Research Article
Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems
Table 31
MBO using parallel quick sort algorithm with 8 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 | 190 | 260 | 90.7097 | 2 | 6 | 3.5636 | 12 | 55 | 39.8897 | B2 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 205 | 231 | 16.0884 | 1 | 3 | 1.3408 | 5 | 27 | 11.3853 | B3 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 201 | 218 | 12.8483 | 2 | 4 | 1.2487 | 15 | 25 | 8.4055 | B4 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 197 | 224 | 13.2765 | 2 | 4 | 1.6198 | 9 | 30 | 10.1960 | B5 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 203 | 226 | 16.9506 | 1 | 5 | 2.5425 | 5 | 31 | 15.3820 | B6 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 179 | 209 | 26.6540 | 3 | 8 | 4.1551 | 16 | 46 | 20.1586 | B7 | 6 | 6 | 6.0645 | 0.2497 | 0.00 | 159 | 170 | 8.6506 | 2 | 5 | 2.3958 | 9 | 26 | 10.8302 | B8 | 4 | 4 | 4.5806 | 1.2852 | 0.00 | 161 | 208 | 24.9863 | 2 | 9 | 8.2168 | 11 | 49 | 44.8206 | B9 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 156 | 169 | 9.0874 | 1 | 5 | 2.9975 | 4 | 25 | 14.9742 | B10 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 160 | 187 | 29.3461 | 1 | 4 | 1.9143 | 4 | 21 | 10.0919 | B11 | 4 | 4 | 4.2581 | 0.4448 | 0.00 | 221 | 265 | 38.7226 | 3 | 12 | 7.1297 | 18 | 92 | 57.9354 | B12 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 189 | 244 | 25.8799 | 2 | 4 | 1.8917 | 9 | 30 | 13.7061 | B13 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 175 | 212 | 26.0266 | 2 | 5 | 2.0609 | 9 | 29 | 12.7301 | B14 | 3 | 3 | 3.5161 | 0.5080 | 0.00 | 191 | 233 | 25.7782 | 2 | 5 | 2.1251 | 10 | 32 | 17.8553 | B15 | 1 | 1 | 1.4839 | 0.9263 | 0.00 | 158 | 172 | 15.6618 | 2 | 5 | 2.1266 | 8 | 25 | 10.8872 | B16 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 219 | 241 | 17.5973 | 2 | 8 | 4.4454 | 10 | 51 | 28.6909 | B17 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 155 | 178 | 22.8931 | 2 | 5 | 1.4142 | 8 | 23 | 6.1196 | B18 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 157 | 170 | 16.5604 | 2 | 5 | 1.9620 | 8 | 23 | 10.1844 | B19 | 13 | 13 | 13.2903 | 0.9016 | 0.00 | 184 | 212 | 13.5299 | 2 | 6 | 2.9024 | 10 | 38 | 15.5537 | B20 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 179 | 195 | 11.0056 | 2 | 8 | 5.7083 | 8 | 44 | 29.5659 | B21 | 9 | 9 | 9.1613 | 0.3739 | 0.00 | 173 | 223 | 67.1284 | 4 | 10 | 8.0616 | 19 | 60 | 50.9887 | B22 | 6 | 6 | 6.1613 | 0.3739 | 0.00 | 193 | 273 | 88.1693 | 3 | 6 | 3.0764 | 12 | 46 | 37.1433 | B23 | 6 | 6 | 6.2258 | 0.4973 | 0.00 | 187 | 232 | 20.6745 | 2 | 6 | 4.7992 | 14 | 44 | 30.3885 | B24 | 5 | 5 | 5.4516 | 0.7229 | 0.00 | 185 | 216 | 28.3318 | 2 | 5 | 2.5046 | 14 | 32 | 12.6408 | B25 | 4 | 4 | 4.3548 | 0.7094 | 0.00 | 180 | 220 | 38.7354 | 2 | 7 | 3.3575 | 11 | 41 | 21.8570 | B26 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 222 | 267 | 65.9248 | 2 | 9 | 6.2550 | 11 | 63 | 40.3980 | B27 | 3 | 3 | 3.0968 | 0.3005 | 0.00 | 163 | 187 | 72.6372 | 1 | 6 | 4.0640 | 4 | 32 | 19.3312 | B28 | 3 | 3 | 3.2903 | 0.4614 | 0.00 | 161 | 188 | 57.0519 | 2 | 5 | 2.3773 | 8 | 26 | 13.4644 | B29 | 3 | 3 | 3.1290 | 0.3408 | 0.00 | 153 | 176 | 30.2510 | 2 | 5 | 1.9615 | 9 | 24 | 10.0626 | B30 | 2 | 2 | 2.3871 | 0.5584 | 0.00 | 153 | 175 | 21.4547 | 3 | 9 | 6.7079 | 12 | 41 | 29.4979 | B31 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 161 | 211 | 43.1659 | 2 | 10 | 4.5541 | 10 | 58 | 30.4089 | B32 | 4 | 4 | 4.3871 | 1.0223 | 0.00 | 155 | 191 | 40.5896 | 1 | 7 | 6.1083 | 4 | 38 | 31.5310 | B33 | 4 | 4 | 4.1935 | 0.6011 | 0.00 | 156 | 214 | 47.1663 | 2 | 6 | 3.0204 | 12 | 37 | 18.9796 | B34 | 4 | 4 | 4.2581 | 0.6816 | 0.00 | 156 | 169 | 21.7325 | 2 | 5 | 2.2855 | 10 | 26 | 10.2277 | B35 | 4 | 4 | 4.4516 | 0.8500 | 0.00 | 155 | 184 | 36.3288 | 1 | 5 | 2.4861 | 4 | 25 | 14.0484 | B36 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 159 | 172 | 12.9491 | 2 | 9 | 5.4378 | 8 | 44 | 24.1031 | B37 | 10 | 10 | 10.5806 | 0.9228 | 0.00 | 154 | 165 | 12.0246 | 2 | 7 | 6.6159 | 9 | 35 | 31.7865 | B38 | 8 | 8 | 8.0968 | 0.3005 | 0.00 | 155 | 162 | 8.0036 | 2 | 11 | 9.7551 | 8 | 50 | 41.9069 | B39 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 154 | 162 | 6.2843 | 2 | 5 | 2.1109 | 8 | 23 | 9.1885 | B40 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 160 | 185 | 31.2620 | 2 | 5 | 1.9898 | 9 | 27 | 11.3643 | B41 | 8 | 8 | 8.1613 | 0.8980 | 0.00 | 157 | 191 | 35.3240 | 3 | 9 | 5.6883 | 12 | 52 | 34.1054 | B42 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 153 | 191 | 35.1184 | 2 | 4 | 2.0557 | 8 | 25 | 14.0413 | B43 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 153 | 195 | 46.0170 | 2 | 4 | 1.8163 | 8 | 26 | 13.6305 | B44 | 5 | 5 | 5.9677 | 1.4256 | 0.00 | 155 | 180 | 30.1549 | 1 | 5 | 2.3372 | 4 | 23 | 10.0189 | B45 | 5 | 5 | 5.8710 | 1.3842 | 0.00 | 154 | 162 | 10.2862 | 1 | 5 | 2.5661 | 4 | 24 | 11.2124 | B46 | 8 | 8 | 8.0645 | 0.2497 | 0.00 | 159 | 197 | 41.1302 | 2 | 10 | 6.8400 | 8 | 53 | 42.0245 | B47 | 5 | 5 | 5.0968 | 0.5388 | 0.00 | 156 | 185 | 49.5067 | 2 | 6 | 2.5703 | 9 | 34 | 21.4733 | B48 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 154 | 183 | 34.0827 | 2 | 5 | 2.5493 | 9 | 28 | 13.3359 | B49 | 5 | 5 | 5.2581 | 0.6816 | 0.00 | 155 | 171 | 26.4985 | 2 | 6 | 4.9605 | 8 | 27 | 22.1096 | B50 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 159 | 293 | 137.7965 | 2 | 6 | 4.3729 | 10 | 44 | 30.5390 | B51 | 27 | 27 | 28.2903 | 0.8638 | 0.00 | 237 | 261 | 14.2311 | 4 | 21 | 9.5117 | 22 | 144 | 67.3566 | B52 | 18 | 18 | 18.7742 | 0.8835 | 0.00 | 219 | 233 | 14.9013 | 3 | 21 | 10.1319 | 19 | 133 | 65.4978 | B53 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 201 | 230 | 12.1596 | 5 | 11 | 3.8566 | 28 | 66 | 25.8455 | B54 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 202 | 217 | 12.3461 | 3 | 8 | 2.6401 | 21 | 48 | 16.3395 | B55 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 214 | 240 | 12.0357 | 4 | 11 | 4.1032 | 23 | 74 | 26.0514 | B56 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 204 | 224 | 12.4441 | 4 | 11 | 4.5166 | 22 | 66 | 28.6479 | B57 | 6 | 6 | 6.0323 | 0.1796 | 0.00 | 208 | 228 | 12.0374 | 4 | 11 | 3.5765 | 24 | 67 | 21.0756 | B58 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 206 | 224 | 11.6898 | 4 | 9 | 4.5009 | 16 | 56 | 28.0782 | B59 | 9 | 9 | 9.1290 | 0.4275 | 0.00 | 174 | 241 | 39.2589 | 5 | 16 | 9.8178 | 23 | 103 | 60.2449 | B60 | 4 | 4 | 4.7419 | 1.7883 | 0.00 | 154 | 159 | 3.9053 | 3 | 12 | 5.6472 | 12 | 51 | 24.0830 | B61 | 4 | 4 | 4.1613 | 0.3739 | 0.00 | 154 | 157 | 4.0611 | 3 | 12 | 7.1637 | 12 | 51 | 29.2026 | B62 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 154 | 157 | 4.8422 | 4 | 10 | 5.3876 | 17 | 43 | 22.6520 | B63 | 27 | 27 | 27.1935 | 0.4016 | 0.00 | 158 | 169 | 5.2271 | 3 | 14 | 7.9795 | 14 | 66 | 35.6641 | B64 | 18 | 18 | 18.2903 | 0.6426 | 0.00 | 155 | 159 | 2.8364 | 3 | 19 | 10.2648 | 14 | 84 | 42.7305 | B65 | 14 | 14 | 14.0968 | 0.3005 | 0.00 | 154 | 163 | 8.1524 | 3 | 14 | 7.8763 | 13 | 62 | 35.1641 | B66 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 166 | 13.0996 | 7 | 12 | 3.6136 | 28 | 54 | 17.3759 | B67 | 11 | 11 | 11.0968 | 0.3005 | 0.00 | 166 | 263 | 83.3463 | 3 | 15 | 9.6607 | 17 | 109 | 100.7377 | B68 | 8 | 8 | 8.1935 | 0.6011 | 0.00 | 155 | 184 | 23.4952 | 4 | 12 | 6.7003 | 19 | 60 | 35.4280 | B69 | 8 | 8 | 8.5806 | 0.7199 | 0.00 | 158 | 211 | 64.9205 | 5 | 12 | 6.2117 | 22 | 75 | 65.2722 | B70 | 6 | 6 | 6.7097 | 0.8638 | 0.00 | 155 | 231 | 135.2276 | 3 | 13 | 6.6360 | 18 | 83 | 66.1519 | B71 | 6 | 6 | 6.2258 | 0.6170 | 0.00 | 162 | 200 | 53.9548 | 5 | 12 | 8.4985 | 27 | 67 | 46.9196 | B72 | 4 | 4 | 4.3226 | 0.5993 | 0.00 | 154 | 160 | 4.7503 | 6 | 12 | 5.8701 | 24 | 53 | 24.2337 | B73 | 4 | 4 | 4.4839 | 0.6256 | 0.00 | 154 | 181 | 34.0598 | 3 | 13 | 7.3084 | 14 | 63 | 39.7601 | B74 | 3 | 3 | 3.3871 | 0.5584 | 0.00 | 154 | 163 | 4.2860 | 3 | 12 | 6.5822 | 18 | 53 | 27.1781 | B75 | 11 | 11 | 11.6129 | 0.9892 | 0.00 | 168 | 183 | 13.2764 | 4 | 18 | 9.8581 | 18 | 89 | 45.1418 | B76 | 5 | 5 | 5.1935 | 0.6011 | 0.00 | 163 | 193 | 35.1540 | 4 | 13 | 6.0851 | 20 | 70 | 40.9876 | B77 | 5 | 5 | 5.2581 | 0.6816 | 0.00 | 154 | 186 | 23.2987 | 4 | 15 | 8.8359 | 24 | 73 | 39.9299 | B78 | 4 | 4 | 4.7097 | 1.1887 | 0.00 | 156 | 170 | 10.0336 | 5 | 15 | 6.8506 | 23 | 69 | 31.6560 | B79 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 156 | 164 | 6.0066 | 3 | 10 | 3.5484 | 12 | 46 | 15.1387 | B80 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 158 | 6.2756 | 5 | 11 | 3.4811 | 20 | 48 | 14.9292 | B81 | 11 | 11 | 11.4839 | 0.9263 | 0.00 | 154 | 159 | 5.5222 | 3 | 12 | 7.9278 | 16 | 54 | 31.9301 | B82 | 10 | 10 | 10.5484 | 0.8500 | 0.00 | 154 | 156 | 2.3344 | 4 | 12 | 5.7675 | 16 | 51 | 24.5353 | B83 | 12 | 12 | 12.0000 | 0.0000 | 0.00 | 157 | 164 | 4.1408 | 4 | 13 | 6.6827 | 16 | 60 | 29.7937 | B84 | 12 | 12 | 12.0645 | 0.3592 | 0.00 | 154 | 158 | 5.3961 | 4 | 11 | 5.1974 | 16 | 49 | 22.7398 | B85 | 8 | 8 | 8.9032 | 1.4687 | 0.00 | 154 | 157 | 2.9860 | 5 | 11 | 4.7201 | 21 | 47 | 19.4751 | B86 | 8 | 8 | 8.2258 | 0.8835 | 0.00 | 154 | 156 | 2.0765 | 3 | 8 | 4.5371 | 12 | 34 | 18.4101 | B87 | 10 | 10 | 10.5161 | 0.9957 | 0.00 | 162 | 171 | 4.9756 | 7 | 19 | 8.8350 | 29 | 87 | 40.9288 | B88 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 157 | 2.9647 | 4 | 10 | 4.8012 | 17 | 43 | 20.1409 | B89 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 157 | 3.8529 | 4 | 10 | 4.7071 | 18 | 45 | 19.3560 | B90 | 5 | 5 | 5.1935 | 0.7492 | 0.00 | 154 | 156 | 1.4398 | 3 | 10 | 4.2256 | 12 | 43 | 17.4126 |
| ā | ā | AVG | 8.1079 | 0.4472 | 0.00 | 169 | 195 | 26.3893 | 2 | 9 | 4.8796 | 13 | 49 | 27.5041 |
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