Research Article
Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems
Table 27
MBO using parallel merge sort algorithm with 32 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 | 156 | 202 | 73.4610 | 3 | 7 | 2.8048 | 13 | 41 | 25.2275 | B2 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 159 | 8.6862 | 3 | 4 | 1.4473 | 12 | 22 | 9.7667 | B3 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 155 | 3.1575 | 1 | 4 | 1.6481 | 4 | 17 | 7.1419 | B4 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 159 | 12.7325 | 3 | 5 | 2.2756 | 12 | 23 | 10.9487 | B5 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 159 | 7.8248 | 2 | 5 | 2.0583 | 8 | 24 | 8.4883 | B6 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 168 | 11.3770 | 2 | 10 | 6.2576 | 10 | 44 | 28.5622 | B7 | 6 | 6 | 6.0645 | 0.2497 | 0.00 | 153 | 162 | 10.6669 | 3 | 6 | 2.3623 | 13 | 29 | 12.9453 | B8 | 4 | 4 | 4.1935 | 0.6011 | 0.00 | 152 | 157 | 4.6720 | 2 | 12 | 9.9450 | 8 | 51 | 41.2599 | B9 | 3 | 3 | 3.0968 | 0.3005 | 0.00 | 153 | 157 | 5.1856 | 1 | 5 | 2.5098 | 4 | 25 | 10.4043 | B10 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 152 | 159 | 8.1494 | 1 | 3 | 1.7001 | 4 | 16 | 7.8501 | B11 | 4 | 4 | 4.2581 | 0.4448 | 0.00 | 153 | 164 | 11.3640 | 3 | 12 | 7.4554 | 14 | 52 | 32.6614 | B12 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 157 | 5.4880 | 1 | 4 | 1.8026 | 4 | 17 | 7.6960 | B13 | 4 | 4 | 4.0645 | 0.3592 | 0.00 | 152 | 159 | 9.9945 | 2 | 5 | 2.4679 | 9 | 22 | 10.6621 | B14 | 3 | 3 | 3.2581 | 0.4448 | 0.00 | 152 | 157 | 7.2963 | 2 | 5 | 2.6632 | 8 | 23 | 11.1257 | B15 | 1 | 1 | 1.5161 | 0.8896 | 0.00 | 152 | 162 | 14.1797 | 2 | 6 | 2.7731 | 8 | 25 | 12.0180 | B16 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 155 | 178 | 28.1446 | 3 | 6 | 2.8459 | 12 | 32 | 12.6052 | B17 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 163 | 9.4999 | 1 | 4 | 1.6669 | 4 | 19 | 7.8038 | B18 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 153 | 176 | 50.4821 | 1 | 5 | 2.3431 | 5 | 22 | 12.0773 | B19 | 13 | 13 | 13.1935 | 0.7492 | 0.00 | 153 | 167 | 23.5020 | 2 | 7 | 4.6575 | 12 | 34 | 25.0622 | B20 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 196 | 65.9215 | 2 | 7 | 4.9246 | 9 | 39 | 27.7927 | B21 | 9 | 9 | 9.3548 | 0.4864 | 0.00 | 154 | 197 | 89.8626 | 2 | 11 | 8.3362 | 8 | 56 | 40.0088 | B22 | 6 | 6 | 6.1613 | 0.5829 | 0.00 | 155 | 213 | 63.0063 | 2 | 5 | 2.0161 | 8 | 32 | 18.9462 | B23 | 6 | 6 | 6.1935 | 0.4016 | 0.00 | 155 | 241 | 100.2556 | 3 | 7 | 5.8505 | 12 | 48 | 39.5844 | B24 | 5 | 5 | 5.2903 | 0.5884 | 0.00 | 152 | 164 | 31.9873 | 2 | 6 | 3.1288 | 8 | 28 | 12.6167 | B25 | 4 | 4 | 4.1613 | 0.3739 | 0.00 | 152 | 155 | 2.4839 | 2 | 6 | 4.9858 | 8 | 26 | 20.2954 | B26 | 5 | 5 | 5.0645 | 0.2497 | 0.00 | 155 | 162 | 5.6949 | 2 | 7 | 5.6531 | 8 | 34 | 24.0685 | B27 | 3 | 3 | 3.0968 | 0.3005 | 0.00 | 154 | 158 | 2.8860 | 2 | 6 | 3.6580 | 9 | 28 | 15.0662 | B28 | 3 | 3 | 3.1613 | 0.4544 | 0.00 | 152 | 156 | 3.2326 | 2 | 7 | 3.2322 | 8 | 30 | 13.6381 | B29 | 3 | 3 | 3.0968 | 0.3005 | 0.00 | 152 | 155 | 3.9811 | 2 | 5 | 2.2785 | 8 | 23 | 9.0958 | B30 | 2 | 2 | 2.5161 | 0.6256 | 0.00 | 152 | 156 | 4.9036 | 2 | 7 | 5.6843 | 8 | 30 | 23.2274 | B31 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 155 | 164 | 5.3710 | 1 | 7 | 4.3247 | 4 | 33 | 19.4109 | B32 | 4 | 4 | 4.1935 | 0.7492 | 0.00 | 152 | 157 | 3.1191 | 2 | 6 | 3.7035 | 8 | 28 | 15.7836 | B33 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 153 | 156 | 2.9574 | 3 | 5 | 2.7712 | 12 | 23 | 11.8504 | B34 | 4 | 4 | 4.0645 | 0.3592 | 0.00 | 152 | 156 | 4.1986 | 2 | 7 | 7.1646 | 8 | 32 | 31.8354 | B35 | 4 | 4 | 4.3226 | 0.7478 | 0.00 | 152 | 155 | 3.3758 | 2 | 5 | 3.0862 | 8 | 22 | 12.7461 | B36 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 155 | 162 | 5.9413 | 2 | 7 | 3.9284 | 9 | 34 | 16.4346 | B37 | 10 | 10 | 10.3226 | 0.7478 | 0.00 | 154 | 157 | 3.3153 | 2 | 7 | 5.8622 | 8 | 29 | 23.8995 | B38 | 8 | 8 | 8.2581 | 1.2641 | 0.00 | 152 | 156 | 4.6789 | 2 | 10 | 8.4328 | 8 | 42 | 34.3955 | B39 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 152 | 159 | 6.1503 | 2 | 5 | 2.9153 | 8 | 25 | 12.1929 | B40 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 155 | 168 | 23.4268 | 3 | 5 | 1.5513 | 13 | 23 | 7.9119 | B41 | 8 | 8 | 8.1613 | 0.8980 | 0.00 | 154 | 161 | 4.2011 | 4 | 9 | 6.6078 | 16 | 42 | 27.6753 | B42 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 153 | 157 | 6.3106 | 2 | 4 | 1.7828 | 8 | 18 | 7.7493 | B43 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 160 | 7.4285 | 2 | 5 | 2.6019 | 8 | 23 | 11.7932 | B44 | 5 | 5 | 5.8710 | 1.3842 | 0.00 | 154 | 161 | 7.9767 | 2 | 5 | 2.0687 | 12 | 22 | 9.0735 | B45 | 5 | 5 | 5.8710 | 1.3842 | 0.00 | 153 | 156 | 5.2525 | 2 | 5 | 3.0603 | 8 | 25 | 12.6925 | B46 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 154 | 165 | 8.5232 | 1 | 9 | 7.2947 | 4 | 40 | 32.4977 | B47 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 153 | 163 | 7.4939 | 2 | 6 | 3.3732 | 8 | 27 | 13.6618 | B48 | 5 | 5 | 5.0645 | 0.3592 | 0.00 | 155 | 190 | 88.3159 | 3 | 5 | 2.3550 | 12 | 26 | 10.0136 | B49 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 153 | 167 | 23.7535 | 2 | 6 | 2.2562 | 8 | 25 | 9.6192 | B50 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 153 | 206 | 111.6447 | 1 | 5 | 2.3619 | 4 | 30 | 22.2696 | B51 | 27 | 27 | 28.1613 | 0.7347 | 0.00 | 160 | 233 | 106.5829 | 4 | 19 | 9.9746 | 16 | 113 | 64.2842 | B52 | 18 | 18 | 18.8387 | 0.7347 | 0.00 | 154 | 164 | 6.9436 | 6 | 21 | 9.2897 | 27 | 91 | 41.3948 | B53 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 155 | 164 | 13.5560 | 5 | 11 | 3.1833 | 22 | 47 | 13.7809 | B54 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 156 | 163 | 4.5475 | 4 | 8 | 2.4274 | 17 | 37 | 11.2196 | B55 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 159 | 170 | 8.7338 | 5 | 10 | 3.2038 | 26 | 47 | 13.2918 | B56 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 154 | 166 | 10.0578 | 6 | 10 | 3.3742 | 27 | 47 | 16.6980 | B57 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 155 | 169 | 18.2314 | 6 | 11 | 5.5162 | 25 | 52 | 24.6267 | B58 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 154 | 162 | 4.3901 | 3 | 10 | 5.1287 | 12 | 44 | 22.2686 | B59 | 9 | 9 | 9.1613 | 0.5829 | 0.00 | 161 | 176 | 14.3747 | 5 | 14 | 7.2798 | 23 | 70 | 36.4352 | B60 | 4 | 4 | 4.2903 | 1.1312 | 0.00 | 157 | 173 | 14.4923 | 6 | 14 | 6.1914 | 25 | 64 | 28.9730 | B61 | 4 | 4 | 4.1613 | 0.5829 | 0.00 | 155 | 163 | 6.7429 | 4 | 9 | 4.0040 | 16 | 42 | 16.5396 | B62 | 4 | 4 | 4.0323 | 0.1796 | 0.00 | 154 | 160 | 3.5345 | 4 | 10 | 4.6504 | 16 | 43 | 19.3696 | B63 | 27 | 27 | 27.2258 | 0.4250 | 0.00 | 159 | 172 | 5.1895 | 3 | 20 | 11.1084 | 13 | 91 | 50.3296 | B64 | 18 | 18 | 18.1935 | 0.4016 | 0.00 | 157 | 173 | 22.8970 | 6 | 21 | 9.5444 | 25 | 102 | 51.5291 | B65 | 14 | 14 | 14.0645 | 0.2497 | 0.00 | 156 | 229 | 88.8105 | 6 | 16 | 6.8318 | 29 | 96 | 56.9926 | B66 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 155 | 198 | 64.6472 | 4 | 10 | 4.2088 | 20 | 55 | 27.5365 | B67 | 11 | 11 | 11.0968 | 0.3005 | 0.00 | 166 | 269 | 216.8374 | 3 | 15 | 9.5772 | 14 | 118 | 195.6026 | B68 | 8 | 8 | 8.2258 | 0.9205 | 0.00 | 154 | 170 | 13.6269 | 4 | 11 | 6.2202 | 17 | 53 | 26.0361 | B69 | 8 | 8 | 8.5161 | 0.7244 | 0.00 | 155 | 168 | 15.0527 | 6 | 13 | 6.1990 | 26 | 59 | 36.8672 | B70 | 6 | 6 | 6.5484 | 0.8884 | 0.00 | 153 | 156 | 5.1117 | 3 | 14 | 8.3743 | 14 | 62 | 34.9847 | B71 | 6 | 6 | 6.1290 | 0.4995 | 0.00 | 154 | 160 | 5.1506 | 4 | 11 | 4.5231 | 16 | 49 | 19.3207 | B72 | 4 | 4 | 4.3548 | 0.5507 | 0.00 | 152 | 157 | 3.9059 | 6 | 16 | 8.5049 | 25 | 67 | 36.2737 | B73 | 4 | 4 | 4.5161 | 0.6768 | 0.00 | 152 | 166 | 25.8682 | 4 | 13 | 9.0983 | 17 | 57 | 39.4182 | B74 | 3 | 3 | 3.5484 | 0.7676 | 0.00 | 154 | 169 | 18.5330 | 3 | 13 | 7.3941 | 13 | 57 | 32.0482 | B75 | 11 | 11 | 11.6452 | 0.9504 | 0.00 | 156 | 166 | 10.2917 | 6 | 14 | 9.4745 | 26 | 64 | 42.2402 | B76 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 153 | 202 | 49.9134 | 6 | 13 | 6.4288 | 25 | 73 | 35.4865 | B77 | 5 | 5 | 5.3871 | 0.8032 | 0.00 | 152 | 161 | 11.1016 | 4 | 13 | 7.0557 | 17 | 56 | 28.8527 | B78 | 4 | 4 | 4.7742 | 1.3344 | 0.00 | 153 | 159 | 7.9270 | 4 | 13 | 6.6488 | 17 | 55 | 29.2830 | B79 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 153 | 166 | 11.9017 | 2 | 9 | 3.9646 | 8 | 41 | 16.3156 | B80 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 154 | 162 | 9.6500 | 6 | 11 | 5.3587 | 24 | 50 | 23.5722 | B81 | 11 | 11 | 11.3548 | 0.8386 | 0.00 | 153 | 158 | 6.6857 | 5 | 13 | 7.0744 | 20 | 56 | 29.7124 | B82 | 10 | 10 | 10.4516 | 0.7676 | 0.00 | 152 | 160 | 10.6532 | 5 | 13 | 5.9386 | 20 | 55 | 27.4567 | B83 | 12 | 12 | 12.0968 | 0.5388 | 0.00 | 153 | 170 | 19.9290 | 5 | 11 | 3.8451 | 24 | 51 | 17.9308 | B84 | 12 | 12 | 12.0000 | 0.0000 | 0.00 | 154 | 161 | 6.7725 | 4 | 13 | 7.3941 | 16 | 55 | 31.6225 | B85 | 8 | 8 | 8.8387 | 1.2409 | 0.00 | 154 | 164 | 14.7388 | 5 | 14 | 7.2984 | 22 | 62 | 34.7666 | B86 | 8 | 8 | 8.0968 | 0.5388 | 0.00 | 153 | 162 | 10.3043 | 4 | 10 | 4.3183 | 16 | 44 | 18.7357 | B87 | 10 | 10 | 10.1290 | 0.4995 | 0.00 | 154 | 166 | 10.6363 | 5 | 18 | 8.1722 | 21 | 80 | 36.7600 | B88 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 160 | 6.2300 | 6 | 11 | 4.4717 | 24 | 50 | 18.2966 | B89 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 181 | 63.1321 | 4 | 10 | 3.9393 | 16 | 50 | 22.3958 | B90 | 5 | 5 | 5.4839 | 1.1216 | 0.00 | 154 | 158 | 5.3563 | 3 | 10 | 4.3045 | 12 | 41 | 18.0081 |
| ā | ā | AVG | 8.0756 | 0.4173 | 0.00 | 154 | 170 | 21.8506 | 3 | 9 | 4.8937 | 14 | 44 | 24.7712 |
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