Research Article
Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems
Table 24
MBO using parallel merge sort algorithm with 4 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 | 158 | 216 | 109.1743 | 2 | 6 | 3.6142 | 9 | 42 | 25.9406 | B2 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 157 | 6.6604 | 2 | 4 | 1.2365 | 10 | 18 | 7.4686 | B3 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 166 | 47.4789 | 1 | 4 | 1.2960 | 4 | 18 | 8.4496 | B4 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 155 | 2.5716 | 1 | 5 | 2.6331 | 4 | 20 | 10.8924 | B5 | 11 | 11 | 11.3871 | 1.4984 | 0.00 | 153 | 167 | 45.7047 | 1 | 6 | 3.3085 | 4 | 29 | 18.6757 | B6 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 162 | 9.6934 | 2 | 9 | 5.7726 | 8 | 40 | 24.3002 | B7 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 154 | 167 | 41.5747 | 3 | 6 | 2.6845 | 12 | 26 | 10.8095 | B8 | 4 | 4 | 4.3226 | 0.7478 | 0.00 | 153 | 155 | 2.5003 | 2 | 11 | 9.7807 | 8 | 49 | 39.5824 | B9 | 3 | 3 | 3.0645 | 0.2497 | 0.00 | 152 | 168 | 58.7230 | 2 | 6 | 2.9494 | 8 | 27 | 17.1893 | B10 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 152 | 166 | 41.0109 | 2 | 4 | 1.9355 | 8 | 20 | 9.1206 | B11 | 4 | 4 | 4.1290 | 0.3408 | 0.00 | 155 | 160 | 4.3005 | 2 | 10 | 6.9986 | 8 | 43 | 29.6649 | B12 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 153 | 166 | 41.1127 | 1 | 4 | 1.8044 | 4 | 19 | 7.2704 | B13 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 155 | 2.5059 | 2 | 6 | 4.9324 | 8 | 25 | 20.2386 | B14 | 3 | 3 | 3.1935 | 0.4016 | 0.00 | 152 | 167 | 46.3310 | 1 | 5 | 2.2269 | 4 | 26 | 14.4843 | B15 | 1 | 1 | 1.3548 | 0.8386 | 0.00 | 152 | 154 | 2.6249 | 2 | 5 | 3.1356 | 8 | 24 | 12.8711 | B16 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 154 | 171 | 46.8582 | 3 | 8 | 4.1048 | 12 | 36 | 19.3441 | B17 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 157 | 4.7342 | 2 | 5 | 1.9903 | 8 | 21 | 8.5249 | B18 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 166 | 40.2106 | 3 | 5 | 1.9210 | 12 | 26 | 11.5105 | B19 | 13 | 13 | 13.1935 | 0.7492 | 0.00 | 152 | 157 | 9.6044 | 2 | 7 | 4.3160 | 8 | 29 | 17.8754 | B20 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 165 | 54.4453 | 2 | 7 | 3.8504 | 8 | 32 | 17.1361 | B21 | 9 | 9 | 9.2258 | 0.4250 | 0.00 | 154 | 173 | 54.5359 | 2 | 11 | 7.4947 | 10 | 51 | 32.7887 | B22 | 6 | 6 | 6.0968 | 0.3005 | 0.00 | 154 | 160 | 5.8877 | 3 | 5 | 2.8044 | 12 | 24 | 11.6705 | B23 | 6 | 6 | 6.0645 | 0.2497 | 0.00 | 152 | 169 | 48.5055 | 2 | 7 | 4.5711 | 8 | 35 | 21.3986 | B24 | 5 | 5 | 5.2581 | 0.5755 | 0.00 | 152 | 154 | 2.3010 | 2 | 6 | 2.7875 | 8 | 25 | 11.3416 | B25 | 4 | 4 | 4.1935 | 0.4016 | 0.00 | 152 | 167 | 46.4296 | 2 | 6 | 2.6644 | 8 | 27 | 23.6771 | B26 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 154 | 158 | 3.7574 | 3 | 8 | 6.3478 | 15 | 37 | 26.7206 | B27 | 3 | 3 | 3.0323 | 0.1796 | 0.00 | 154 | 168 | 47.1433 | 2 | 5 | 3.5903 | 9 | 26 | 19.3762 | B28 | 3 | 3 | 3.3226 | 0.4752 | 0.00 | 152 | 158 | 19.6735 | 1 | 5 | 3.6966 | 4 | 23 | 15.3801 | B29 | 3 | 3 | 3.1613 | 0.4544 | 0.00 | 152 | 163 | 41.5225 | 2 | 5 | 3.3315 | 8 | 25 | 35.7845 | B30 | 2 | 2 | 2.4839 | 0.5699 | 0.00 | 152 | 165 | 44.6843 | 2 | 7 | 5.1800 | 8 | 30 | 22.1249 | B31 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 153 | 161 | 6.9997 | 3 | 8 | 4.2651 | 12 | 37 | 18.4910 | B32 | 4 | 4 | 4.2903 | 0.9016 | 0.00 | 155 | 205 | 147.1775 | 1 | 8 | 5.0298 | 5 | 40 | 29.8585 | B33 | 4 | 4 | 4.0645 | 0.3592 | 0.00 | 153 | 172 | 25.2682 | 2 | 5 | 3.2974 | 8 | 25 | 13.9995 | B34 | 4 | 4 | 4.3226 | 0.7478 | 0.00 | 152 | 155 | 3.4554 | 1 | 6 | 6.1399 | 4 | 28 | 24.5491 | B35 | 4 | 4 | 4.3871 | 0.8032 | 0.00 | 152 | 157 | 7.2196 | 2 | 5 | 2.8979 | 8 | 23 | 11.7220 | B36 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 158 | 172 | 15.0594 | 3 | 10 | 5.7384 | 12 | 46 | 26.7314 | B37 | 10 | 10 | 10.4516 | 0.8500 | 0.00 | 154 | 166 | 14.1400 | 2 | 8 | 6.8311 | 8 | 38 | 28.5876 | B38 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 155 | 164 | 12.4326 | 2 | 8 | 5.6068 | 8 | 37 | 23.8998 | B39 | 5 | 5 | 5.3548 | 1.3796 | 0.00 | 154 | 163 | 12.5069 | 2 | 5 | 2.0884 | 8 | 22 | 9.4440 | B40 | 5 | 5 | 5.2581 | 0.6816 | 0.00 | 153 | 165 | 16.5927 | 2 | 5 | 3.6106 | 8 | 24 | 15.9870 | B41 | 8 | 8 | 8.1613 | 0.8980 | 0.00 | 156 | 166 | 9.9435 | 1 | 10 | 8.3483 | 4 | 47 | 36.1707 | B42 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 155 | 174 | 34.2187 | 2 | 4 | 1.6350 | 8 | 19 | 8.1873 | B43 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 153 | 198 | 46.1624 | 1 | 4 | 2.1423 | 4 | 24 | 13.0368 | B44 | 5 | 5 | 5.7742 | 1.3344 | 0.00 | 156 | 183 | 32.3323 | 2 | 5 | 1.6919 | 10 | 25 | 9.0367 | B45 | 5 | 5 | 5.8065 | 1.4005 | 0.00 | 152 | 157 | 4.5948 | 2 | 5 | 2.8658 | 9 | 24 | 12.1692 | B46 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 157 | 176 | 28.1980 | 3 | 10 | 7.1360 | 14 | 50 | 40.1945 | B47 | 5 | 5 | 5.1935 | 0.7492 | 0.00 | 155 | 183 | 36.2397 | 2 | 6 | 2.5649 | 8 | 31 | 16.0299 | B48 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 152 | 166 | 23.6329 | 2 | 5 | 2.2832 | 8 | 24 | 10.1954 | B49 | 5 | 5 | 5.2581 | 0.6816 | 0.00 | 152 | 155 | 2.8071 | 2 | 5 | 2.4613 | 8 | 22 | 10.1229 | B50 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 152 | 155 | 4.6881 | 2 | 7 | 5.3336 | 8 | 30 | 25.5601 | B51 | 27 | 27 | 28.2903 | 1.0064 | 0.00 | 159 | 164 | 4.3110 | 4 | 22 | 9.2894 | 16 | 98 | 40.3385 | B52 | 18 | 18 | 19.0645 | 1.0935 | 0.00 | 154 | 159 | 5.8249 | 5 | 22 | 9.8280 | 22 | 95 | 42.6600 | B53 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 178 | 32.7949 | 4 | 11 | 3.7102 | 19 | 51 | 18.7233 | B54 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 164 | 19.9278 | 3 | 7 | 2.7140 | 12 | 34 | 14.0533 | B55 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 155 | 160 | 3.4790 | 2 | 10 | 4.3510 | 8 | 46 | 18.3698 | B56 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 154 | 156 | 1.7121 | 2 | 10 | 3.2772 | 8 | 42 | 13.7300 | B57 | 6 | 6 | 6.0323 | 0.1796 | 0.00 | 153 | 160 | 16.4040 | 4 | 10 | 3.8788 | 17 | 45 | 16.0311 | B58 | 6 | 6 | 6.0323 | 0.1796 | 0.00 | 154 | 168 | 26.7755 | 3 | 10 | 3.9119 | 12 | 45 | 16.9634 | B59 | 9 | 9 | 9.2258 | 0.4973 | 0.00 | 155 | 194 | 38.6829 | 3 | 15 | 8.8444 | 13 | 76 | 44.3162 | B60 | 4 | 4 | 4.9032 | 1.7001 | 0.00 | 154 | 169 | 24.2931 | 3 | 12 | 6.6625 | 13 | 54 | 30.0641 | B61 | 4 | 4 | 4.1290 | 0.5623 | 0.00 | 155 | 268 | 200.8557 | 4 | 12 | 7.0176 | 16 | 109 | 179.0541 | B62 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 153 | 157 | 4.2149 | 3 | 9 | 3.8691 | 13 | 40 | 15.6801 | B63 | 27 | 27 | 27.2581 | 0.5143 | 0.00 | 154 | 165 | 10.6263 | 6 | 16 | 9.2118 | 24 | 71 | 40.8554 | B64 | 18 | 18 | 18.4516 | 0.8099 | 0.00 | 154 | 178 | 18.2276 | 7 | 19 | 9.1876 | 31 | 91 | 45.9490 | B65 | 14 | 14 | 14.0323 | 0.1796 | 0.00 | 155 | 161 | 7.8149 | 6 | 15 | 7.3228 | 25 | 68 | 30.9394 | B66 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 155 | 194 | 41.5668 | 6 | 10 | 3.4251 | 24 | 52 | 21.8884 | B67 | 11 | 11 | 11.0323 | 0.1796 | 0.00 | 158 | 210 | 67.1852 | 1 | 13 | 6.8971 | 4 | 72 | 42.9510 | B68 | 8 | 8 | 8.3226 | 1.2751 | 0.00 | 153 | 197 | 51.5259 | 4 | 13 | 7.9708 | 16 | 68 | 52.5572 | B69 | 8 | 8 | 8.5806 | 0.6720 | 0.00 | 155 | 208 | 84.9156 | 5 | 11 | 5.6323 | 21 | 60 | 31.5805 | B70 | 6 | 6 | 6.5484 | 0.8884 | 0.00 | 154 | 231 | 66.9705 | 4 | 15 | 8.5271 | 29 | 91 | 56.9068 | B71 | 6 | 6 | 6.0645 | 0.3592 | 0.00 | 157 | 217 | 70.6903 | 3 | 12 | 6.9808 | 14 | 71 | 46.9560 | B72 | 4 | 4 | 4.2258 | 0.4250 | 0.00 | 161 | 189 | 40.5461 | 5 | 13 | 7.1670 | 24 | 68 | 41.0736 | B73 | 4 | 4 | 4.4516 | 0.6239 | 0.00 | 156 | 177 | 29.4202 | 4 | 13 | 5.3836 | 20 | 59 | 23.6061 | B74 | 3 | 3 | 3.3871 | 0.5584 | 0.00 | 154 | 161 | 4.3200 | 3 | 13 | 7.5998 | 12 | 55 | 32.4734 | B75 | 11 | 11 | 11.7742 | 1.0866 | 0.00 | 155 | 172 | 13.9606 | 4 | 15 | 9.4963 | 16 | 69 | 45.7583 | B76 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 154 | 159 | 4.2812 | 4 | 13 | 6.7199 | 16 | 55 | 28.2946 | B77 | 5 | 5 | 5.9677 | 1.1968 | 0.00 | 154 | 157 | 3.0589 | 4 | 12 | 7.3398 | 16 | 54 | 30.8010 | B78 | 4 | 4 | 4.6452 | 1.1120 | 0.00 | 153 | 156 | 2.6757 | 1 | 13 | 7.3425 | 4 | 56 | 30.7701 | B79 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 154 | 161 | 5.2525 | 4 | 10 | 2.9487 | 18 | 43 | 12.1078 | B80 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 155 | 202 | 147.0668 | 3 | 11 | 5.4449 | 16 | 50 | 26.2353 | B81 | 11 | 11 | 11.4516 | 0.9605 | 0.00 | 155 | 208 | 59.8935 | 7 | 13 | 4.7648 | 28 | 74 | 32.8557 | B82 | 10 | 10 | 10.6452 | 0.7978 | 0.00 | 155 | 190 | 37.9565 | 4 | 13 | 7.3710 | 20 | 68 | 41.9503 | B83 | 12 | 12 | 12.0000 | 0.0000 | 0.00 | 155 | 162 | 6.1394 | 3 | 10 | 5.8394 | 12 | 48 | 28.0464 | B84 | 12 | 12 | 12.1935 | 0.6011 | 0.00 | 154 | 158 | 2.8090 | 7 | 12 | 6.3531 | 28 | 53 | 25.9466 | B85 | 8 | 8 | 9.1613 | 1.7146 | 0.00 | 154 | 156 | 1.8346 | 4 | 13 | 6.5165 | 16 | 57 | 27.0130 | B86 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 153 | 157 | 3.0107 | 3 | 11 | 3.7543 | 14 | 47 | 15.8781 | B87 | 10 | 10 | 10.8065 | 1.0462 | 0.00 | 156 | 168 | 14.7487 | 6 | 17 | 9.3396 | 24 | 78 | 43.8068 | B88 | 8 | 8 | 8.1935 | 1.0776 | 0.00 | 154 | 157 | 2.8132 | 4 | 10 | 5.2145 | 16 | 44 | 21.6391 | B89 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 157 | 2.5607 | 3 | 10 | 4.7956 | 13 | 44 | 20.3743 | B90 | 5 | 5 | 5.3871 | 1.0223 | 0.00 | 154 | 156 | 2.1397 | 4 | 11 | 4.6769 | 16 | 46 | 19.3850 |
| ā | ā | AVG | 8.1183 | 0.4847 | 0.00 | 153 | 170 | 28.8802 | 2 | 9 | 4.9501 | 12 | 43 | 25.6019 |
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