Scientific Programming

Research Article

Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems

Table 30

MBO using parallel quick 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 0.00 154 188 70.6184 1 6 4.1450 7 35 21.4910
B2 11 11 11.0000 0.0000 0.00 152 182 34.7551 2 3 1.4591 8 19 11.0777
B3 11 11 11.0000 0.0000 0.00 153 177 33.6228 2 4 1.7083 8 19 7.7936
B4 11 11 11.0000 0.0000 0.00 153 170 28.4944 2 4 1.7314 8 21 7.5054
B5 11 11 11.0000 0.0000 0.00 153 177 33.1479 2 4 2.1347 8 23 13.0829
B6 7 7 7.0000 0.0000 0.00 161 192 19.0742 3 9 5.1148 15 50 25.7463
B7 6 6 6.0323 0.1796 0.00 152 159 9.1029 1 5 2.5413 4 23 12.2419
B8 4 4 4.4516 1.2339 0.00 152 159 12.7028 2 11 8.2441 8 46 33.8427
B9 3 3 3.0968 0.3005 0.00 158 257 84.1696 1 6 3.5033 14 44 31.5700
B10 3 3 3.0000 0.0000 0.00 153 183 28.7203 2 4 2.5145 8 24 18.5823
B11 4 4 4.0968 0.3005 0.00 156 165 7.6151 3 11 6.1848 13 50 27.3824
B12 4 4 4.0000 0.0000 0.00 152 155 2.0000 2 4 1.5596 8 16 6.3920
B13 4 4 4.0645 0.3592 0.00 152 154 1.8538 3 4 2.1089 12 19 8.8271
B14 3 3 3.2903 0.4614 0.00 152 160 9.8399 1 5 2.5222 4 24 10.5106
B15 1 1 1.4516 0.8500 0.00 152 156 3.8373 1 5 3.5542 4 24 14.7010
B16 14 14 14.0000 0.0000 0.00 154 173 25.6756 3 9 4.8887 12 41 27.1373
B17 13 13 13.0000 0.0000 0.00 153 157 6.4014 2 5 1.6950 8 21 7.1785
B18 13 13 13.0000 0.0000 0.00 152 155 5.7326 2 5 2.4926 8 22 10.7346
B19 13 13 13.0000 0.0000 0.00 152 157 7.7789 3 7 3.6761 12 30 15.0969
B20 13 13 13.0000 0.0000 0.00 152 155 4.7308 2 6 3.0810 8 27 12.7058
B21 9 9 9.0968 0.3005 0.00 154 158 2.9072 3 11 7.1601 12 46 30.0206
B22 6 6 6.0645 0.2497 0.00 154 182 76.4377 3 6 2.7909 12 39 63.2356
B23 6 6 6.1290 0.4275 0.00 152 160 13.7304 2 7 4.4337 8 33 23.9618
B24 5 5 5.3871 0.6672 0.00 152 154 2.6893 3 6 2.5123 12 27 10.0762
B25 4 4 4.1935 0.6011 0.00 152 155 3.2505 2 6 2.8128 10 26 11.2697
B26 5 5 5.0000 0.0000 0.00 153 158 4.2021 2 8 6.8480 8 37 28.5317
B27 3 3 3.0968 0.3005 0.00 152 159 7.4229 3 8 6.4966 12 34 27.3041
B28 3 3 3.1935 0.4016 0.00 152 174 36.7644 2 6 4.5661 10 30 20.8310
B29 3 3 3.2258 0.4250 0.00 152 154 1.6224 1 5 1.8526 4 20 7.7248
B30 2 2 2.3871 0.5584 0.00 152 153 2.0651 2 6 3.0268 8 25 12.0320
B31 7 7 7.0000 0.0000 0.00 154 158 3.8702 2 9 5.1157 8 40 21.2321
B32 4 4 4.0000 0.0000 0.00 153 155 2.0925 2 6 3.6732 8 27 15.0795
B33 4 4 4.0645 0.3592 0.00 152 154 2.3150 1 5 2.5089 4 24 10.0413
B34 4 4 4.2581 0.6816 0.00 152 154 3.8401 2 6 4.1587 8 28 17.4530
B35 4 4 4.7097 0.9727 0.00 152 153 1.4701 1 7 5.4404 4 29 21.7851
B36 13 13 13.0000 0.0000 0.00 154 157 3.1167 2 6 3.5128 8 29 14.5407
B37 10 10 10.4516 0.8500 0.00 152 155 2.1840 1 5 3.6124 4 24 14.6059
B38 8 8 8.0323 0.1796 0.00 152 155 3.6706 2 14 9.2075 8 59 37.5165
B39 5 5 5.1613 0.8980 0.00 152 153 1.7339 2 5 2.6929 8 22 10.9139
B40 5 5 5.2581 0.6816 0.00 152 153 1.6091 2 5 2.4279 8 23 10.0457
B41 8 8 8.0000 0.0000 0.00 154 158 4.7956 2 7 4.4959 8 32 18.6759
B42 8 8 8.0000 0.0000 0.00 152 154 1.7469 2 4 2.2418 8 17 9.4866
B43 8 8 8.0000 0.0000 0.00 152 154 2.0064 1 5 2.4552 4 21 10.1844
B44 5 5 6.2581 1.5048 0.00 152 153 1.3647 1 6 3.6715 4 25 14.7284
B45 5 5 6.2903 1.5534 0.00 152 154 3.6805 3 5 2.3316 12 22 9.3036
B46 8 8 8.1290 0.3408 0.00 154 158 2.9719 3 9 6.7561 12 39 28.1927
B47 5 5 5.0968 0.5388 0.00 153 165 8.1313 2 5 2.2322 9 22 9.6494
B48 5 5 5.1935 0.6011 0.00 156 169 11.8787 1 6 4.2139 4 27 18.5138
B49 5 5 5.2581 0.6816 0.00 152 182 30.8552 2 5 2.3787 10 24 10.4171
B50 5 5 5.2581 0.6816 0.00 152 196 63.4998 3 8 5.8501 12 40 28.8074
B51 27 27 28.2581 1.2902 0.00 154 167 15.4226 7 21 7.9024 29 95 36.2584
B52 18 18 18.5806 0.9228 0.00 154 157 4.2457 7 20 9.5797 29 85 41.1011
B53 11 11 11.0000 0.0000 0.00 154 156 2.3477 5 10 3.7096 20 41 15.1854
B54 11 11 11.0000 0.0000 0.00 152 154 2.3408 6 9 2.1973 24 37 9.2985
B55 7 7 7.0000 0.0000 0.00 154 157 2.9607 4 11 4.6251 20 48 20.0461
B56 6 6 6.0000 0.0000 0.00 154 156 3.9259 5 10 3.7273 20 44 15.4734
B57 6 6 6.1290 0.4995 0.00 152 155 1.9394 4 11 3.9784 16 48 16.3756
B58 6 6 6.0000 0.0000 0.00 153 155 1.8439 4 9 3.4241 16 39 13.8646
B59 9 9 9.1290 0.4275 0.00 154 158 5.4091 4 11 4.9422 19 49 20.9249
B60 4 4 4.6452 1.4955 0.00 153 156 2.4622 5 12 6.4630 21 52 27.5544
B61 4 4 4.0323 0.1796 0.00 153 156 2.9838 3 11 7.3924 12 46 30.1892
B62 4 4 4.0323 0.1796 0.00 153 165 11.7614 3 9 4.1137 12 41 18.7758
B63 27 27 27.1935 0.4016 0.00 155 174 17.4625 6 17 9.3253 25 77 41.1960
B64 18 18 18.2903 0.5287 0.00 154 168 12.6685 4 18 9.1350 16 81 44.2824
B65 14 14 14.0323 0.1796 0.00 155 167 9.6409 3 15 7.6449 15 69 33.6520
B66 13 13 13.0000 0.0000 0.00 153 160 6.3507 4 9 3.0157 19 42 13.7272
B67 11 11 11.0000 0.0000 0.00 155 175 15.9737 6 15 8.3154 26 73 40.7381
B68 8 8 8.3226 1.2751 0.00 153 164 16.0762 3 11 6.8135 13 52 31.3006
B69 8 8 8.4839 0.6768 0.00 153 157 4.3202 4 12 6.9641 17 53 28.7297
B70 6 6 6.6452 0.9504 0.00 152 155 4.3401 4 15 8.3663 16 65 33.8478
B71 6 6 6.0645 0.3592 0.00 154 158 3.7631 7 13 6.9158 30 58 28.7037
B72 4 4 4.3226 0.6525 0.00 153 156 2.3215 4 13 8.2617 16 55 33.7554
B73 4 4 4.6774 0.6525 0.00 153 159 6.6099 3 11 5.8756 12 48 25.2215
B74 3 3 3.5484 0.5680 0.00 152 158 6.5660 4 13 7.7735 17 54 32.1404
B75 11 11 11.7419 1.0945 0.00 155 162 9.8424 5 18 7.4919 21 77 31.6711
B76 5 5 5.1935 0.6011 0.00 154 169 17.1585 6 14 6.6203 26 64 36.1670
B77 5 5 5.5161 0.8896 0.00 153 166 17.0023 3 13 6.6431 14 56 28.0002
B78 4 4 4.8387 1.4628 0.00 154 167 16.8144 4 17 8.5824 18 77 36.9169
B79 14 14 14.0000 0.0000 0.00 158 182 31.2523 4 9 6.0580 20 48 28.0606
B80 11 11 11.2581 1.4368 0.00 154 168 12.6654 4 11 4.0099 16 51 21.3734
B81 11 11 11.3871 0.9549 0.00 153 164 10.3919 4 15 9.5243 19 67 42.0640
B82 10 10 10.6452 0.7094 0.00 153 160 9.4966 5 11 5.4876 23 51 27.6218
B83 12 12 12.0000 0.0000 0.00 154 157 2.8341 4 12 4.8057 19 51 19.9222
B84 12 12 12.2903 0.7829 0.00 153 157 5.0586 5 14 8.1952 20 59 34.1199
B85 8 8 8.9677 1.3536 0.00 154 162 10.7207 8 15 6.6079 33 65 31.6611
B86 8 8 8.0323 0.1796 0.00 152 166 10.2565 4 9 3.7700 16 40 17.8689
B87 10 10 10.7097 0.9727 0.00 154 166 10.2930 7 19 8.5170 28 82 37.4828
B88 8 8 8.0000 0.0000 0.00 160 177 8.3988 4 10 4.3527 18 50 20.4859
B89 8 8 8.0323 0.1796 0.00 154 173 15.7080 2 10 8.1272 8 49 40.5965
B90 5 5 5.2903 0.9016 0.00 154 164 9.5502 4 11 5.5830 16 49 26.4783
   AVG 8.1108 0.4544 0.00 153 163 12.2109 3 9 4.9019 13 41 22.4733