Scientific Programming

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
   AVG 8.1072 0.4325 0.00 154 169 18.9543 2 8 4.7619 12 42 23.6231