Scientific Programming

Research Article

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

Table 25

MBO using parallel merge 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 0.00 153 175 52.9600 2 7 3.4650 10 40 24.1691
B2 11 11 11.0000 0.0000 0.00 152 155 4.2538 1 4 1.3663 4 17 6.3123
B3 11 11 11.0000 0.0000 0.00 152 154 2.2737 2 4 1.2675 8 16 4.9966
B4 11 11 11.0000 0.0000 0.00 152 154 2.1875 3 5 1.6669 12 22 6.6451
B5 11 11 11.0000 0.0000 0.00 152 154 3.5484 1 5 4.6460 4 22 19.1976
B6 7 7 7.0000 0.0000 0.00 154 159 6.9589 3 9 5.6927 12 41 23.3150
B7 6 6 6.0323 0.1796 0.00 152 155 2.6567 2 5 3.3376 8 24 13.6479
B8 4 4 4.2581 0.6816 0.00 152 154 2.2500 2 10 7.8339 8 43 31.7022
B9 3 3 3.0645 0.2497 0.00 152 154 2.8853 1 6 4.2480 4 26 17.5545
B10 3 3 3.0000 0.0000 0.00 152 155 4.3342 2 4 2.2017 8 19 9.0625
B11 4 4 4.1613 0.3739 0.00 154 158 4.0725 3 11 6.8310 12 46 28.0720
B12 4 4 4.0000 0.0000 0.00 152 154 2.2041 1 4 1.7487 4 18 7.3882
B13 4 4 4.0645 0.3592 0.00 152 157 8.3824 2 6 4.0825 8 24 16.4007
B14 3 3 3.4516 0.5059 0.00 152 156 10.8955 2 5 2.0848 8 21 8.3643
B15 1 1 1.2903 0.7829 0.00 152 153 1.8322 2 5 2.4110 8 23 9.8292
B16 14 14 14.0000 0.0000 0.00 155 160 4.5349 2 7 3.6044 10 32 14.9542
B17 13 13 13.0000 0.0000 0.00 152 155 2.2423 2 4 1.6145 8 20 6.7850
B18 13 13 13.0000 0.0000 0.00 152 154 3.8763 1 5 2.1553 4 22 9.3721
B19 13 13 13.0000 0.0000 0.00 152 153 1.4796 2 7 6.3034 8 28 25.4949
B20 13 13 13.0000 0.0000 0.00 152 153 1.4803 2 8 5.1278 8 33 20.5847
B21 9 9 9.1613 0.3739 0.00 154 158 2.8485 2 12 10.3146 8 52 42.6586
B22 6 6 6.2581 0.6308 0.00 152 155 3.1380 2 6 2.8459 8 25 11.7755
B23 6 6 6.1935 0.5428 0.00 152 153 2.0198 2 10 7.3810 8 43 30.1207
B24 5 5 5.2581 0.5755 0.00 152 154 1.9355 1 7 3.5024 4 28 14.1402
B25 4 4 4.2581 0.5143 0.00 152 153 2.0562 2 6 3.2132 8 26 12.9135
B26 5 5 5.0000 0.0000 0.00 154 158 4.3165 2 9 6.1518 8 39 26.6302
B27 3 3 3.0645 0.2497 0.00 152 155 2.3085 2 7 3.3033 8 30 13.5624
B28 3 3 3.2581 0.5755 0.00 152 153 1.9680 2 5 3.0261 8 24 13.0409
B29 3 3 3.2258 0.4250 0.00 152 154 2.4705 2 4 1.8228 8 18 7.6122
B30 2 2 2.5484 0.6239 0.00 152 154 3.7018 2 7 5.7358 8 28 23.3637
B31 7 7 7.0000 0.0000 0.00 154 158 3.0953 2 10 6.2340 8 42 25.8763
B32 4 4 4.3871 1.2826 0.00 152 155 2.7875 2 8 5.7081 8 36 23.1095
B33 4 4 4.1935 0.6011 0.00 152 154 3.7125 2 5 3.5753 8 21 15.1291
B34 4 4 4.1290 0.4995 0.00 152 153 1.5268 2 5 4.2205 8 23 16.8363
B35 4 4 4.6452 0.9504 0.00 152 152 1.0984 1 5 2.2177 4 21 8.8371
B36 13 13 13.0000 0.0000 0.00 154 158 3.6041 4 9 4.6647 16 39 19.2969
B37 10 10 10.3871 0.8032 0.00 152 155 4.3569 1 6 2.7689 4 24 11.4273
B38 8 8 8.2258 0.4973 0.00 152 154 2.2026 2 9 7.5453 8 40 30.0411
B39 5 5 5.0000 0.0000 0.00 152 154 2.2327 2 5 2.9759 9 22 11.9398
B40 5 5 5.1935 0.6011 0.00 152 153 1.9989 2 5 2.7552 8 22 11.5980
B41 8 8 8.0000 0.0000 0.00 154 159 4.8193 3 10 5.9482 14 45 24.6265
B42 8 8 8.0000 0.0000 0.00 152 154 2.3692 2 4 2.3592 8 20 9.9095
B43 8 8 8.0645 0.3592 0.00 152 154 1.8526 1 5 2.9563 4 21 12.2532
B44 5 5 6.3548 1.5176 0.00 152 153 1.1538 2 5 2.9494 8 24 11.9644
B45 5 5 6.1613 1.4854 0.00 152 153 1.5443 2 5 2.6917 8 23 10.8397
B46 8 8 8.0323 0.1796 0.00 155 159 4.2805 2 9 6.9125 8 41 28.3549
B47 5 5 5.0968 0.5388 0.00 152 154 2.0294 2 5 2.0811 8 21 8.4729
B48 5 5 5.1935 0.6011 0.00 152 154 1.6428 2 4 2.2647 8 20 9.1640
B49 5 5 5.2581 0.6816 0.00 151 153 3.5342 2 5 2.6482 8 21 10.6357
B50 5 5 5.1290 0.4995 0.00 152 153 3.1826 2 5 2.8493 8 22 11.5451
B51 27 27 27.9355 0.8139 0.00 154 161 3.4660 10 26 8.4370 41 111 35.6271
B52 18 18 18.9355 1.0626 0.00 154 157 3.3758 8 24 9.0310 32 102 36.6151
B53 11 11 11.0000 0.0000 0.00 153 155 1.8334 6 11 4.6911 24 45 19.0585
B54 11 11 11.0000 0.0000 0.00 152 154 3.7637 3 8 2.6941 12 35 11.1208
B55 7 7 7.0000 0.0000 0.00 154 158 3.2984 3 11 5.1034 13 49 21.0208
B56 6 6 6.0000 0.0000 0.00 153 156 3.0093 4 11 3.8401 16 48 15.2743
B57 6 6 6.1290 0.4275 0.00 153 155 2.8387 4 11 5.4081 16 46 22.2407
B58 6 6 6.0645 0.2497 0.00 152 155 4.2566 3 10 3.8702 12 43 15.8509
B59 9 9 9.0323 0.1796 0.00 155 158 3.0526 5 14 6.9780 22 60 29.3752
B60 4 4 4.3871 1.2021 0.00 153 156 2.1687 5 14 7.0227 21 59 29.2113
B61 4 4 4.1613 0.4544 0.00 153 156 4.8604 3 12 6.3903 12 52 27.7761
B62 4 4 4.0323 0.1796 0.00 152 154 2.3678 4 10 4.8644 17 45 20.3279
B63 27 27 27.1935 0.4016 0.00 156 162 4.4719 4 15 7.7450 16 66 32.7914
B64 18 18 18.0968 0.3005 0.00 154 157 2.4722 5 19 8.3824 23 81 35.1227
B65 14 14 14.0323 0.1796 0.00 153 156 4.1228 6 15 8.5828 24 65 35.2348
B66 13 13 13.0000 0.0000 0.00 152 155 2.5179 7 9 2.7072 28 41 11.3806
B67 11 11 11.1290 0.3408 0.00 154 159 4.6810 4 12 6.4386 17 52 27.4067
B68 8 8 8.2258 0.9205 0.00 154 157 3.4830 3 14 9.5942 12 61 40.0795
B69 8 8 8.6129 0.7154 0.00 153 156 4.5924 4 11 5.9648 16 48 24.0260
B70 6 6 6.3548 0.7549 0.00 152 159 9.1831 3 14 6.6604 12 60 29.2535
B71 6 6 6.0000 0.0000 0.00 154 160 5.0885 6 14 6.2436 28 60 26.1248
B72 4 4 4.2581 0.5143 0.00 153 156 2.0956 3 11 5.6317 13 49 23.2173
B73 4 4 4.3548 0.6607 0.00 152 155 4.3015 3 12 7.6978 12 51 31.3144
B74 3 3 3.4839 0.5699 0.00 152 154 2.1038 3 11 6.2472 12 45 25.2912
B75 11 11 11.7419 0.9298 0.00 154 160 4.5345 3 17 8.7525 13 72 37.3021
B76 5 5 5.0645 0.3592 0.00 153 156 2.3192 4 12 6.1097 19 53 25.0673
B77 5 5 5.5161 0.8896 0.00 152 155 4.3891 3 12 7.1977 12 52 29.2321
B78 4 4 4.6774 1.1072 0.00 152 155 2.3908 4 15 6.2862 17 62 25.6253
B79 14 14 14.0000 0.0000 0.00 155 159 3.0324 6 10 4.4923 24 43 18.5246
B80 11 11 11.0000 0.0000 0.00 153 157 3.3665 4 11 3.6697 16 46 15.4853
B81 11 11 11.3871 0.8032 0.00 152 156 4.2659 3 14 8.3982 12 61 34.5279
B82 10 10 10.6774 0.7911 0.00 153 155 1.8613 5 12 5.4156 21 53 22.2498
B83 12 12 12.1935 0.7492 0.00 154 160 4.3436 2 11 5.9686 8 50 25.0351
B84 12 12 12.1290 0.4995 0.00 153 156 2.6567 6 13 6.1890 25 55 25.4035
B85 8 8 9.5806 1.8934 0.00 153 156 3.8652 3 13 6.6922 13 55 27.3698
B86 8 8 8.0000 0.0000 0.00 152 155 2.2504 4 10 4.1195 16 43 17.4584
B87 10 10 10.4839 0.9263 0.00 155 159 3.6559 4 18 8.6221 16 79 36.8990
B88 8 8 8.0000 0.0000 0.00 154 156 2.8530 4 10 3.8077 16 41 15.5335
B89 8 8 8.0000 0.0000 0.00 152 156 4.3232 3 9 3.6948 12 39 15.6479
B90 5 5 5.3871 1.0223 0.00 152 155 3.4501 3 11 4.1108 13 45 16.8234
   AVG 8.1029 0.4293 0.00 152 155 3.8451 2 9 4.8785 12 40 20.2717