Research Article
Efficient Parallel Sorting for Migrating Birds Optimization When Solving Machine-Part Cell Formation Problems
Table 26
MBO using parallel merge 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 | 156 | 174 | 38.3904 | 1 | 6 | 3.8370 | 4 | 33 | 26.3519 | B2 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 170 | 37.5675 | 2 | 4 | 1.4338 | 8 | 21 | 9.5525 | B3 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 153 | 1.4421 | 2 | 4 | 1.3384 | 8 | 18 | 5.5949 | B4 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 184 | 126.1403 | 3 | 5 | 1.9620 | 12 | 25 | 9.3102 | B5 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 153 | 176 | 53.4639 | 1 | 5 | 2.5716 | 4 | 25 | 14.3306 | B6 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 170 | 28.7805 | 3 | 10 | 4.5744 | 12 | 47 | 22.7679 | B7 | 6 | 6 | 6.0323 | 0.1796 | 0.00 | 155 | 178 | 33.1697 | 3 | 5 | 3.8685 | 12 | 28 | 17.8745 | B8 | 4 | 4 | 4.3871 | 0.8032 | 0.00 | 152 | 177 | 28.8102 | 2 | 12 | 10.4629 | 9 | 57 | 49.2948 | B9 | 3 | 3 | 3.1290 | 0.3408 | 0.00 | 154 | 177 | 40.8947 | 2 | 6 | 6.0373 | 10 | 33 | 28.3257 | B10 | 3 | 3 | 3.0000 | 0.0000 | 0.00 | 154 | 200 | 42.9216 | 3 | 4 | 1.3125 | 12 | 24 | 8.8010 | B11 | 4 | 4 | 4.2258 | 0.4250 | 0.00 | 154 | 208 | 57.8835 | 2 | 11 | 7.2915 | 9 | 61 | 47.9815 | B12 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 154 | 161 | 7.1918 | 2 | 3 | 1.6271 | 8 | 16 | 7.6983 | B13 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 156 | 241 | 69.3555 | 2 | 5 | 2.0452 | 11 | 34 | 24.6320 | B14 | 3 | 3 | 3.1935 | 0.4016 | 0.00 | 153 | 180 | 41.3214 | 2 | 5 | 2.6700 | 10 | 28 | 12.9253 | B15 | 1 | 1 | 1.4516 | 0.9605 | 0.00 | 152 | 167 | 20.7708 | 3 | 6 | 2.0992 | 12 | 26 | 11.3581 | B16 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 155 | 193 | 49.9363 | 1 | 8 | 5.0855 | 5 | 47 | 33.2326 | B17 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 153 | 179 | 33.2854 | 2 | 4 | 1.7604 | 8 | 23 | 9.0254 | B18 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 176 | 28.2143 | 2 | 5 | 2.2442 | 8 | 26 | 12.5006 | B19 | 13 | 13 | 13.1935 | 0.7492 | 0.00 | 153 | 205 | 61.2246 | 2 | 6 | 4.9091 | 8 | 38 | 28.1094 | B20 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 152 | 155 | 4.7306 | 2 | 8 | 5.9932 | 10 | 35 | 24.7893 | B21 | 9 | 9 | 9.3226 | 0.4752 | 0.00 | 155 | 167 | 12.4572 | 2 | 8 | 7.2314 | 12 | 39 | 31.2266 | B22 | 6 | 6 | 6.1613 | 0.3739 | 0.00 | 152 | 156 | 3.6509 | 3 | 7 | 3.6945 | 12 | 29 | 15.2464 | B23 | 6 | 6 | 6.0645 | 0.2497 | 0.00 | 152 | 155 | 4.2187 | 2 | 8 | 5.2534 | 8 | 34 | 21.9115 | B24 | 5 | 5 | 5.4516 | 0.7229 | 0.00 | 152 | 153 | 1.5651 | 1 | 5 | 2.7048 | 4 | 24 | 11.3314 | B25 | 4 | 4 | 4.3871 | 0.7154 | 0.00 | 152 | 153 | 1.5317 | 2 | 6 | 2.5012 | 8 | 26 | 10.3027 | B26 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 154 | 157 | 3.2883 | 1 | 8 | 5.9864 | 4 | 36 | 24.8583 | B27 | 3 | 3 | 3.0645 | 0.2497 | 0.00 | 152 | 156 | 3.6957 | 1 | 5 | 2.6453 | 4 | 23 | 11.2241 | B28 | 3 | 3 | 3.3548 | 0.5507 | 0.00 | 152 | 154 | 1.6415 | 1 | 6 | 2.6506 | 4 | 25 | 11.1220 | B29 | 3 | 3 | 3.2903 | 0.5287 | 0.00 | 152 | 153 | 1.8228 | 2 | 5 | 2.5239 | 8 | 21 | 10.6774 | B30 | 2 | 2 | 2.4839 | 0.6768 | 0.00 | 152 | 154 | 3.7411 | 2 | 9 | 7.4944 | 10 | 36 | 29.9656 | B31 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 154 | 158 | 3.1174 | 3 | 9 | 3.2322 | 13 | 39 | 14.2112 | B32 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 155 | 4.6167 | 2 | 7 | 4.6467 | 8 | 31 | 19.3095 | B33 | 4 | 4 | 4.1290 | 0.4995 | 0.00 | 152 | 154 | 2.5653 | 2 | 4 | 2.4947 | 8 | 20 | 10.4209 | B34 | 4 | 4 | 4.1290 | 0.4995 | 0.00 | 152 | 154 | 3.5070 | 2 | 8 | 6.2436 | 8 | 36 | 25.3171 | B35 | 4 | 4 | 4.6452 | 0.9504 | 0.00 | 152 | 153 | 1.8866 | 1 | 5 | 3.1398 | 4 | 22 | 13.0124 | B36 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 154 | 157 | 3.0980 | 2 | 7 | 4.4587 | 8 | 32 | 19.6268 | B37 | 10 | 10 | 10.3226 | 0.7478 | 0.00 | 153 | 156 | 2.3582 | 2 | 6 | 3.8032 | 8 | 28 | 15.7390 | B38 | 8 | 8 | 8.0645 | 0.2497 | 0.00 | 152 | 154 | 3.6121 | 2 | 11 | 9.1926 | 9 | 47 | 36.9595 | B39 | 5 | 5 | 5.1613 | 0.8980 | 0.00 | 152 | 153 | 1.7858 | 3 | 5 | 1.9126 | 12 | 22 | 7.5316 | B40 | 5 | 5 | 5.1290 | 0.4995 | 0.00 | 152 | 153 | 1.5568 | 2 | 6 | 3.7757 | 8 | 26 | 15.1195 | B41 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 158 | 4.4959 | 3 | 8 | 4.4325 | 12 | 37 | 19.3518 | B42 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 154 | 1.8416 | 2 | 4 | 2.9146 | 8 | 19 | 11.7187 | B43 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 152 | 153 | 1.9527 | 2 | 4 | 2.2500 | 8 | 20 | 9.6155 | B44 | 5 | 5 | 6.0645 | 1.4591 | 0.00 | 152 | 153 | 1.9757 | 2 | 5 | 2.3859 | 8 | 23 | 9.7173 | B45 | 5 | 5 | 6.1935 | 1.5366 | 0.00 | 152 | 154 | 3.6550 | 3 | 7 | 4.0113 | 12 | 29 | 16.0929 | B46 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 155 | 158 | 3.2614 | 3 | 8 | 4.9381 | 13 | 35 | 20.3281 | B47 | 5 | 5 | 5.0000 | 0.0000 | 0.00 | 152 | 155 | 1.8769 | 2 | 5 | 1.8590 | 8 | 22 | 7.6797 | B48 | 5 | 5 | 5.0645 | 0.3592 | 0.00 | 152 | 154 | 2.0925 | 2 | 5 | 2.5012 | 8 | 22 | 10.5511 | B49 | 5 | 5 | 5.3226 | 1.1658 | 0.00 | 152 | 155 | 3.6409 | 2 | 6 | 3.4125 | 8 | 26 | 14.2755 | B50 | 5 | 5 | 5.3226 | 0.7478 | 0.00 | 152 | 157 | 3.3205 | 3 | 6 | 4.1309 | 12 | 28 | 16.7865 | B51 | 27 | 27 | 28.0323 | 0.7521 | 0.00 | 158 | 168 | 4.9579 | 5 | 18 | 10.2663 | 21 | 82 | 45.4441 | B52 | 18 | 18 | 18.9032 | 1.1062 | 0.00 | 155 | 163 | 4.9174 | 3 | 20 | 9.9102 | 12 | 87 | 41.3697 | B53 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 155 | 159 | 3.0438 | 3 | 11 | 5.6777 | 13 | 48 | 23.7862 | B54 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 152 | 158 | 3.8968 | 3 | 8 | 2.6384 | 12 | 37 | 11.8709 | B55 | 7 | 7 | 7.0000 | 0.0000 | 0.00 | 155 | 164 | 4.9862 | 4 | 11 | 5.2009 | 16 | 51 | 23.2484 | B56 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 154 | 160 | 5.1881 | 3 | 10 | 3.0761 | 14 | 42 | 12.8828 | B57 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 153 | 159 | 7.0420 | 4 | 15 | 8.2207 | 16 | 64 | 35.1398 | B58 | 6 | 6 | 6.0000 | 0.0000 | 0.00 | 152 | 159 | 8.3060 | 6 | 10 | 3.8362 | 25 | 46 | 17.9194 | B59 | 9 | 9 | 9.0645 | 0.2497 | 0.00 | 154 | 158 | 4.4036 | 3 | 13 | 6.4481 | 13 | 57 | 25.8823 | B60 | 4 | 4 | 4.6452 | 1.7426 | 0.00 | 154 | 157 | 3.1356 | 3 | 11 | 6.5308 | 12 | 47 | 26.7605 | B61 | 4 | 4 | 4.0645 | 0.2497 | 0.00 | 153 | 155 | 2.7337 | 4 | 10 | 4.5938 | 18 | 43 | 18.8219 | B62 | 4 | 4 | 4.0000 | 0.0000 | 0.00 | 152 | 154 | 2.3592 | 3 | 10 | 4.4376 | 12 | 42 | 18.0429 | B63 | 27 | 27 | 27.2258 | 0.4973 | 0.00 | 154 | 159 | 4.5781 | 3 | 16 | 8.9346 | 14 | 71 | 38.5607 | B64 | 18 | 18 | 18.1613 | 0.3739 | 0.00 | 154 | 157 | 2.6036 | 2 | 21 | 10.4142 | 9 | 89 | 43.2948 | B65 | 14 | 14 | 14.0645 | 0.2497 | 0.00 | 153 | 156 | 2.2977 | 9 | 16 | 7.2749 | 37 | 68 | 30.2108 | B66 | 13 | 13 | 13.0000 | 0.0000 | 0.00 | 153 | 155 | 4.6939 | 4 | 9 | 4.0798 | 16 | 39 | 16.7346 | B67 | 11 | 11 | 11.0323 | 0.1796 | 0.00 | 154 | 158 | 3.7491 | 4 | 13 | 6.3256 | 20 | 57 | 27.2279 | B68 | 8 | 8 | 8.2581 | 1.2641 | 0.00 | 154 | 156 | 2.0780 | 4 | 14 | 8.1412 | 17 | 61 | 33.2352 | B69 | 8 | 8 | 8.5161 | 0.5699 | 0.00 | 153 | 155 | 1.9806 | 3 | 11 | 6.3845 | 12 | 48 | 25.9051 | B70 | 6 | 6 | 6.4839 | 0.8112 | 0.00 | 152 | 155 | 4.0201 | 6 | 14 | 7.0459 | 26 | 60 | 28.5073 | B71 | 6 | 6 | 6.0968 | 0.3962 | 0.00 | 154 | 157 | 2.9403 | 4 | 12 | 6.6669 | 17 | 51 | 26.8024 | B72 | 4 | 4 | 4.2258 | 0.4973 | 0.00 | 153 | 156 | 2.5425 | 4 | 12 | 4.9425 | 17 | 50 | 19.7463 | B73 | 4 | 4 | 4.6129 | 0.8032 | 0.00 | 153 | 156 | 4.3359 | 4 | 12 | 7.1703 | 16 | 52 | 29.2444 | B74 | 3 | 3 | 3.5806 | 0.7648 | 0.00 | 152 | 154 | 2.1597 | 3 | 12 | 6.5769 | 12 | 51 | 26.8259 | B75 | 11 | 11 | 11.7097 | 1.0064 | 0.00 | 155 | 158 | 2.7669 | 4 | 16 | 8.1914 | 16 | 67 | 34.7627 | B76 | 5 | 5 | 5.2581 | 0.6816 | 0.00 | 154 | 156 | 2.1938 | 4 | 15 | 8.8187 | 16 | 64 | 36.6178 | B77 | 5 | 5 | 5.3226 | 0.7478 | 0.00 | 152 | 155 | 3.8935 | 3 | 12 | 5.2079 | 12 | 51 | 21.4117 | B78 | 4 | 4 | 4.5806 | 1.4323 | 0.00 | 152 | 155 | 2.1292 | 5 | 16 | 7.5307 | 21 | 67 | 29.9967 | B79 | 14 | 14 | 14.0000 | 0.0000 | 0.00 | 155 | 159 | 3.9738 | 4 | 10 | 4.1530 | 17 | 43 | 16.7283 | B80 | 11 | 11 | 11.0000 | 0.0000 | 0.00 | 154 | 156 | 1.8293 | 6 | 11 | 4.1832 | 24 | 45 | 17.7170 | B81 | 11 | 11 | 11.4516 | 0.9605 | 0.00 | 152 | 155 | 3.8187 | 4 | 12 | 6.0628 | 17 | 49 | 24.8217 | B82 | 10 | 10 | 10.5484 | 0.8500 | 0.00 | 153 | 155 | 2.7044 | 3 | 11 | 6.4430 | 12 | 47 | 26.5292 | B83 | 12 | 12 | 12.0000 | 0.0000 | 0.00 | 155 | 158 | 2.8105 | 6 | 10 | 3.6928 | 24 | 44 | 15.9765 | B84 | 12 | 12 | 12.0000 | 0.0000 | 0.00 | 153 | 157 | 5.0225 | 2 | 10 | 4.6216 | 9 | 44 | 18.9497 | B85 | 8 | 8 | 9.4839 | 1.6304 | 0.00 | 152 | 155 | 1.9587 | 3 | 13 | 8.1050 | 12 | 57 | 33.4782 | B86 | 8 | 8 | 8.1290 | 0.5623 | 0.00 | 152 | 154 | 1.6611 | 3 | 11 | 4.6358 | 13 | 45 | 18.8382 | B87 | 10 | 10 | 10.4194 | 0.8860 | 0.00 | 154 | 158 | 2.7913 | 4 | 18 | 9.6760 | 17 | 76 | 41.0048 | B88 | 8 | 8 | 8.0000 | 0.0000 | 0.00 | 154 | 156 | 3.9358 | 5 | 10 | 3.5021 | 21 | 44 | 14.3271 | B89 | 8 | 8 | 8.0323 | 0.1796 | 0.00 | 152 | 155 | 2.0294 | 4 | 11 | 5.5903 | 17 | 47 | 22.9967 | B90 | 5 | 5 | 5.3871 | 1.0223 | 0.00 | 152 | 154 | 1.8334 | 5 | 11 | 5.2521 | 20 | 46 | 21.4332 |
| ā | ā | AVG | 8.1007 | 0.4296 | 0.00 | 153 | 161 | 11.5292 | 2 | 9 | 4.9112 | 12 | 40 | 21.5416 |
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