Research Article
Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems
Table 28
MBO using sequential quick sort algorithm.
| 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 | 190 | 58.2650 | 2 | 7 | 3.8624 | 11 | 43 | 33.3476 | B2 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 161 | 11.6192 | 2 | 4 | 1.4074 | 8 | 19 | 6.0245 | B3 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 155 | 2.5085 | 2 | 4 | 1.5176 | 8 | 17 | 6.5214 | B4 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 182 | 101.4110 | 2 | 4 | 1.8246 | 8 | 22 | 9.4797 | B5 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 156 | 6.3229 | 2 | 5 | 3.4426 | 9 | 22 | 13.9587 | B6 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 161 | 13.5107 | 3 | 8 | 4.1693 | 12 | 37 | 17.3353 | B7 | 6 | 6 | 6.0323 | 0.1796 | 0.00 | 153 | 168 | 13.8935 | 3 | 6 | 2.9068 | 12 | 31 | 13.1726 | B8 | 4 | 4 | 4.0645 | 0.3592 | 0.00 | 152 | 182 | 34.6447 | 2 | 10 | 7.8375 | 8 | 49 | 35.8762 | B9 | 3 | 3 | 3.1290 | 0.3408 | 0.00 | 152 | 156 | 9.6349 | 2 | 6 | 5.9664 | 8 | 29 | 33.1260 | B10 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 152 | 154 | 2.1771 | 2 | 4 | 1.1968 | 8 | 16 | 4.7947 | B11 | 4 | 4 | 4.1290 | 0.3408 | 0.00 | 154 | 157 | 3.1084 | 1 | 11 | 8.3456 | 4 | 46 | 34.7346 | B12 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 155 | 3.0374 | 1 | 3 | 1.5794 | 5 | 15 | 6.4709 | B13 | 4 | 4 | 4.2258 | 0.7169 | 0.00 | 152 | 153 | 1.8814 | 2 | 5 | 5.3585 | 8 | 23 | 22.5828 | B14 | 3 | 3 | 3.3548 | 0.4864 | 0.00 | 152 | 154 | 1.6533 | 2 | 5 | 2.3971 | 8 | 23 | 9.8987 | B15 | 1 | 1 | 1.1290 | 0.4995 | 0.00 | 152 | 153 | 1.5027 | 2 | 6 | 2.2912 | 8 | 24 | 9.3735 | B16 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 154 | 158 | 6.5646 | 2 | 8 | 4.7026 | 8 | 34 | 19.1483 | B17 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 153 | 155 | 2.0283 | 2 | 5 | 1.8860 | 9 | 21 | 7.4763 | B18 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 157 | 7.3231 | 1 | 6 | 2.4995 | 4 | 25 | 10.3130 | B19 | 13 | 13 | 13.0968 | 0.5388 | 0.00 | 152 | 159 | 6.4381 | 2 | 7 | 6.0690 | 8 | 33 | 24.6737 | B20 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 153 | 159 | 7.5257 | 2 | 7 | 4.6504 | 8 | 31 | 19.5123 | B21 | 9 | 9 | 9.2903 | 0.4614 | 0.00 | 154 | 158 | 4.8569 | 2 | 9 | 7.8941 | 8 | 41 | 32.4426 | B22 | 6 | 6 | 6.1613 | 0.3739 | 0.00 | 152 | 160 | 7.6086 | 3 | 6 | 2.7611 | 12 | 26 | 12.0577 | B23 | 6 | 6 | 6.1613 | 0.3739 | 0.00 | 152 | 157 | 5.0575 | 4 | 10 | 7.1245 | 16 | 43 | 29.3833 | B24 | 5 | 5 | 5.2903 | 0.5287 | 0.00 | 152 | 159 | 6.8078 | 2 | 7 | 4.8146 | 9 | 30 | 19.7313 | B25 | 4 | 4 | 4.1613 | 0.3739 | 0.00 | 152 | 155 | 4.9514 | 2 | 6 | 2.5430 | 8 | 24 | 10.4495 | B26 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 154 | 163 | 8.4537 | 2 | 8 | 4.4837 | 8 | 36 | 18.4994 | B27 | 3 | 3 | 3.0323 | 0.1796 | 0.00 | 153 | 158 | 6.3527 | 1 | 7 | 5.5072 | 5 | 29 | 22.6066 | B28 | 3 | 3 | 3.2581 | 0.4448 | 0.00 | 152 | 162 | 9.1764 | 2 | 6 | 4.4041 | 8 | 26 | 20.0669 | B29 | 3 | 3 | 3.1613 | 0.3739 | 0.00 | 152 | 163 | 8.9060 | 1 | 5 | 2.9534 | 4 | 23 | 12.2417 | B30 | 2 | 2 | 2.6129 | 0.8032 | 0.00 | 152 | 162 | 11.2350 | 2 | 7 | 6.3716 | 8 | 30 | 26.7117 | B31 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 155 | 172 | 13.0047 | 3 | 8 | 5.2176 | 14 | 40 | 23.0526 | B32 | 4 | 4 | 4.0968 | 0.5388 | 0.00 | 154 | 163 | 16.2313 | 2 | 8 | 5.0189 | 8 | 36 | 22.6064 | B33 | 4 | 4 | 4.0645 | 0.3592 | 0.00 | 153 | 161 | 8.5798 | 2 | 5 | 2.5016 | 8 | 22 | 10.6692 | B34 | 4 | 4 | 4.1290 | 0.4995 | 0.00 | 152 | 158 | 9.0177 | 2 | 6 | 5.0302 | 8 | 27 | 20.6482 | B35 | 4 | 4 | 4.6452 | 0.9504 | 0.00 | 152 | 153 | 1.5098 | 1 | 5 | 4.4678 | 4 | 23 | 18.0923 | B36 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 174 | 26.3191 | 3 | 8 | 4.2014 | 12 | 41 | 24.8909 | B37 | 10 | 10 | 10.5161 | 0.8896 | 0.00 | 153 | 161 | 12.2450 | 2 | 7 | 3.9136 | 8 | 30 | 15.9159 | B38 | 8 | 8 | 8.0968 | 0.3962 | 0.00 | 152 | 157 | 6.5512 | 2 | 10 | 8.7204 | 8 | 43 | 35.7477 | B39 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 152 | 161 | 13.6204 | 3 | 5 | 2.3431 | 12 | 25 | 10.6618 | B40 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 152 | 163 | 9.7288 | 2 | 5 | 2.1438 | 8 | 21 | 9.9864 | B41 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 155 | 165 | 12.7196 | 1 | 10 | 6.2553 | 5 | 48 | 26.9376 | B42 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 157 | 3.5951 | 2 | 4 | 1.7804 | 8 | 19 | 7.5267 | B43 | 8 | 8 | 8.0645 | 0.3592 | 0.00 | 152 | 155 | 2.4947 | 2 | 5 | 5.3110 | 8 | 24 | 22.0386 | B44 | 5 | 5 | 6.0645 | 1.4591 | 0.00 | 152 | 155 | 3.3302 | 2 | 6 | 3.3601 | 8 | 25 | 13.7010 | B45 | 5 | 5 | 6.4516 | 1.5240 | 0.00 | 152 | 154 | 1.4135 | 2 | 5 | 2.2907 | 8 | 21 | 9.2427 | B46 | 8 | 8 | 8.1290 | 0.3408 | 0.00 | 154 | 161 | 4.7801 | 3 | 9 | 6.7587 | 14 | 42 | 29.0482 | B47 | 5 | 5 | 5.0968 | 0.5388 | 0.00 | 153 | 156 | 2.5392 | 1 | 4 | 1.8139 | 4 | 20 | 7.8833 | B48 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 152 | 155 | 4.2327 | 2 | 5 | 2.4021 | 8 | 23 | 9.6806 | B49 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 152 | 155 | 3.8960 | 3 | 7 | 4.9298 | 12 | 31 | 20.3514 | B50 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 152 | 157 | 7.6718 | 2 | 5 | 2.2728 | 8 | 24 | 9.2511 | B51 | 27 | 27 | 28.2258 | 0.9205 | 0.00 | 155 | 161 | 4.3769 | 4 | 19 | 9.2586 | 20 | 82 | 39.4718 | B52 | 18 | 18 | 18.9032 | 1.1062 | 0.00 | 154 | 158 | 4.4286 | 7 | 20 | 9.4888 | 29 | 85 | 40.2330 | B53 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 154 | 157 | 2.8269 | 4 | 10 | 4.1346 | 16 | 44 | 16.8027 | B54 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 156 | 2.3075 | 4 | 9 | 3.2052 | 16 | 38 | 13.3121 | B55 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 158 | 2.9370 | 4 | 10 | 5.4839 | 16 | 45 | 22.7564 | B56 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 154 | 157 | 2.2337 | 4 | 8 | 2.6184 | 16 | 36 | 11.1519 | B57 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 153 | 157 | 4.3503 | 6 | 10 | 4.0231 | 24 | 43 | 16.3044 | B58 | 6 | 6 | 6.1290 | 0.3408 | 0.00 | 154 | 157 | 2.8189 | 5 | 10 | 3.8882 | 20 | 44 | 15.7987 | B59 | 9 | 9 | 9.1935 | 0.6011 | 0.00 | 154 | 160 | 3.4817 | 3 | 13 | 8.1588 | 12 | 59 | 34.8749 | B60 | 4 | 4 | 4.5161 | 1.3631 | 0.00 | 154 | 157 | 2.8511 | 3 | 12 | 4.7288 | 12 | 50 | 19.8736 | B61 | 4 | 4 | 4.2258 | 0.6170 | 0.00 | 153 | 156 | 3.6237 | 3 | 11 | 4.2571 | 17 | 48 | 17.2788 | B62 | 4 | 4 | 4.0323 | 0.1796 | 0.00 | 152 | 155 | 2.5098 | 4 | 10 | 3.6820 | 16 | 41 | 15.5667 | B63 | 27 | 27 | 27.2581 | 0.4448 | 0.00 | 155 | 164 | 6.3053 | 4 | 19 | 10.1183 | 19 | 84 | 42.8466 | B64 | 18 | 18 | 18.3548 | 0.5507 | 0.00 | 154 | 175 | 29.3106 | 7 | 20 | 9.2391 | 37 | 95 | 41.8859 | B65 | 14 | 14 | 14.1935 | 0.4016 | 0.00 | 154 | 162 | 11.5242 | 5 | 14 | 6.2896 | 22 | 61 | 26.2881 | B66 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 174 | 31.3824 | 6 | 11 | 3.7301 | 24 | 51 | 22.7029 | B67 | 11 | 11 | 11.0323 | 0.1796 | 0.00 | 155 | 166 | 11.5943 | 6 | 12 | 5.7328 | 24 | 53 | 23.5936 | B68 | 8 | 8 | 8.5806 | 1.7469 | 0.00 | 154 | 160 | 5.9015 | 3 | 11 | 6.2869 | 12 | 48 | 25.7106 | B69 | 8 | 8 | 8.5161 | 0.8112 | 0.00 | 153 | 165 | 12.9041 | 4 | 10 | 5.4759 | 16 | 47 | 24.7696 | B70 | 6 | 6 | 6.6452 | 0.8386 | 0.00 | 153 | 160 | 11.3877 | 2 | 12 | 7.7095 | 8 | 52 | 31.6072 | B71 | 6 | 6 | 6.1290 | 0.4995 | 0.00 | 157 | 178 | 18.6546 | 2 | 11 | 5.3096 | 11 | 54 | 28.3288 | B72 | 4 | 4 | 4.2581 | 0.7732 | 0.00 | 154 | 171 | 19.4453 | 4 | 11 | 6.3664 | 16 | 54 | 29.4289 | B73 | 4 | 4 | 4.4194 | 0.6204 | 0.00 | 154 | 174 | 16.4459 | 5 | 10 | 4.0422 | 21 | 51 | 19.9695 | B74 | 3 | 3 | 3.5484 | 0.6239 | 0.00 | 156 | 187 | 33.9678 | 5 | 12 | 7.8744 | 20 | 67 | 49.6365 | B75 | 11 | 11 | 11.5806 | 1.0255 | 0.00 | 159 | 200 | 45.3931 | 4 | 17 | 9.9043 | 17 | 95 | 67.7548 | B76 | 5 | 5 | 5.0645 | 0.3592 | 0.00 | 154 | 171 | 37.0215 | 4 | 14 | 6.9785 | 17 | 67 | 30.3144 | B77 | 5 | 5 | 5.3871 | 0.8032 | 0.00 | 154 | 161 | 7.2560 | 4 | 14 | 7.2969 | 17 | 62 | 31.3623 | B78 | 4 | 4 | 4.5806 | 1.1188 | 0.00 | 153 | 166 | 11.1021 | 8 | 15 | 4.9588 | 32 | 69 | 24.4737 | B79 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 155 | 173 | 15.1100 | 5 | 9 | 2.9421 | 20 | 44 | 16.3185 | B80 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 154 | 164 | 13.3813 | 4 | 11 | 3.7198 | 17 | 48 | 16.2591 | B81 | 11 | 11 | 11.5484 | 1.1787 | 0.00 | 155 | 177 | 20.2888 | 2 | 13 | 8.5572 | 8 | 64 | 39.3331 | B82 | 10 | 10 | 10.7419 | 0.7732 | 0.00 | 154 | 227 | 142.7347 | 3 | 10 | 5.1533 | 13 | 56 | 31.9425 | B83 | 12 | 12 | 12.3548 | 1.5176 | 0.00 | 154 | 180 | 28.3520 | 3 | 11 | 6.7907 | 13 | 58 | 36.4259 | B84 | 12 | 12 | 12.0000 | 0.0000 | 0.00 | 155 | 165 | 12.8809 | 2 | 12 | 5.0773 | 9 | 54 | 23.5388 | B85 | 8 | 8 | 9.4516 | 1.6899 | 0.00 | 154 | 164 | 17.4202 | 3 | 13 | 6.9161 | 13 | 59 | 29.5533 | B86 | 8 | 8 | 8.1613 | 0.5829 | 0.00 | 153 | 155 | 2.0525 | 4 | 11 | 6.3534 | 16 | 49 | 25.9607 | B87 | 10 | 10 | 10.3871 | 0.9549 | 0.00 | 154 | 159 | 5.2984 | 5 | 16 | 9.5733 | 20 | 68 | 40.5421 | B88 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 157 | 2.8466 | 5 | 10 | 3.0610 | 21 | 43 | 12.7689 | B89 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 154 | 156 | 2.3349 | 4 | 10 | 5.9039 | 16 | 43 | 23.9970 | B90 | 5 | 5 | 5.3871 | 1.0223 | 0.00 | 153 | 155 | 2.5778 | 3 | 11 | 4.7201 | 13 | 46 | 18.9533 |
| ā | ā | AVG | 8.1111 | 0.4529 | 0.00 | 153 | 163 | 12.7284 | 2 | 9 | 4.9168 | 12 | 41 | 22.1071 |
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