Scientific Programming

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
   AVG 8.1007 0.4296 0.00 153 161 11.5292 2 9 4.9112 12 40 21.5416