Research Article
Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems
Table 29
MBO using parallel quick sort algorithm with 1 thread.
| | 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 | 193 | 68.9999 | 2 | 7 | 3.1195 | 9 | 41 | 17.8353 | | B2 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 165 | 18.8674 | 2 | 4 | 1.1538 | 8 | 19 | 8.8834 | | B3 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 161 | 19.3106 | 2 | 4 | 1.3827 | 8 | 19 | 6.5820 | | B4 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 167 | 25.8893 | 2 | 4 | 1.8014 | 8 | 20 | 9.8274 | | B5 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 154 | 177 | 33.0442 | 2 | 5 | 2.6769 | 9 | 29 | 17.8432 | | B6 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 165 | 11.4363 | 1 | 8 | 5.7640 | 4 | 38 | 25.6395 | | B7 | 6 | 6 | 6.0645 | 0.2497 | 0.00 | 153 | 159 | 3.8032 | 2 | 8 | 5.1941 | 9 | 36 | 22.4181 | | B8 | 4 | 4 | 4.2581 | 0.6816 | 0.00 | 152 | 158 | 5.4317 | 3 | 9 | 7.4731 | 12 | 38 | 30.7397 | | B9 | 3 | 3 | 3.0968 | 0.3005 | 0.00 | 153 | 168 | 20.1787 | 2 | 5 | 2.6102 | 10 | 25 | 11.7018 | | B10 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 152 | 158 | 7.1719 | 2 | 4 | 1.5794 | 8 | 17 | 6.8647 | | B11 | 4 | 4 | 4.1613 | 0.3739 | 0.00 | 154 | 162 | 8.1435 | 4 | 11 | 8.0349 | 16 | 48 | 34.9012 | | B12 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 154 | 1.6950 | 2 | 4 | 1.7064 | 8 | 18 | 6.9414 | | B13 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 154 | 2.0832 | 2 | 6 | 3.3636 | 8 | 25 | 13.6855 | | B14 | 3 | 3 | 3.4516 | 0.5680 | 0.00 | 152 | 168 | 22.8717 | 2 | 6 | 4.3793 | 8 | 27 | 19.2045 | | B15 | 1 | 1 | 1.4194 | 0.8860 | 0.00 | 153 | 175 | 34.8684 | 3 | 7 | 3.2531 | 12 | 33 | 16.1056 | | B16 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 159 | 221 | 63.7515 | 2 | 7 | 4.2848 | 11 | 41 | 21.9744 | | B17 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 178 | 48.9971 | 2 | 4 | 1.7026 | 9 | 22 | 9.6839 | | B18 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 155 | 4.3855 | 3 | 6 | 2.3655 | 12 | 24 | 10.3454 | | B19 | 13 | 13 | 13.0968 | 0.5388 | 0.00 | 152 | 153 | 2.1513 | 2 | 7 | 5.6009 | 8 | 30 | 22.7850 | | B20 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 153 | 1.5027 | 2 | 7 | 5.0298 | 8 | 32 | 20.2303 | | B21 | 9 | 9 | 9.0968 | 0.3005 | 0.00 | 154 | 158 | 3.0132 | 1 | 10 | 8.6519 | 4 | 43 | 35.6950 | | B22 | 6 | 6 | 6.1613 | 0.3739 | 0.00 | 152 | 156 | 4.0430 | 2 | 6 | 4.0364 | 8 | 26 | 16.4319 | | B23 | 6 | 6 | 6.0968 | 0.3005 | 0.00 | 152 | 153 | 1.4803 | 3 | 6 | 4.5416 | 12 | 27 | 18.2106 | | B24 | 5 | 5 | 5.3871 | 0.6152 | 0.00 | 152 | 153 | 1.5394 | 2 | 5 | 2.4132 | 8 | 23 | 9.6668 | | B25 | 4 | 4 | 4.4516 | 0.8500 | 0.00 | 152 | 154 | 1.8757 | 2 | 5 | 1.8567 | 8 | 23 | 7.7759 | | B26 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 154 | 158 | 4.2421 | 2 | 9 | 6.0213 | 8 | 40 | 25.2638 | | B27 | 3 | 3 | 3.0323 | 0.1796 | 0.00 | 152 | 156 | 3.4467 | 1 | 6 | 4.3334 | 4 | 27 | 17.5791 | | B28 | 3 | 3 | 3.3548 | 0.5507 | 0.00 | 152 | 154 | 2.4328 | 3 | 5 | 1.9724 | 12 | 24 | 8.1028 | | B29 | 3 | 3 | 3.2581 | 0.4448 | 0.00 | 152 | 154 | 3.9059 | 2 | 5 | 2.6126 | 8 | 23 | 10.6863 | | B30 | 2 | 2 | 2.2581 | 0.5143 | 0.00 | 152 | 154 | 1.8062 | 4 | 8 | 3.8077 | 16 | 32 | 15.4194 | | B31 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 166 | 12.3793 | 3 | 9 | 3.5214 | 12 | 39 | 14.8130 | | B32 | 4 | 4 | 4.1935 | 0.7492 | 0.00 | 154 | 161 | 9.6416 | 3 | 8 | 5.6009 | 12 | 35 | 23.3415 | | B33 | 4 | 4 | 4.1290 | 0.4995 | 0.00 | 152 | 160 | 7.4242 | 1 | 5 | 2.9712 | 4 | 24 | 12.6727 | | B34 | 4 | 4 | 4.0645 | 0.3592 | 0.00 | 152 | 156 | 4.2459 | 3 | 6 | 4.2170 | 12 | 28 | 17.9599 | | B35 | 4 | 4 | 4.9032 | 1.0118 | 0.00 | 153 | 166 | 10.7510 | 2 | 5 | 3.7626 | 8 | 26 | 16.9638 | | B36 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 155 | 177 | 17.3078 | 3 | 8 | 4.6900 | 12 | 38 | 23.3320 | | B37 | 10 | 10 | 10.5161 | 0.8896 | 0.00 | 153 | 165 | 14.0154 | 2 | 6 | 4.9622 | 8 | 26 | 20.6570 | | B38 | 8 | 8 | 8.0645 | 0.2497 | 0.00 | 152 | 165 | 14.2440 | 2 | 11 | 7.5177 | 8 | 52 | 33.8136 | | B39 | 5 | 5 | 5.3548 | 1.3796 | 0.00 | 154 | 168 | 10.6828 | 2 | 6 | 2.8136 | 8 | 27 | 13.6350 | | B40 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 152 | 162 | 7.7362 | 2 | 5 | 2.0832 | 8 | 22 | 8.8589 | | B41 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 177 | 24.0561 | 1 | 10 | 7.6418 | 4 | 47 | 36.2878 | | B42 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 153 | 182 | 36.9639 | 2 | 4 | 1.4081 | 8 | 20 | 10.2833 | | B43 | 8 | 8 | 8.0968 | 0.5388 | 0.00 | 162 | 268 | 137.6530 | 2 | 4 | 2.1463 | 12 | 33 | 27.5295 | | B44 | 5 | 5 | 5.8710 | 1.3842 | 0.00 | 155 | 172 | 21.8345 | 2 | 5 | 3.8857 | 8 | 27 | 19.0926 | | B45 | 5 | 5 | 5.8710 | 1.3842 | 0.00 | 153 | 182 | 50.6757 | 2 | 6 | 3.1036 | 8 | 29 | 20.3958 | | B46 | 8 | 8 | 8.1935 | 0.4016 | 0.00 | 172 | 219 | 56.1605 | 3 | 10 | 5.7329 | 15 | 60 | 43.2816 | | B47 | 5 | 5 | 5.0968 | 0.5388 | 0.00 | 166 | 207 | 40.9797 | 2 | 6 | 5.1442 | 10 | 40 | 29.2231 | | B48 | 5 | 5 | 5.0645 | 0.3592 | 0.00 | 163 | 170 | 5.2351 | 2 | 5 | 2.6258 | 8 | 26 | 12.1034 | | B49 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 160 | 170 | 8.4292 | 2 | 5 | 3.0754 | 9 | 24 | 13.6420 | | B50 | 5 | 5 | 5.5806 | 0.9228 | 0.00 | 160 | 174 | 21.8488 | 1 | 6 | 5.7528 | 4 | 28 | 25.8977 | | B51 | 27 | 27 | 28.3548 | 0.9504 | 0.00 | 167 | 198 | 36.1613 | 3 | 20 | 9.4901 | 14 | 106 | 48.8988 | | B52 | 18 | 18 | 18.7742 | 0.6688 | 0.00 | 155 | 159 | 3.0282 | 4 | 19 | 10.1538 | 17 | 84 | 42.9794 | | B53 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 154 | 159 | 4.8285 | 5 | 10 | 3.0593 | 20 | 43 | 13.3710 | | B54 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 156 | 2.9388 | 3 | 9 | 3.0061 | 12 | 38 | 12.4134 | | B55 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 164 | 12.3552 | 4 | 13 | 6.6611 | 16 | 57 | 28.3718 | | B56 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 154 | 175 | 24.3904 | 5 | 9 | 3.9809 | 22 | 44 | 17.8687 | | B57 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 153 | 163 | 6.9322 | 4 | 11 | 5.2964 | 16 | 50 | 24.4128 | | B58 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 153 | 156 | 3.5822 | 5 | 10 | 5.6569 | 21 | 41 | 23.9429 | | B59 | 9 | 9 | 9.0323 | 0.1796 | 0.00 | 155 | 166 | 5.9601 | 2 | 12 | 6.4739 | 8 | 54 | 27.6165 | | B60 | 4 | 4 | 4.5161 | 1.3631 | 0.00 | 154 | 163 | 7.2272 | 5 | 11 | 4.4119 | 21 | 49 | 19.4739 | | B61 | 4 | 4 | 4.2581 | 0.6308 | 0.00 | 154 | 158 | 6.1989 | 2 | 9 | 3.6644 | 8 | 41 | 15.6830 | | B62 | 4 | 4 | 4.1290 | 0.5623 | 0.00 | 153 | 156 | 2.4999 | 5 | 10 | 4.2704 | 20 | 42 | 17.9183 | | B63 | 27 | 27 | 27.2903 | 0.4614 | 0.00 | 155 | 166 | 6.3789 | 5 | 17 | 8.5487 | 26 | 77 | 38.2296 | | B64 | 18 | 18 | 18.2903 | 0.5287 | 0.00 | 157 | 165 | 6.0370 | 7 | 23 | 9.6062 | 28 | 104 | 42.0711 | | B65 | 14 | 14 | 14.1613 | 0.4544 | 0.00 | 154 | 160 | 4.3692 | 4 | 15 | 8.1672 | 17 | 65 | 36.0926 | | B66 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 163 | 8.8223 | 5 | 9 | 2.8923 | 20 | 42 | 12.0080 | | B67 | 11 | 11 | 11.0323 | 0.1796 | 0.00 | 159 | 170 | 7.5927 | 4 | 12 | 5.8966 | 17 | 55 | 26.7593 | | B68 | 8 | 8 | 8.5484 | 1.7481 | 0.00 | 154 | 162 | 7.1544 | 3 | 11 | 5.3146 | 12 | 50 | 22.5538 | | B69 | 8 | 8 | 8.3548 | 0.5507 | 0.00 | 153 | 156 | 2.4425 | 4 | 12 | 6.3070 | 16 | 51 | 25.7643 | | B70 | 6 | 6 | 6.2581 | 0.6308 | 0.00 | 153 | 156 | 2.2671 | 3 | 10 | 5.7856 | 12 | 44 | 23.9520 | | B71 | 6 | 6 | 6.0645 | 0.3592 | 0.00 | 156 | 181 | 27.7347 | 2 | 13 | 8.4332 | 11 | 64 | 39.5748 | | B72 | 4 | 4 | 4.1290 | 0.3408 | 0.00 | 155 | 177 | 29.3796 | 8 | 14 | 5.3225 | 36 | 64 | 23.1387 | | B73 | 4 | 4 | 4.5484 | 0.5680 | 0.00 | 153 | 182 | 46.2198 | 5 | 12 | 5.6883 | 20 | 63 | 40.8649 | | B74 | 3 | 3 | 3.4839 | 0.6768 | 0.00 | 153 | 181 | 24.0085 | 5 | 13 | 7.7974 | 22 | 62 | 38.6443 | | B75 | 11 | 11 | 11.7742 | 1.0866 | 0.00 | 164 | 216 | 65.0219 | 7 | 19 | 8.5961 | 30 | 102 | 42.8679 | | B76 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 154 | 159 | 3.2132 | 4 | 12 | 6.9587 | 19 | 50 | 28.7074 | | B77 | 5 | 5 | 5.9355 | 1.0626 | 0.00 | 154 | 159 | 2.5791 | 3 | 11 | 6.9711 | 13 | 50 | 29.2492 | | B78 | 4 | 4 | 4.7419 | 1.4135 | 0.00 | 153 | 158 | 2.8838 | 4 | 15 | 9.7257 | 20 | 64 | 40.5362 | | B79 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 156 | 162 | 5.3378 | 4 | 11 | 5.1178 | 18 | 49 | 21.6838 | | B80 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 159 | 2.9928 | 4 | 10 | 3.3575 | 16 | 46 | 14.4630 | | B81 | 11 | 11 | 11.2903 | 1.0064 | 0.00 | 153 | 158 | 2.8994 | 5 | 12 | 5.9435 | 21 | 52 | 25.2294 | | B82 | 10 | 10 | 10.6129 | 0.9892 | 0.00 | 154 | 158 | 2.6680 | 2 | 10 | 5.5058 | 8 | 45 | 22.8974 | | B83 | 12 | 12 | 12.0000 | 0.0000 | 0.00 | 156 | 165 | 6.5898 | 4 | 10 | 3.6210 | 20 | 46 | 14.5889 | | B84 | 12 | 12 | 12.0645 | 0.3592 | 0.00 | 155 | 163 | 5.1148 | 4 | 10 | 5.6932 | 18 | 44 | 24.3315 | | B85 | 8 | 8 | 8.9355 | 1.2893 | 0.00 | 155 | 161 | 5.5007 | 4 | 16 | 8.2380 | 16 | 69 | 35.8578 | | B86 | 8 | 8 | 8.0645 | 0.2497 | 0.00 | 153 | 165 | 10.2890 | 3 | 10 | 4.3411 | 15 | 46 | 18.2102 | | B87 | 10 | 10 | 10.5484 | 0.9605 | 0.00 | 157 | 177 | 13.8084 | 5 | 18 | 7.6776 | 23 | 87 | 37.4388 | | B88 | 8 | 8 | 8.2581 | 1.4368 | 0.00 | 154 | 166 | 13.5674 | 5 | 10 | 5.8803 | 24 | 46 | 24.4021 | | B89 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 156 | 168 | 18.2189 | 6 | 9 | 3.7301 | 24 | 43 | 20.6299 | | B90 | 5 | 5 | 5.3871 | 1.0223 | 0.00 | 153 | 164 | 9.5021 | 4 | 12 | 5.7030 | 18 | 54 | 24.8741 |
| | | | AVG | 8.1115 | 0.4667 | 0.00 | 154 | 167 | 15.5926 | 3 | 9 | 4.8703 | 13 | 42 | 22.3487 |
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