Scientific Programming

Research Article

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

Table 31

MBO using parallel quick 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 0.00 190 260 90.7097 2 6 3.5636 12 55 39.8897
B2 11 11 11.0000 0.0000 0.00 205 231 16.0884 1 3 1.3408 5 27 11.3853
B3 11 11 11.0000 0.0000 0.00 201 218 12.8483 2 4 1.2487 15 25 8.4055
B4 11 11 11.0000 0.0000 0.00 197 224 13.2765 2 4 1.6198 9 30 10.1960
B5 11 11 11.0000 0.0000 0.00 203 226 16.9506 1 5 2.5425 5 31 15.3820
B6 7 7 7.0000 0.0000 0.00 179 209 26.6540 3 8 4.1551 16 46 20.1586
B7 6 6 6.0645 0.2497 0.00 159 170 8.6506 2 5 2.3958 9 26 10.8302
B8 4 4 4.5806 1.2852 0.00 161 208 24.9863 2 9 8.2168 11 49 44.8206
B9 3 3 3.0000 0.0000 0.00 156 169 9.0874 1 5 2.9975 4 25 14.9742
B10 3 3 3.0000 0.0000 0.00 160 187 29.3461 1 4 1.9143 4 21 10.0919
B11 4 4 4.2581 0.4448 0.00 221 265 38.7226 3 12 7.1297 18 92 57.9354
B12 4 4 4.0000 0.0000 0.00 189 244 25.8799 2 4 1.8917 9 30 13.7061
B13 4 4 4.0000 0.0000 0.00 175 212 26.0266 2 5 2.0609 9 29 12.7301
B14 3 3 3.5161 0.5080 0.00 191 233 25.7782 2 5 2.1251 10 32 17.8553
B15 1 1 1.4839 0.9263 0.00 158 172 15.6618 2 5 2.1266 8 25 10.8872
B16 14 14 14.0000 0.0000 0.00 219 241 17.5973 2 8 4.4454 10 51 28.6909
B17 13 13 13.0000 0.0000 0.00 155 178 22.8931 2 5 1.4142 8 23 6.1196
B18 13 13 13.0000 0.0000 0.00 157 170 16.5604 2 5 1.9620 8 23 10.1844
B19 13 13 13.2903 0.9016 0.00 184 212 13.5299 2 6 2.9024 10 38 15.5537
B20 13 13 13.0000 0.0000 0.00 179 195 11.0056 2 8 5.7083 8 44 29.5659
B21 9 9 9.1613 0.3739 0.00 173 223 67.1284 4 10 8.0616 19 60 50.9887
B22 6 6 6.1613 0.3739 0.00 193 273 88.1693 3 6 3.0764 12 46 37.1433
B23 6 6 6.2258 0.4973 0.00 187 232 20.6745 2 6 4.7992 14 44 30.3885
B24 5 5 5.4516 0.7229 0.00 185 216 28.3318 2 5 2.5046 14 32 12.6408
B25 4 4 4.3548 0.7094 0.00 180 220 38.7354 2 7 3.3575 11 41 21.8570
B26 5 5 5.0000 0.0000 0.00 222 267 65.9248 2 9 6.2550 11 63 40.3980
B27 3 3 3.0968 0.3005 0.00 163 187 72.6372 1 6 4.0640 4 32 19.3312
B28 3 3 3.2903 0.4614 0.00 161 188 57.0519 2 5 2.3773 8 26 13.4644
B29 3 3 3.1290 0.3408 0.00 153 176 30.2510 2 5 1.9615 9 24 10.0626
B30 2 2 2.3871 0.5584 0.00 153 175 21.4547 3 9 6.7079 12 41 29.4979
B31 7 7 7.0000 0.0000 0.00 161 211 43.1659 2 10 4.5541 10 58 30.4089
B32 4 4 4.3871 1.0223 0.00 155 191 40.5896 1 7 6.1083 4 38 31.5310
B33 4 4 4.1935 0.6011 0.00 156 214 47.1663 2 6 3.0204 12 37 18.9796
B34 4 4 4.2581 0.6816 0.00 156 169 21.7325 2 5 2.2855 10 26 10.2277
B35 4 4 4.4516 0.8500 0.00 155 184 36.3288 1 5 2.4861 4 25 14.0484
B36 13 13 13.0000 0.0000 0.00 159 172 12.9491 2 9 5.4378 8 44 24.1031
B37 10 10 10.5806 0.9228 0.00 154 165 12.0246 2 7 6.6159 9 35 31.7865
B38 8 8 8.0968 0.3005 0.00 155 162 8.0036 2 11 9.7551 8 50 41.9069
B39 5 5 5.0000 0.0000 0.00 154 162 6.2843 2 5 2.1109 8 23 9.1885
B40 5 5 5.1290 0.4995 0.00 160 185 31.2620 2 5 1.9898 9 27 11.3643
B41 8 8 8.1613 0.8980 0.00 157 191 35.3240 3 9 5.6883 12 52 34.1054
B42 8 8 8.0000 0.0000 0.00 153 191 35.1184 2 4 2.0557 8 25 14.0413
B43 8 8 8.0000 0.0000 0.00 153 195 46.0170 2 4 1.8163 8 26 13.6305
B44 5 5 5.9677 1.4256 0.00 155 180 30.1549 1 5 2.3372 4 23 10.0189
B45 5 5 5.8710 1.3842 0.00 154 162 10.2862 1 5 2.5661 4 24 11.2124
B46 8 8 8.0645 0.2497 0.00 159 197 41.1302 2 10 6.8400 8 53 42.0245
B47 5 5 5.0968 0.5388 0.00 156 185 49.5067 2 6 2.5703 9 34 21.4733
B48 5 5 5.1290 0.4995 0.00 154 183 34.0827 2 5 2.5493 9 28 13.3359
B49 5 5 5.2581 0.6816 0.00 155 171 26.4985 2 6 4.9605 8 27 22.1096
B50 5 5 5.1935 0.6011 0.00 159 293 137.7965 2 6 4.3729 10 44 30.5390
B51 27 27 28.2903 0.8638 0.00 237 261 14.2311 4 21 9.5117 22 144 67.3566
B52 18 18 18.7742 0.8835 0.00 219 233 14.9013 3 21 10.1319 19 133 65.4978
B53 11 11 11.0000 0.0000 0.00 201 230 12.1596 5 11 3.8566 28 66 25.8455
B54 11 11 11.0000 0.0000 0.00 202 217 12.3461 3 8 2.6401 21 48 16.3395
B55 7 7 7.0000 0.0000 0.00 214 240 12.0357 4 11 4.1032 23 74 26.0514
B56 6 6 6.0000 0.0000 0.00 204 224 12.4441 4 11 4.5166 22 66 28.6479
B57 6 6 6.0323 0.1796 0.00 208 228 12.0374 4 11 3.5765 24 67 21.0756
B58 6 6 6.0000 0.0000 0.00 206 224 11.6898 4 9 4.5009 16 56 28.0782
B59 9 9 9.1290 0.4275 0.00 174 241 39.2589 5 16 9.8178 23 103 60.2449
B60 4 4 4.7419 1.7883 0.00 154 159 3.9053 3 12 5.6472 12 51 24.0830
B61 4 4 4.1613 0.3739 0.00 154 157 4.0611 3 12 7.1637 12 51 29.2026
B62 4 4 4.0000 0.0000 0.00 154 157 4.8422 4 10 5.3876 17 43 22.6520
B63 27 27 27.1935 0.4016 0.00 158 169 5.2271 3 14 7.9795 14 66 35.6641
B64 18 18 18.2903 0.6426 0.00 155 159 2.8364 3 19 10.2648 14 84 42.7305
B65 14 14 14.0968 0.3005 0.00 154 163 8.1524 3 14 7.8763 13 62 35.1641
B66 13 13 13.0000 0.0000 0.00 154 166 13.0996 7 12 3.6136 28 54 17.3759
B67 11 11 11.0968 0.3005 0.00 166 263 83.3463 3 15 9.6607 17 109 100.7377
B68 8 8 8.1935 0.6011 0.00 155 184 23.4952 4 12 6.7003 19 60 35.4280
B69 8 8 8.5806 0.7199 0.00 158 211 64.9205 5 12 6.2117 22 75 65.2722
B70 6 6 6.7097 0.8638 0.00 155 231 135.2276 3 13 6.6360 18 83 66.1519
B71 6 6 6.2258 0.6170 0.00 162 200 53.9548 5 12 8.4985 27 67 46.9196
B72 4 4 4.3226 0.5993 0.00 154 160 4.7503 6 12 5.8701 24 53 24.2337
B73 4 4 4.4839 0.6256 0.00 154 181 34.0598 3 13 7.3084 14 63 39.7601
B74 3 3 3.3871 0.5584 0.00 154 163 4.2860 3 12 6.5822 18 53 27.1781
B75 11 11 11.6129 0.9892 0.00 168 183 13.2764 4 18 9.8581 18 89 45.1418
B76 5 5 5.1935 0.6011 0.00 163 193 35.1540 4 13 6.0851 20 70 40.9876
B77 5 5 5.2581 0.6816 0.00 154 186 23.2987 4 15 8.8359 24 73 39.9299
B78 4 4 4.7097 1.1887 0.00 156 170 10.0336 5 15 6.8506 23 69 31.6560
B79 14 14 14.0000 0.0000 0.00 156 164 6.0066 3 10 3.5484 12 46 15.1387
B80 11 11 11.0000 0.0000 0.00 153 158 6.2756 5 11 3.4811 20 48 14.9292
B81 11 11 11.4839 0.9263 0.00 154 159 5.5222 3 12 7.9278 16 54 31.9301
B82 10 10 10.5484 0.8500 0.00 154 156 2.3344 4 12 5.7675 16 51 24.5353
B83 12 12 12.0000 0.0000 0.00 157 164 4.1408 4 13 6.6827 16 60 29.7937
B84 12 12 12.0645 0.3592 0.00 154 158 5.3961 4 11 5.1974 16 49 22.7398
B85 8 8 8.9032 1.4687 0.00 154 157 2.9860 5 11 4.7201 21 47 19.4751
B86 8 8 8.2258 0.8835 0.00 154 156 2.0765 3 8 4.5371 12 34 18.4101
B87 10 10 10.5161 0.9957 0.00 162 171 4.9756 7 19 8.8350 29 87 40.9288
B88 8 8 8.0000 0.0000 0.00 154 157 2.9647 4 10 4.8012 17 43 20.1409
B89 8 8 8.0000 0.0000 0.00 154 157 3.8529 4 10 4.7071 18 45 19.3560
B90 5 5 5.1935 0.7492 0.00 154 156 1.4398 3 10 4.2256 12 43 17.4126
   AVG 8.1079 0.4472 0.00 169 195 26.3893 2 9 4.8796 13 49 27.5041