Scientific Programming

Research Article

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

Table 23

MBO using parallel merge sort algorithm with 1 thread.
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 0.00 159 206 78.6150 2 6 3.2038 14 43 35.4355
B2 11 11 11.0000 0.0000 0.00 155 173 19.0187 1 4 1.5141 6 21 8.1043
B3 11 11 11.0000 0.0000 0.00 154 172 13.6524 1 3 1.2495 4 16 5.5298
B4 11 11 11.0000 0.0000 0.00 153 172 16.4752 3 5 1.6552 12 24 10.3208
B5 11 11 11.0000 0.0000 0.00 152 155 5.0775 2 5 3.1064 8 24 12.5736
B6 7 7 7.0000 0.0000 0.00 155 185 36.0141 3 10 6.0544 13 48 27.2948
B7 6 6 6.0000 0.0000 0.00 159 202 24.7416 2 6 4.4252 9 35 21.5014
B8 4 4 4.4516 0.8500 0.00 158 197 88.5635 3 12 8.1669 17 58 40.5206
B9 3 3 3.0645 0.2497 0.00 153 172 12.9714 2 5 2.3122 12 23 9.5575
B10 3 3 3.0000 0.0000 0.00 152 168 13.5060 1 4 2.2609 7 20 10.8349
B11 4 4 4.2258 0.4250 0.00 156 186 18.4762 1 10 7.4314 5 53 41.0204
B12 4 4 4.0000 0.0000 0.00 160 178 17.7416 2 4 1.7585 8 21 10.0164
B13 4 4 4.0000 0.0000 0.00 152 171 19.3874 2 4 2.2714 8 21 10.1196
B14 3 3 3.2903 0.4614 0.00 152 169 15.2222 2 6 4.9287 8 28 22.3718
B15 1 1 1.0968 0.5388 0.00 153 165 11.9830 2 6 3.4694 8 29 16.5698
B16 14 14 14.0000 0.0000 0.00 155 163 9.5187 2 7 3.4128 8 33 14.8828
B17 13 13 13.0000 0.0000 0.00 153 155 2.8564 2 5 2.0225 8 21 8.8107
B18 13 13 13.0000 0.0000 0.00 152 155 2.6401 2 5 2.2264 8 24 9.3277
B19 13 13 13.3871 1.0223 0.00 152 155 3.7145 2 7 4.0236 8 30 16.7423
B20 13 13 13.0000 0.0000 0.00 152 154 2.2240 2 6 3.6308 8 28 14.7566
B21 9 9 9.1935 0.4016 0.00 154 161 4.3366 3 11 6.9041 12 47 29.4637
B22 6 6 6.1935 0.4016 0.00 153 156 2.2926 1 5 2.4203 4 23 10.0929
B23 6 6 6.0645 0.2497 0.00 152 155 4.3901 2 7 4.9174 8 31 19.7046
B24 5 5 5.3548 0.6607 0.00 152 155 2.7712 2 6 5.4696 8 28 22.2898
B25 4 4 4.3871 0.6672 0.00 152 156 3.3534 3 7 3.7411 12 29 15.0894
B26 5 5 5.0323 0.1796 0.00 155 162 5.0227 2 7 3.3376 9 34 13.9975
B27 3 3 3.0323 0.1796 0.00 154 157 4.5927 3 6 3.4619 12 27 14.2464
B28 3 3 3.0968 0.3005 0.00 152 156 3.8156 2 6 2.3714 8 25 10.0092
B29 3 3 3.3548 0.4864 0.00 152 155 3.1271 2 4 2.4913 8 19 10.2875
B30 2 2 2.5484 0.6752 0.00 154 157 3.3421 1 8 7.1106 6 33 29.8981
B31 7 7 7.0000 0.0000 0.00 158 166 5.7951 1 10 5.4402 5 44 23.6942
B32 4 4 4.1935 0.7492 0.00 153 159 3.6603 2 7 4.7390 8 31 20.0530
B33 4 4 4.0645 0.3592 0.00 153 158 3.9906 2 6 3.3872 8 25 13.7612
B34 4 4 4.2581 0.6816 0.00 152 158 3.7035 2 5 3.5636 8 25 14.7240
B35 4 4 4.4516 0.8500 0.00 153 158 4.3965 2 5 3.3916 8 22 14.3879
B36 13 13 13.0000 0.0000 0.00 156 166 6.3017 1 10 5.6101 5 44 24.9727
B37 10 10 10.3226 0.7478 0.00 154 157 2.4314 2 8 6.6553 8 34 27.1586
B38 8 8 8.1613 0.4544 0.00 152 156 4.2246 3 10 8.3402 12 44 34.0656
B39 5 5 5.0000 0.0000 0.00 153 159 11.6618 3 5 2.3363 12 23 9.8435
B40 5 5 5.1935 0.6011 0.00 152 160 6.3128 2 5 2.0645 9 25 8.9185
B41 8 8 8.1613 0.8980 0.00 154 169 10.6175 1 8 5.2096 4 36 22.4695
B42 8 8 8.0000 0.0000 0.00 153 166 10.1747 2 4 1.9438 8 18 8.0620
B43 8 8 8.0000 0.0000 0.00 152 165 10.7002 2 5 2.1568 12 24 9.2664
B44 5 5 5.7742 1.3344 0.00 153 161 8.5650 2 4 1.8062 8 21 7.8376
B45 5 5 5.9677 1.4256 0.00 152 159 8.0203 2 5 2.6453 8 24 10.7374
B46 8 8 8.0645 0.2497 0.00 155 172 12.5416 2 9 6.5325 8 44 31.3379
B47 5 5 5.0968 0.5388 0.00 153 162 6.1438 2 6 2.2423 8 26 9.7972
B48 5 5 5.1290 0.4995 0.00 152 157 3.8888 2 5 2.3646 8 23 9.8283
B49 5 5 5.2581 0.6816 0.00 153 166 11.7214 3 5 2.3335 14 25 9.2466
B50 5 5 5.3226 0.7478 0.00 158 297 112.2328 2 5 4.2598 8 46 59.0964
B51 27 27 28.1935 1.0139 0.00 170 210 50.5103 9 21 8.4341 40 120 65.5098
B52 18 18 19.0000 1.2383 0.00 160 174 12.9624 7 21 8.9031 29 96 39.5778
B53 11 11 11.0000 0.0000 0.00 161 178 16.1011 4 10 3.4251 17 49 15.4218
B54 11 11 11.0000 0.0000 0.00 164 225 110.0060 4 9 2.2274 17 53 25.5038
B55 7 7 7.0000 0.0000 0.00 170 227 95.8822 6 12 4.8697 35 73 34.6457
B56 6 6 6.0000 0.0000 0.00 158 176 22.7563 4 10 4.1773 18 46 17.2158
B57 6 6 6.0323 0.1796 0.00 158 164 3.8771 6 11 4.7317 29 49 20.2836
B58 6 6 6.0000 0.0000 0.00 157 167 7.3482 4 10 4.1721 17 47 17.6931
B59 9 9 9.1290 0.3408 0.00 162 176 9.1676 4 12 7.6146 16 60 35.3615
B60 4 4 4.2581 0.9989 0.00 160 167 5.9831 3 13 7.2062 14 62 31.0985
B61 4 4 4.1290 0.3408 0.00 160 165 3.8543 6 12 6.4014 25 53 28.3432
B62 4 4 4.0000 0.0000 0.00 158 164 4.8012 4 10 5.3501 18 43 23.0980
B63 27 27 27.2903 0.4614 0.00 167 175 6.0466 2 16 7.7237 9 76 36.5377
B64 18 18 18.3871 1.0223 0.00 160 168 5.1665 3 19 9.7662 15 86 43.3281
B65 14 14 14.0323 0.1796 0.00 160 165 3.8291 4 16 8.6324 17 71 37.8486
B66 13 13 13.0000 0.0000 0.00 158 164 4.3960 4 9 3.8069 17 42 17.3308
B67 11 11 11.0000 0.0000 0.00 161 169 5.7328 3 13 6.7766 15 60 30.8939
B68 8 8 8.5161 1.3873 0.00 157 166 4.9242 5 12 5.9210 20 55 25.9415
B69 8 8 8.7097 0.8244 0.00 159 186 80.6533 4 10 3.5186 20 59 78.6617
B70 6 6 6.3548 0.6082 0.00 157 164 4.1299 5 11 6.0651 21 49 26.3690
B71 6 6 6.3226 0.9087 0.00 164 173 4.9813 3 13 7.2318 15 64 34.0172
B72 4 4 4.2581 0.5143 0.00 162 169 7.0074 4 13 7.3266 18 61 31.5165
B73 4 4 4.3548 0.5507 0.00 155 163 7.4271 4 10 4.5181 16 46 19.8506
B74 3 3 3.3871 0.6152 0.00 154 159 6.2096 4 12 6.5673 18 54 27.7339
B75 11 11 11.8710 0.9217 0.00 156 166 6.2745 7 19 9.0094 32 84 39.6957
B76 5 5 5.1290 0.4995 0.00 154 159 4.0391 3 12 7.1859 12 53 30.5339
B77 5 5 5.6129 0.9892 0.00 154 158 2.9061 3 12 6.2763 12 52 26.0995
B78 4 4 4.7097 1.1887 0.00 152 157 4.4870 3 15 8.9251 12 64 37.0953
B79 14 14 14.0000 0.0000 0.00 154 160 3.9374 4 10 3.9070 17 46 16.9129
B80 11 11 11.0000 0.0000 0.00 154 159 3.6503 4 10 3.0409 16 43 12.6801
B81 11 11 11.2258 0.7169 0.00 154 157 2.5025 3 12 7.2826 13 51 29.8398
B82 10 10 10.7097 0.7829 0.00 153 160 9.2766 4 10 4.2187 19 45 17.2205
B83 12 12 12.1290 0.7184 0.00 154 161 5.0024 5 13 7.6357 23 59 32.3602
B84 12 12 12.0968 0.5388 0.00 154 159 3.8746 3 11 5.8103 12 49 25.2224
B85 8 8 9.3548 1.4731 0.00 153 157 3.7096 4 13 7.1319 19 57 29.5541
B86 8 8 8.0000 0.0000 0.00 152 157 4.4661 4 11 4.7817 16 46 19.8128
B87 10 10 10.3871 0.9193 0.00 156 165 5.2583 6 18 8.5468 25 81 38.3296
B88 8 8 8.0000 0.0000 0.00 154 159 6.6066 4 11 3.8846 16 47 16.1636
B89 8 8 8.0323 0.1796 0.00 153 158 4.5929 3 10 5.0891 12 42 21.2703
B90 5 5 5.7742 1.3344 0.00 153 157 2.6204 6 11 3.8401 24 46 15.4224
   AVG 8.1065 0.4446 0.00 155 168 13.9276 3 9 4.7812 13 42 22.9180