Scientific Programming

Research Article

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

Table 28

MBO using sequential quick sort algorithm.
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 0.00 156 190 58.2650 2 7 3.8624 11 43 33.3476
B2 11 11 11.0000 0.0000 0.00 153 161 11.6192 2 4 1.4074 8 19 6.0245
B3 11 11 11.0000 0.0000 0.00 152 155 2.5085 2 4 1.5176 8 17 6.5214
B4 11 11 11.0000 0.0000 0.00 152 182 101.4110 2 4 1.8246 8 22 9.4797
B5 11 11 11.0000 0.0000 0.00 152 156 6.3229 2 5 3.4426 9 22 13.9587
B6 7 7 7.0000 0.0000 0.00 154 161 13.5107 3 8 4.1693 12 37 17.3353
B7 6 6 6.0323 0.1796 0.00 153 168 13.8935 3 6 2.9068 12 31 13.1726
B8 4 4 4.0645 0.3592 0.00 152 182 34.6447 2 10 7.8375 8 49 35.8762
B9 3 3 3.1290 0.3408 0.00 152 156 9.6349 2 6 5.9664 8 29 33.1260
B10 3 3 3.0000 0.0000 0.00 152 154 2.1771 2 4 1.1968 8 16 4.7947
B11 4 4 4.1290 0.3408 0.00 154 157 3.1084 1 11 8.3456 4 46 34.7346
B12 4 4 4.0000 0.0000 0.00 152 155 3.0374 1 3 1.5794 5 15 6.4709
B13 4 4 4.2258 0.7169 0.00 152 153 1.8814 2 5 5.3585 8 23 22.5828
B14 3 3 3.3548 0.4864 0.00 152 154 1.6533 2 5 2.3971 8 23 9.8987
B15 1 1 1.1290 0.4995 0.00 152 153 1.5027 2 6 2.2912 8 24 9.3735
B16 14 14 14.0000 0.0000 0.00 154 158 6.5646 2 8 4.7026 8 34 19.1483
B17 13 13 13.0000 0.0000 0.00 153 155 2.0283 2 5 1.8860 9 21 7.4763
B18 13 13 13.0000 0.0000 0.00 152 157 7.3231 1 6 2.4995 4 25 10.3130
B19 13 13 13.0968 0.5388 0.00 152 159 6.4381 2 7 6.0690 8 33 24.6737
B20 13 13 13.0000 0.0000 0.00 153 159 7.5257 2 7 4.6504 8 31 19.5123
B21 9 9 9.2903 0.4614 0.00 154 158 4.8569 2 9 7.8941 8 41 32.4426
B22 6 6 6.1613 0.3739 0.00 152 160 7.6086 3 6 2.7611 12 26 12.0577
B23 6 6 6.1613 0.3739 0.00 152 157 5.0575 4 10 7.1245 16 43 29.3833
B24 5 5 5.2903 0.5287 0.00 152 159 6.8078 2 7 4.8146 9 30 19.7313
B25 4 4 4.1613 0.3739 0.00 152 155 4.9514 2 6 2.5430 8 24 10.4495
B26 5 5 5.0000 0.0000 0.00 154 163 8.4537 2 8 4.4837 8 36 18.4994
B27 3 3 3.0323 0.1796 0.00 153 158 6.3527 1 7 5.5072 5 29 22.6066
B28 3 3 3.2581 0.4448 0.00 152 162 9.1764 2 6 4.4041 8 26 20.0669
B29 3 3 3.1613 0.3739 0.00 152 163 8.9060 1 5 2.9534 4 23 12.2417
B30 2 2 2.6129 0.8032 0.00 152 162 11.2350 2 7 6.3716 8 30 26.7117
B31 7 7 7.0000 0.0000 0.00 155 172 13.0047 3 8 5.2176 14 40 23.0526
B32 4 4 4.0968 0.5388 0.00 154 163 16.2313 2 8 5.0189 8 36 22.6064
B33 4 4 4.0645 0.3592 0.00 153 161 8.5798 2 5 2.5016 8 22 10.6692
B34 4 4 4.1290 0.4995 0.00 152 158 9.0177 2 6 5.0302 8 27 20.6482
B35 4 4 4.6452 0.9504 0.00 152 153 1.5098 1 5 4.4678 4 23 18.0923
B36 13 13 13.0000 0.0000 0.00 154 174 26.3191 3 8 4.2014 12 41 24.8909
B37 10 10 10.5161 0.8896 0.00 153 161 12.2450 2 7 3.9136 8 30 15.9159
B38 8 8 8.0968 0.3962 0.00 152 157 6.5512 2 10 8.7204 8 43 35.7477
B39 5 5 5.0000 0.0000 0.00 152 161 13.6204 3 5 2.3431 12 25 10.6618
B40 5 5 5.0000 0.0000 0.00 152 163 9.7288 2 5 2.1438 8 21 9.9864
B41 8 8 8.0000 0.0000 0.00 155 165 12.7196 1 10 6.2553 5 48 26.9376
B42 8 8 8.0000 0.0000 0.00 152 157 3.5951 2 4 1.7804 8 19 7.5267
B43 8 8 8.0645 0.3592 0.00 152 155 2.4947 2 5 5.3110 8 24 22.0386
B44 5 5 6.0645 1.4591 0.00 152 155 3.3302 2 6 3.3601 8 25 13.7010
B45 5 5 6.4516 1.5240 0.00 152 154 1.4135 2 5 2.2907 8 21 9.2427
B46 8 8 8.1290 0.3408 0.00 154 161 4.7801 3 9 6.7587 14 42 29.0482
B47 5 5 5.0968 0.5388 0.00 153 156 2.5392 1 4 1.8139 4 20 7.8833
B48 5 5 5.1935 0.6011 0.00 152 155 4.2327 2 5 2.4021 8 23 9.6806
B49 5 5 5.1290 0.4995 0.00 152 155 3.8960 3 7 4.9298 12 31 20.3514
B50 5 5 5.1935 0.6011 0.00 152 157 7.6718 2 5 2.2728 8 24 9.2511
B51 27 27 28.2258 0.9205 0.00 155 161 4.3769 4 19 9.2586 20 82 39.4718
B52 18 18 18.9032 1.1062 0.00 154 158 4.4286 7 20 9.4888 29 85 40.2330
B53 11 11 11.0000 0.0000 0.00 154 157 2.8269 4 10 4.1346 16 44 16.8027
B54 11 11 11.0000 0.0000 0.00 153 156 2.3075 4 9 3.2052 16 38 13.3121
B55 7 7 7.0000 0.0000 0.00 154 158 2.9370 4 10 5.4839 16 45 22.7564
B56 6 6 6.0000 0.0000 0.00 154 157 2.2337 4 8 2.6184 16 36 11.1519
B57 6 6 6.0000 0.0000 0.00 153 157 4.3503 6 10 4.0231 24 43 16.3044
B58 6 6 6.1290 0.3408 0.00 154 157 2.8189 5 10 3.8882 20 44 15.7987
B59 9 9 9.1935 0.6011 0.00 154 160 3.4817 3 13 8.1588 12 59 34.8749
B60 4 4 4.5161 1.3631 0.00 154 157 2.8511 3 12 4.7288 12 50 19.8736
B61 4 4 4.2258 0.6170 0.00 153 156 3.6237 3 11 4.2571 17 48 17.2788
B62 4 4 4.0323 0.1796 0.00 152 155 2.5098 4 10 3.6820 16 41 15.5667
B63 27 27 27.2581 0.4448 0.00 155 164 6.3053 4 19 10.1183 19 84 42.8466
B64 18 18 18.3548 0.5507 0.00 154 175 29.3106 7 20 9.2391 37 95 41.8859
B65 14 14 14.1935 0.4016 0.00 154 162 11.5242 5 14 6.2896 22 61 26.2881
B66 13 13 13.0000 0.0000 0.00 154 174 31.3824 6 11 3.7301 24 51 22.7029
B67 11 11 11.0323 0.1796 0.00 155 166 11.5943 6 12 5.7328 24 53 23.5936
B68 8 8 8.5806 1.7469 0.00 154 160 5.9015 3 11 6.2869 12 48 25.7106
B69 8 8 8.5161 0.8112 0.00 153 165 12.9041 4 10 5.4759 16 47 24.7696
B70 6 6 6.6452 0.8386 0.00 153 160 11.3877 2 12 7.7095 8 52 31.6072
B71 6 6 6.1290 0.4995 0.00 157 178 18.6546 2 11 5.3096 11 54 28.3288
B72 4 4 4.2581 0.7732 0.00 154 171 19.4453 4 11 6.3664 16 54 29.4289
B73 4 4 4.4194 0.6204 0.00 154 174 16.4459 5 10 4.0422 21 51 19.9695
B74 3 3 3.5484 0.6239 0.00 156 187 33.9678 5 12 7.8744 20 67 49.6365
B75 11 11 11.5806 1.0255 0.00 159 200 45.3931 4 17 9.9043 17 95 67.7548
B76 5 5 5.0645 0.3592 0.00 154 171 37.0215 4 14 6.9785 17 67 30.3144
B77 5 5 5.3871 0.8032 0.00 154 161 7.2560 4 14 7.2969 17 62 31.3623
B78 4 4 4.5806 1.1188 0.00 153 166 11.1021 8 15 4.9588 32 69 24.4737
B79 14 14 14.0000 0.0000 0.00 155 173 15.1100 5 9 2.9421 20 44 16.3185
B80 11 11 11.0000 0.0000 0.00 154 164 13.3813 4 11 3.7198 17 48 16.2591
B81 11 11 11.5484 1.1787 0.00 155 177 20.2888 2 13 8.5572 8 64 39.3331
B82 10 10 10.7419 0.7732 0.00 154 227 142.7347 3 10 5.1533 13 56 31.9425
B83 12 12 12.3548 1.5176 0.00 154 180 28.3520 3 11 6.7907 13 58 36.4259
B84 12 12 12.0000 0.0000 0.00 155 165 12.8809 2 12 5.0773 9 54 23.5388
B85 8 8 9.4516 1.6899 0.00 154 164 17.4202 3 13 6.9161 13 59 29.5533
B86 8 8 8.1613 0.5829 0.00 153 155 2.0525 4 11 6.3534 16 49 25.9607
B87 10 10 10.3871 0.9549 0.00 154 159 5.2984 5 16 9.5733 20 68 40.5421
B88 8 8 8.0000 0.0000 0.00 154 157 2.8466 5 10 3.0610 21 43 12.7689
B89 8 8 8.0323 0.1796 0.00 154 156 2.3349 4 10 5.9039 16 43 23.9970
B90 5 5 5.3871 1.0223 0.00 153 155 2.5778 3 11 4.7201 13 46 18.9533
   AVG 8.1111 0.4529 0.00 153 163 12.7284 2 9 4.9168 12 41 22.1071