Scientific Programming

Research Article

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

Table 27

MBO using parallel merge 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 0.00 156 202 73.4610 3 7 2.8048 13 41 25.2275
B2 11 11 11.0000 0.0000 0.00 153 159 8.6862 3 4 1.4473 12 22 9.7667
B3 11 11 11.0000 0.0000 0.00 152 155 3.1575 1 4 1.6481 4 17 7.1419
B4 11 11 11.0000 0.0000 0.00 153 159 12.7325 3 5 2.2756 12 23 10.9487
B5 11 11 11.0000 0.0000 0.00 153 159 7.8248 2 5 2.0583 8 24 8.4883
B6 7 7 7.0000 0.0000 0.00 154 168 11.3770 2 10 6.2576 10 44 28.5622
B7 6 6 6.0645 0.2497 0.00 153 162 10.6669 3 6 2.3623 13 29 12.9453
B8 4 4 4.1935 0.6011 0.00 152 157 4.6720 2 12 9.9450 8 51 41.2599
B9 3 3 3.0968 0.3005 0.00 153 157 5.1856 1 5 2.5098 4 25 10.4043
B10 3 3 3.0000 0.0000 0.00 152 159 8.1494 1 3 1.7001 4 16 7.8501
B11 4 4 4.2581 0.4448 0.00 153 164 11.3640 3 12 7.4554 14 52 32.6614
B12 4 4 4.0000 0.0000 0.00 152 157 5.4880 1 4 1.8026 4 17 7.6960
B13 4 4 4.0645 0.3592 0.00 152 159 9.9945 2 5 2.4679 9 22 10.6621
B14 3 3 3.2581 0.4448 0.00 152 157 7.2963 2 5 2.6632 8 23 11.1257
B15 1 1 1.5161 0.8896 0.00 152 162 14.1797 2 6 2.7731 8 25 12.0180
B16 14 14 14.0000 0.0000 0.00 155 178 28.1446 3 6 2.8459 12 32 12.6052
B17 13 13 13.0000 0.0000 0.00 152 163 9.4999 1 4 1.6669 4 19 7.8038
B18 13 13 13.0000 0.0000 0.00 153 176 50.4821 1 5 2.3431 5 22 12.0773
B19 13 13 13.1935 0.7492 0.00 153 167 23.5020 2 7 4.6575 12 34 25.0622
B20 13 13 13.0000 0.0000 0.00 152 196 65.9215 2 7 4.9246 9 39 27.7927
B21 9 9 9.3548 0.4864 0.00 154 197 89.8626 2 11 8.3362 8 56 40.0088
B22 6 6 6.1613 0.5829 0.00 155 213 63.0063 2 5 2.0161 8 32 18.9462
B23 6 6 6.1935 0.4016 0.00 155 241 100.2556 3 7 5.8505 12 48 39.5844
B24 5 5 5.2903 0.5884 0.00 152 164 31.9873 2 6 3.1288 8 28 12.6167
B25 4 4 4.1613 0.3739 0.00 152 155 2.4839 2 6 4.9858 8 26 20.2954
B26 5 5 5.0645 0.2497 0.00 155 162 5.6949 2 7 5.6531 8 34 24.0685
B27 3 3 3.0968 0.3005 0.00 154 158 2.8860 2 6 3.6580 9 28 15.0662
B28 3 3 3.1613 0.4544 0.00 152 156 3.2326 2 7 3.2322 8 30 13.6381
B29 3 3 3.0968 0.3005 0.00 152 155 3.9811 2 5 2.2785 8 23 9.0958
B30 2 2 2.5161 0.6256 0.00 152 156 4.9036 2 7 5.6843 8 30 23.2274
B31 7 7 7.0000 0.0000 0.00 155 164 5.3710 1 7 4.3247 4 33 19.4109
B32 4 4 4.1935 0.7492 0.00 152 157 3.1191 2 6 3.7035 8 28 15.7836
B33 4 4 4.0000 0.0000 0.00 153 156 2.9574 3 5 2.7712 12 23 11.8504
B34 4 4 4.0645 0.3592 0.00 152 156 4.1986 2 7 7.1646 8 32 31.8354
B35 4 4 4.3226 0.7478 0.00 152 155 3.3758 2 5 3.0862 8 22 12.7461
B36 13 13 13.0000 0.0000 0.00 155 162 5.9413 2 7 3.9284 9 34 16.4346
B37 10 10 10.3226 0.7478 0.00 154 157 3.3153 2 7 5.8622 8 29 23.8995
B38 8 8 8.2581 1.2641 0.00 152 156 4.6789 2 10 8.4328 8 42 34.3955
B39 5 5 5.0000 0.0000 0.00 152 159 6.1503 2 5 2.9153 8 25 12.1929
B40 5 5 5.1290 0.4995 0.00 155 168 23.4268 3 5 1.5513 13 23 7.9119
B41 8 8 8.1613 0.8980 0.00 154 161 4.2011 4 9 6.6078 16 42 27.6753
B42 8 8 8.0000 0.0000 0.00 153 157 6.3106 2 4 1.7828 8 18 7.7493
B43 8 8 8.0000 0.0000 0.00 152 160 7.4285 2 5 2.6019 8 23 11.7932
B44 5 5 5.8710 1.3842 0.00 154 161 7.9767 2 5 2.0687 12 22 9.0735
B45 5 5 5.8710 1.3842 0.00 153 156 5.2525 2 5 3.0603 8 25 12.6925
B46 8 8 8.0323 0.1796 0.00 154 165 8.5232 1 9 7.2947 4 40 32.4977
B47 5 5 5.0000 0.0000 0.00 153 163 7.4939 2 6 3.3732 8 27 13.6618
B48 5 5 5.0645 0.3592 0.00 155 190 88.3159 3 5 2.3550 12 26 10.0136
B49 5 5 5.1290 0.4995 0.00 153 167 23.7535 2 6 2.2562 8 25 9.6192
B50 5 5 5.1935 0.6011 0.00 153 206 111.6447 1 5 2.3619 4 30 22.2696
B51 27 27 28.1613 0.7347 0.00 160 233 106.5829 4 19 9.9746 16 113 64.2842
B52 18 18 18.8387 0.7347 0.00 154 164 6.9436 6 21 9.2897 27 91 41.3948
B53 11 11 11.0000 0.0000 0.00 155 164 13.5560 5 11 3.1833 22 47 13.7809
B54 11 11 11.0000 0.0000 0.00 156 163 4.5475 4 8 2.4274 17 37 11.2196
B55 7 7 7.0000 0.0000 0.00 159 170 8.7338 5 10 3.2038 26 47 13.2918
B56 6 6 6.0000 0.0000 0.00 154 166 10.0578 6 10 3.3742 27 47 16.6980
B57 6 6 6.0000 0.0000 0.00 155 169 18.2314 6 11 5.5162 25 52 24.6267
B58 6 6 6.0000 0.0000 0.00 154 162 4.3901 3 10 5.1287 12 44 22.2686
B59 9 9 9.1613 0.5829 0.00 161 176 14.3747 5 14 7.2798 23 70 36.4352
B60 4 4 4.2903 1.1312 0.00 157 173 14.4923 6 14 6.1914 25 64 28.9730
B61 4 4 4.1613 0.5829 0.00 155 163 6.7429 4 9 4.0040 16 42 16.5396
B62 4 4 4.0323 0.1796 0.00 154 160 3.5345 4 10 4.6504 16 43 19.3696
B63 27 27 27.2258 0.4250 0.00 159 172 5.1895 3 20 11.1084 13 91 50.3296
B64 18 18 18.1935 0.4016 0.00 157 173 22.8970 6 21 9.5444 25 102 51.5291
B65 14 14 14.0645 0.2497 0.00 156 229 88.8105 6 16 6.8318 29 96 56.9926
B66 13 13 13.0000 0.0000 0.00 155 198 64.6472 4 10 4.2088 20 55 27.5365
B67 11 11 11.0968 0.3005 0.00 166 269 216.8374 3 15 9.5772 14 118 195.6026
B68 8 8 8.2258 0.9205 0.00 154 170 13.6269 4 11 6.2202 17 53 26.0361
B69 8 8 8.5161 0.7244 0.00 155 168 15.0527 6 13 6.1990 26 59 36.8672
B70 6 6 6.5484 0.8884 0.00 153 156 5.1117 3 14 8.3743 14 62 34.9847
B71 6 6 6.1290 0.4995 0.00 154 160 5.1506 4 11 4.5231 16 49 19.3207
B72 4 4 4.3548 0.5507 0.00 152 157 3.9059 6 16 8.5049 25 67 36.2737
B73 4 4 4.5161 0.6768 0.00 152 166 25.8682 4 13 9.0983 17 57 39.4182
B74 3 3 3.5484 0.7676 0.00 154 169 18.5330 3 13 7.3941 13 57 32.0482
B75 11 11 11.6452 0.9504 0.00 156 166 10.2917 6 14 9.4745 26 64 42.2402
B76 5 5 5.1290 0.4995 0.00 153 202 49.9134 6 13 6.4288 25 73 35.4865
B77 5 5 5.3871 0.8032 0.00 152 161 11.1016 4 13 7.0557 17 56 28.8527
B78 4 4 4.7742 1.3344 0.00 153 159 7.9270 4 13 6.6488 17 55 29.2830
B79 14 14 14.0000 0.0000 0.00 153 166 11.9017 2 9 3.9646 8 41 16.3156
B80 11 11 11.0000 0.0000 0.00 154 162 9.6500 6 11 5.3587 24 50 23.5722
B81 11 11 11.3548 0.8386 0.00 153 158 6.6857 5 13 7.0744 20 56 29.7124
B82 10 10 10.4516 0.7676 0.00 152 160 10.6532 5 13 5.9386 20 55 27.4567
B83 12 12 12.0968 0.5388 0.00 153 170 19.9290 5 11 3.8451 24 51 17.9308
B84 12 12 12.0000 0.0000 0.00 154 161 6.7725 4 13 7.3941 16 55 31.6225
B85 8 8 8.8387 1.2409 0.00 154 164 14.7388 5 14 7.2984 22 62 34.7666
B86 8 8 8.0968 0.5388 0.00 153 162 10.3043 4 10 4.3183 16 44 18.7357
B87 10 10 10.1290 0.4995 0.00 154 166 10.6363 5 18 8.1722 21 80 36.7600
B88 8 8 8.0000 0.0000 0.00 154 160 6.2300 6 11 4.4717 24 50 18.2966
B89 8 8 8.0000 0.0000 0.00 154 181 63.1321 4 10 3.9393 16 50 22.3958
B90 5 5 5.4839 1.1216 0.00 154 158 5.3563 3 10 4.3045 12 41 18.0081
   AVG 8.0756 0.4173 0.00 154 170 21.8506 3 9 4.8937 14 44 24.7712