Research Article
Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems
Table 33
MBO using parallel quick 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 | 157 | 193 | 67.2126 | 4 | 8 | 3.8529 | 19 | 47 | 23.5622 | | B2 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 160 | 6.2348 | 2 | 4 | 1.3190 | 9 | 19 | 7.0225 | | B3 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 158 | 4.9071 | 1 | 4 | 1.8020 | 4 | 19 | 7.5696 | | B4 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 156 | 2.5745 | 2 | 4 | 1.6428 | 8 | 16 | 6.8760 | | B5 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 154 | 160 | 5.0292 | 2 | 6 | 3.4962 | 8 | 29 | 14.8304 | | B6 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 160 | 195 | 70.3551 | 3 | 11 | 7.8781 | 12 | 60 | 43.3428 | | B7 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 155 | 160 | 3.6423 | 2 | 5 | 2.2538 | 9 | 24 | 9.5139 | | B8 | 4 | 4 | 4.1935 | 0.6011 | 0.00 | 154 | 160 | 4.4473 | 2 | 13 | 10.0692 | 8 | 56 | 41.9610 | | B9 | 3 | 3 | 3.0323 | 0.1796 | 0.00 | 153 | 158 | 3.1302 | 2 | 5 | 2.6901 | 8 | 22 | 11.0625 | | B10 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 153 | 161 | 5.0956 | 2 | 4 | 1.9092 | 8 | 19 | 8.2968 | | B11 | 4 | 4 | 4.1613 | 0.3739 | 0.00 | 159 | 174 | 8.7291 | 2 | 11 | 9.6157 | 10 | 55 | 44.6467 | | B12 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 154 | 158 | 3.0515 | 2 | 4 | 2.0483 | 8 | 20 | 8.5759 | | B13 | 4 | 4 | 4.0645 | 0.3592 | 0.00 | 153 | 157 | 3.8356 | 2 | 4 | 1.7677 | 8 | 18 | 7.3472 | | B14 | 3 | 3 | 3.4516 | 0.5059 | 0.00 | 152 | 156 | 3.0789 | 2 | 5 | 3.0164 | 9 | 24 | 12.6226 | | B15 | 1 | 1 | 1.2581 | 0.6816 | 0.00 | 152 | 158 | 7.3659 | 2 | 6 | 2.6069 | 8 | 25 | 11.2249 | | B16 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 154 | 168 | 8.2101 | 2 | 7 | 3.0670 | 10 | 35 | 13.2306 | | B17 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 159 | 3.4867 | 2 | 5 | 1.9389 | 8 | 22 | 8.2489 | | B18 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 156 | 2.6437 | 2 | 4 | 2.0288 | 8 | 20 | 8.4173 | | B19 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 159 | 6.3924 | 2 | 6 | 2.6567 | 8 | 27 | 11.0241 | | B20 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 158 | 8.2973 | 2 | 7 | 3.5360 | 8 | 30 | 14.4425 | | B21 | 9 | 9 | 9.1290 | 0.3408 | 0.00 | 163 | 180 | 10.9634 | 2 | 9 | 6.9766 | 9 | 47 | 33.4055 | | B22 | 6 | 6 | 6.0645 | 0.2497 | 0.00 | 153 | 159 | 3.6133 | 1 | 6 | 3.4591 | 4 | 29 | 14.6736 | | B23 | 6 | 6 | 6.1935 | 0.4016 | 0.00 | 154 | 159 | 5.3000 | 2 | 7 | 5.8411 | 12 | 32 | 24.2679 | | B24 | 5 | 5 | 5.4516 | 0.6752 | 0.00 | 152 | 157 | 3.6320 | 2 | 6 | 2.7658 | 8 | 25 | 11.7582 | | B25 | 4 | 4 | 4.2258 | 0.4250 | 0.00 | 152 | 157 | 3.4273 | 2 | 7 | 4.7573 | 8 | 29 | 19.6816 | | B26 | 5 | 5 | 5.0323 | 0.1796 | 0.00 | 155 | 167 | 7.9712 | 1 | 8 | 5.1750 | 4 | 38 | 22.6477 | | B27 | 3 | 3 | 3.0645 | 0.2497 | 0.00 | 154 | 160 | 5.4513 | 2 | 6 | 4.0284 | 8 | 28 | 17.1102 | | B28 | 3 | 3 | 3.1290 | 0.3408 | 0.00 | 152 | 157 | 3.9081 | 3 | 5 | 1.7096 | 12 | 23 | 7.4421 | | B29 | 3 | 3 | 3.0645 | 0.2497 | 0.00 | 152 | 157 | 4.1860 | 1 | 5 | 2.5911 | 4 | 21 | 10.8956 | | B30 | 2 | 2 | 2.5806 | 0.5642 | 0.00 | 152 | 157 | 3.6694 | 2 | 7 | 6.6775 | 8 | 31 | 28.3555 | | B31 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 155 | 165 | 6.5364 | 1 | 8 | 4.6596 | 4 | 37 | 21.1130 | | B32 | 4 | 4 | 4.1935 | 0.7492 | 0.00 | 153 | 159 | 4.2621 | 1 | 8 | 5.6591 | 4 | 34 | 23.4602 | | B33 | 4 | 4 | 4.1290 | 0.4995 | 0.00 | 152 | 157 | 3.4093 | 3 | 6 | 3.2015 | 12 | 25 | 13.2534 | | B34 | 4 | 4 | 4.3226 | 0.7478 | 0.00 | 153 | 157 | 3.5469 | 2 | 5 | 4.2812 | 9 | 24 | 17.1984 | | B35 | 4 | 4 | 4.3871 | 0.8032 | 0.00 | 153 | 159 | 6.8737 | 1 | 5 | 2.7591 | 4 | 24 | 11.7173 | | B36 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 162 | 191 | 55.9882 | 1 | 8 | 5.3864 | 4 | 42 | 27.3086 | | B37 | 10 | 10 | 10.3226 | 0.7478 | 0.00 | 154 | 163 | 7.1865 | 1 | 8 | 7.0555 | 5 | 35 | 30.6683 | | B38 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 158 | 3.9570 | 3 | 9 | 6.1737 | 12 | 38 | 25.0810 | | B39 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 154 | 159 | 4.1968 | 2 | 5 | 2.3047 | 8 | 22 | 10.0090 | | B40 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 154 | 162 | 8.1181 | 3 | 5 | 1.7506 | 12 | 22 | 7.9040 | | B41 | 8 | 8 | 8.3226 | 1.2487 | 0.00 | 156 | 172 | 11.4272 | 3 | 11 | 7.4741 | 14 | 55 | 38.2555 | | B42 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 155 | 163 | 9.3587 | 2 | 4 | 2.2855 | 8 | 21 | 10.4073 | | B43 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 155 | 215 | 74.3419 | 2 | 5 | 2.0483 | 9 | 29 | 16.7208 | | B44 | 5 | 5 | 5.8710 | 1.3842 | 0.00 | 155 | 208 | 74.1396 | 2 | 6 | 3.7788 | 12 | 35 | 20.5935 | | B45 | 5 | 5 | 6.3548 | 1.5176 | 0.00 | 152 | 174 | 54.0282 | 1 | 5 | 2.9910 | 12 | 26 | 14.9598 | | B46 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 159 | 266 | 116.1782 | 1 | 10 | 5.7489 | 5 | 65 | 52.7578 | | B47 | 5 | 5 | 5.0968 | 0.5388 | 0.00 | 166 | 197 | 82.7696 | 1 | 5 | 2.1287 | 7 | 25 | 11.5699 | | B48 | 5 | 5 | 5.2581 | 0.6816 | 0.00 | 164 | 241 | 91.5422 | 2 | 5 | 2.6392 | 8 | 40 | 34.3044 | | B49 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 169 | 281 | 103.5425 | 2 | 7 | 4.7853 | 10 | 49 | 38.4886 | | B50 | 5 | 5 | 5.3226 | 0.7478 | 0.00 | 157 | 196 | 37.8474 | 2 | 5 | 3.0547 | 9 | 29 | 15.1232 | | B51 | 27 | 27 | 28.0645 | 0.8920 | 0.00 | 158 | 207 | 50.7988 | 3 | 20 | 9.7651 | 15 | 115 | 63.2991 | | B52 | 18 | 18 | 18.7742 | 1.0555 | 0.00 | 160 | 232 | 64.3241 | 4 | 20 | 9.6569 | 17 | 124 | 71.2839 | | B53 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 161 | 174 | 14.6625 | 6 | 11 | 4.6327 | 26 | 50 | 22.0361 | | B54 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 158 | 193 | 115.3675 | 4 | 8 | 2.3550 | 18 | 40 | 12.4287 | | B55 | 7 | 7 | 7.1290 | 0.7184 | 0.00 | 169 | 180 | 6.2545 | 4 | 12 | 5.4335 | 21 | 59 | 26.9609 | | B56 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 163 | 174 | 13.8653 | 4 | 9 | 2.4705 | 18 | 42 | 12.1870 | | B57 | 6 | 6 | 6.2258 | 0.6688 | 0.00 | 161 | 178 | 20.6817 | 5 | 11 | 6.1501 | 26 | 55 | 26.7029 | | B58 | 6 | 6 | 6.0323 | 0.1796 | 0.00 | 161 | 166 | 5.6791 | 2 | 9 | 5.4692 | 10 | 40 | 22.9230 | | B59 | 9 | 9 | 9.0968 | 0.3005 | 0.00 | 170 | 178 | 4.8449 | 4 | 12 | 5.8635 | 19 | 60 | 27.2347 | | B60 | 4 | 4 | 4.2581 | 0.9989 | 0.00 | 162 | 172 | 7.4626 | 3 | 11 | 6.1011 | 14 | 54 | 28.2474 | | B61 | 4 | 4 | 4.0645 | 0.2497 | 0.00 | 159 | 167 | 5.3539 | 4 | 11 | 5.2357 | 18 | 49 | 23.0532 | | B62 | 4 | 4 | 4.0968 | 0.3005 | 0.00 | 159 | 174 | 11.7428 | 2 | 11 | 5.9301 | 9 | 51 | 28.0555 | | B63 | 27 | 27 | 27.2258 | 0.4250 | 0.00 | 176 | 183 | 4.3125 | 5 | 18 | 10.3340 | 24 | 89 | 50.4055 | | B64 | 18 | 18 | 18.2581 | 0.6308 | 0.00 | 163 | 197 | 50.6838 | 4 | 16 | 9.1136 | 19 | 82 | 44.4143 | | B65 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 155 | 165 | 15.1038 | 6 | 16 | 8.3361 | 24 | 69 | 36.6212 | | B66 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 155 | 164 | 9.6089 | 4 | 9 | 3.0533 | 19 | 42 | 14.9758 | | B67 | 11 | 11 | 11.1290 | 0.3408 | 0.00 | 154 | 172 | 13.8726 | 3 | 13 | 8.6648 | 13 | 62 | 38.9473 | | B68 | 8 | 8 | 8.5484 | 1.4338 | 0.00 | 154 | 161 | 8.0448 | 2 | 13 | 6.7357 | 8 | 57 | 28.8067 | | B69 | 8 | 8 | 8.5806 | 0.7199 | 0.00 | 152 | 189 | 51.5676 | 5 | 11 | 4.3643 | 20 | 55 | 26.5377 | | B70 | 6 | 6 | 6.3871 | 0.6152 | 0.00 | 153 | 177 | 47.0718 | 6 | 13 | 5.1690 | 24 | 66 | 39.7750 | | B71 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 161 | 218 | 88.2505 | 7 | 12 | 4.1688 | 34 | 75 | 43.2647 | | B72 | 4 | 4 | 4.1935 | 0.4774 | 0.00 | 154 | 171 | 22.0755 | 4 | 13 | 7.8702 | 17 | 64 | 42.7791 | | B73 | 4 | 4 | 4.6774 | 0.5408 | 0.00 | 156 | 207 | 66.9800 | 4 | 15 | 7.8781 | 16 | 90 | 80.4632 | | B74 | 3 | 3 | 3.4839 | 0.6768 | 0.00 | 158 | 225 | 117.9903 | 4 | 13 | 8.8637 | 18 | 69 | 43.8618 | | B75 | 11 | 11 | 11.6774 | 0.8713 | 0.00 | 175 | 251 | 58.8080 | 5 | 17 | 7.5933 | 34 | 110 | 56.0249 | | B76 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 155 | 179 | 27.7539 | 4 | 13 | 7.2367 | 22 | 63 | 29.9982 | | B77 | 5 | 5 | 5.5484 | 0.9605 | 0.00 | 152 | 159 | 5.4345 | 5 | 12 | 7.0432 | 20 | 51 | 28.9970 | | B78 | 4 | 4 | 4.6452 | 1.1120 | 0.00 | 152 | 163 | 20.6672 | 3 | 11 | 6.2579 | 12 | 49 | 26.2351 | | B79 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 154 | 165 | 8.7211 | 3 | 9 | 3.3344 | 15 | 42 | 15.1123 | | B80 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 214 | 74.0166 | 6 | 10 | 3.1398 | 26 | 58 | 30.2040 | | B81 | 11 | 11 | 11.5484 | 1.0595 | 0.00 | 152 | 192 | 74.2480 | 5 | 16 | 9.2194 | 20 | 85 | 61.0593 | | B82 | 10 | 10 | 10.4839 | 0.7244 | 0.00 | 152 | 163 | 8.3600 | 5 | 11 | 5.7070 | 22 | 50 | 25.8347 | | B83 | 12 | 12 | 12.0000 | 0.0000 | 0.00 | 153 | 159 | 4.4325 | 4 | 13 | 7.7335 | 16 | 55 | 32.6401 | | B84 | 12 | 12 | 12.0645 | 0.3592 | 0.00 | 154 | 162 | 6.8866 | 4 | 11 | 5.2595 | 20 | 51 | 22.9838 | | B85 | 8 | 8 | 9.1290 | 1.4774 | 0.00 | 153 | 160 | 4.7076 | 4 | 13 | 7.8904 | 18 | 56 | 32.4863 | | B86 | 8 | 8 | 8.0645 | 0.2497 | 0.00 | 152 | 173 | 39.7751 | 6 | 11 | 3.4938 | 24 | 53 | 24.8335 | | B87 | 10 | 10 | 10.3871 | 0.8032 | 0.00 | 154 | 247 | 122.0646 | 6 | 18 | 8.3162 | 32 | 127 | 103.6875 | | B88 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 160 | 7.8272 | 4 | 9 | 3.9459 | 16 | 40 | 16.1653 | | B89 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 159 | 3.6638 | 6 | 10 | 3.9273 | 24 | 42 | 16.1224 | | B90 | 5 | 5 | 5.5806 | 1.2048 | 0.00 | 153 | 158 | 5.3959 | 4 | 10 | 3.8771 | 16 | 45 | 16.0706 |
| | | | AVG | 8.0953 | 0.4219 | 0.00 | 156 | 177 | 25.8717 | 3 | 9 | 4.8993 | 13 | 46 | 25.9852 |
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