 | 16.5987 | 2 | 6 | 3.3376 | 8 | 28 | 16.8551 | B33 | 4 | 4 | 4.2581 | 0.6816 | 0.00 | 154 | 165 | 13.2649 | 2 | 5 | 3.3237 | 8 | 22 | 13.7882 | B34 | 4 | 4 | 4.1290 | 0.4995 | 0.00 | 154 | 175 | 30.9978 | 1 | 5 | 4.1265 | 4 | 27 | 22.0238 | B35 | 4 | 4 | 4.5806 | 0.9228 | 0.00 | 153 | 178 | 96.2795 | 2 | 5 | 2.2337 | 8 | 23 | 9.5409 | B36 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 167 | 13.6572 | 2 | 9 | 4.7026 | 8 | 40 | 19.6464 | B37 | 10 | 10 | 10.6452 | 0.9504 | 0.00 | 152 | 156 | 2.9487 | 1 | 5 | 3.7108 | 4 | 23 | 15.0990 | B38 | 8 | 8 | 8.0645 | 0.2497 | 0.00 | 152 | 155 | 2.0182 | 3 | 11 | 8.6129 | 12 | 45 | 34.9003 | B39 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 152 | 156 | 2.2874 | 2 | 4 | 2.1677 | 8 | 20 | 9.0137 | B40 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 152 | 155 | 2.8021 | 3 | 6 | 4.3584 | 12 | 25 | 17.7059 | B41 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 155 | 160 | 4.9095 | 3 | 9 | 5.2548 | 12 | 39 | 21.6216 | B42 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 153 | 157 | 4.8928 | 2 | 4 | 2.8744 | 8 | 20 | 12.4631 | B43 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 163 | 9.2213 | 1 | 5 | 3.8633 | 4 | 24 | 16.0156 | B44 | 5 | 5 | 6.4516 | 1.5240 | 0.00 | 154 | 171 | 24.9946 | 2 | 5 | 2.4132 | 8 | 23 | 14.3787 | B45 | 5 | 5 | 5.9677 | 1.4256 | 0.00 | 154 | 168 | 16.9289 | 2 | 6 | 2.4323 | 8 | 26 | 10.5386 | B46 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 160 | 192 | 33.4808 | 2 | 10 | 8.0861 | 10 | 56 | 44.0563 | B47 | 5 | 5 | 5.1935 | 0.7492 | 0.00 | 155 | 176 | 28.5692 | 2 | 5 | 2.5539 | 8 | 27 | 19.4449 | B48 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 153 | 166 | 16.1625 | 2 | 5 | 2.4569 | 8 | 25 | 12.9483 | B49 | 5 | 5 | 5.2581 | 1.1245 | 0.00 | 154 | 185 | 24.4041 | 2 | 6 | 4.2487 | 12 | 34 | 26.5968 | B50 | 5 | 5 | 5.2581 | 0.6816 | 0.00 | 152 | 163 | 12.7533 | 2 | 5 | 2.7309 | 8 | 24 | 12.5672 | B51 | 27 | 27 | 28.1290 | 1.1472 | 0.00 | 155 | 163 | 4.5195 | 2 | 18 | 8.4909 | 9 | 81 | 36.9657 | B52 | 18 | 18 | 18.9032 | 0.9436 | 0.00 | 155 | 159 | 3.0589 | 5 | 20 | 9.0487 | 22 | 86 | 37.0107 | B53 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 154 | 158 | 3.9611 | 4 | 10 | 3.8532 | 17 | 42 | 15.9685 | B54 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 156 | 2.7739 | 3 | 8 | 2.9461 | 12 | 36 | 12.0974 | B55 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 159 | 4.2006 | 4 | 9 | 3.7540 | 16 | 40 | 15.8327 | B56 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 154 | 159 | 4.3319 | 2 | 11 | 4.5788 | 8 | 46 | 19.1962 | B57 | 6 | 6 | 6.0645 | 0.2497 | 0.00 | 153 | 159 | 9.3087 | 5 | 12 | 5.6773 | 20 | 51 | 24.6464 | B58 | 6 | 6 | 6.0645 | 0.2497 | 0.00 | 153 | 157 | 3.1748 | 5 | 10 | 5.7940 | 20 | 44 | 23.7433 | B59 | 9 | 9 | 9.0645 | 0.2497 | 0.00 | 155 | 160 | 3.7944 | 3 | 13 | 6.6326 | 14 | 58 | 27.4709 | B60 | 4 | 4 | 4.6452 | 1.7233 | 0.00 | 154 | 158 | 5.7524 | 6 | 14 | 5.8481 | 25 | 58 | 25.0316 | B61 | 4 | 4 | 4.0645 | 0.2497 | 0.00 | 153 | 157 | 3.0000 | 3 | 11 | 4.8558 | 12 | 48 | 20.1127 | B62 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 155 | 3.5305 | 2 | 10 | 5.8902 | 8 | 44 | 25.2071 | B63 | 27 | 27 | 27.2581 | 0.4448 | 0.00 | 157 | 162 | 3.2847 | 4 | 17 | 10.0560 | 19 | 75 | 43.2526 | B64 | 18 | 18 | 18.4516 | 0.9946 | 0.00 | 154 | 157 | 4.0473 | 4 | 20 | 8.9582 | 16 | 86 | 36.8209 | B65 | 14 | 14 | 14.1290 | 0.3408 | 0.00 | 154 | 156 | 2.2562 | 5 | 18 | 8.3264 | 21 | 75 | 34.2576 | B66 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 156 | 2.8368 | 5 | 10 | 3.5281 | 23 | 45 | 14.0460 | B67 | 11 | 11 | 11.0968 | 0.3005 | 0.00 | 155 | 159 | 2.1357 | 3 | 11 | 5.8249 | 13 | 50 | 24.4252 | B68 | 8 | 8 | 8.1290 | 0.3408 | 0.00 | 154 | 158 | 4.0166 | 3 | 13 | 6.0748 | 13 | 56 | 25.8166 | B69 | 8 | 8 | 8.3226 | 0.5408 | 0.00 | 154 | 157 | 3.5042 | 3 | 10 | 3.6715 | 13 | 44 | 15.2921 | B70 | 6 | 6 | 6.6129 | 0.6672 | 0.00 | 153 | 156 | 2.5003 | 3 | 12 | 5.7179 | 12 | 52 | 23.5929 | B71 | 6 | 6 | 6.1290 | 0.4995 | 0.00 | 154 | 158 | 3.0494 | 4 | 12 | 6.1740 | 16 | 53 | 25.9316 | B72 | 4 | 4 | 4.2258 | 0.4973 | 0.00 | 153 | 158 | 4.4504 | 4 | 13 | 7.0095 | 16 | 54 | 29.2744 | B73 | 4 | 4 | 4.4839 | 0.7244 | 0.00 | 154 | 157 | 3.1088 | 5 | 15 | 8.0446 | 20 | 62 | 33.2164 | B74 | 3 | 3 | 3.6129 | 0.6672 | 0.00 | 153 | 156 | 2.3601 | 4 | 14 | 7.6069 | 16 | 59 | 31.1370 | B75 | 11 | 11 | 11.6452 | 0.9848 | 0.00 | 155 | 162 | 8.1721 | 3 | 16 | 9.6780 | 16 | 71 | 41.5330 | B76 | 5 | 5 | 5.0645 | 0.3592 | 0.00 | 154 | 168 | 15.3240 | 5 | 12 | 4.8560 | 20 | 56 | 23.5850 | B77 | 5 | 5 | 5.5806 | 0.9228 | 0.00 | 154 | 171 | 25.1381 | 3 | 15 | 9.7619 | 12 | 66 | 41.9013 | B78 | 4 | 4 | 4.8065 | 1.2495 | 0.00 | 159 | 182 | 29.0268 | 4 | 12 | 6.2212 | 17 | 60 | 27.7959 | B79 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 157 | 169 | 15.0903 | 3 | 9 | 3.8852 | 13 | 44 | 15.6725 | B80 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 154 | 162 | 10.4361 | 4 | 11 | 3.9841 | 23 | 47 | 16.2254 | B81 | 11 | 11 | 11.3548 | 0.8386 | 0.00 | 154 | 172 | 19.7290 | 7 | 15 | 7.2530 | 33 | 71 | 32.6199 | B82 | 10 | 10 | 10.4839 | 0.7690 | 0.00 | 156 | 199 | 119.2439 | 5 | 12 | 6.1247 | 20 | 80 | 132.6427 | B83 | 12 | 12 | 12.0000 | 0.0000 | 0.00 | 157 | 188 | 28.7156 | 3 | 11 | 5.8672 | 13 | 56 | 32.9586 | B84 | 12 | 12 | 12.1935 | 0.6011 | 0.00 | 155 | 180 | 30.9175 | 6 | 11 | 5.1700 | 25 | 54 | 26.6157 | B85 | 8 | 8 | 9.0645 | 1.4127 | 0.00 | 154 | 162 | 8.6101 | 3 | 12 | 5.6041 | 12 | 54 | 23.3782 | B86 | 8 | 8 | 8.1290 | 0.7184 | 0.00 | 155 | 178 | 29.0973 | 2 | 10 | 5.2824 | 9 | 47 | 28.5301 | B87 | 10 | 10 | 10.6452 | 1.0503 | 0.00 | 157 | 180 | 28.1470 | 4 | 15 | 6.8785 | 16 | 72 | 29.6574 | B88 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 153 | 194 | 35.9039 | 2 | 9 | 3.5636 | 8 | 51 | 20.8887 | B89 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 155 | 183 | 37.7474 | 3 | 10 | 4.7424 | 14 | 52 | 34.4475 | B90 | 5 | 5 | 5.5806 | 1.2048 | 0.00 | 152 | 178 | 32.5974 | 4 | 10 | 5.5323 | 22 | 51 | 24.4181 |
| ā | ā | AVG | 8.1072 | 0.4325 | 0.00 | 154 | 169 | 18.9543 | 2 | 8 | 4.7619 | 12 | 42 | 23.6231 |
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