Table 2.
Numerical results
| NO | Dim | Algorithm 2.1 | Algorithm 2 | Algorithm 3 | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| NI | NFG | CPU | NI | NFG | CPU | NI | NFG | CPU | ||
| 1 | 9000 | 4 | 20 | 0.124801 | 14 | 48 | 0.405603 | 5 | 26 | 0.249602 |
| 2 | 9000 | 71 | 327 | 1.965613 | 27 | 89 | 0.670804 | 32 | 136 | 0.858005 |
| 3 | 9000 | 7 | 20 | 0.0312 | 37 | 160 | 0.249602 | 27 | 147 | 0.202801 |
| 4 | 9000 | 12 | 49 | 0.280802 | 34 | 161 | 0.717605 | 42 | 219 | 0.951606 |
| 5 | 9000 | 13 | 56 | 0.202801 | 20 | 63 | 0.249602 | 5 | 24 | 0.0624 |
| 6 | 9000 | 65 | 252 | 0.421203 | 43 | 143 | 0.280802 | 3 | 9 | 0.0312 |
| 7 | 9000 | 11 | 37 | 0.0624 | 478 | 979 | 2.215214 | 465 | 1479 | 2.558416 |
| 8 | 9000 | 5 | 20 | 0.0624 | 22 | 55 | 0.156001 | 14 | 54 | 0.156001 |
| 9 | 9000 | 6 | 16 | 0.0312 | 5 | 21 | 0.0624 | 3 | 8 | 0.0312 |
| 10 | 9000 | 2 | 13 | 0.0156 | 2 | 13 | 0.000001 | 2 | 13 | 0.000001 |
| 11 | 9000 | 3 | 17 | 0.0312 | 7 | 34 | 0.0624 | 17 | 87 | 0.218401 |
| 12 | 9000 | 3 | 10 | 0.0312 | 19 | 40 | 0.202801 | 14 | 50 | 0.202801 |
| 13 | 9000 | 3 | 24 | 0.0624 | 3 | 24 | 0.0312 | 3 | 24 | 0.0156 |
| 14 | 9000 | 4 | 12 | 4.305628 | 5 | 14 | 5.382034 | 5 | 14 | 5.226033 |
| 15 | 9000 | 19 | 77 | 9.984064 | 22 | 66 | 9.516061 | 21 | 71 | 10.296066 |
| 16 | 9000 | 3 | 11 | 0.0624 | 6 | 27 | 0.078 | 6 | 18 | 0.0624 |
| 17 | 9000 | 11 | 45 | 0.374402 | 27 | 69 | 0.780005 | 27 | 87 | 0.811205 |
| 18 | 9000 | 5 | 23 | 0.0312 | 3 | 10 | 0.000001 | 3 | 10 | 0.0312 |
| 19 | 9000 | 3 | 9 | 0.0624 | 3 | 9 | 0.0312 | 3 | 19 | 0.0312 |
| 20 | 9000 | 19 | 76 | 0.124801 | 15 | 36 | 0.0624 | 3 | 9 | 0.0312 |
| 21 | 9000 | 12 | 47 | 0.156001 | 13 | 61 | 0.187201 | 15 | 59 | 0.218401 |
| 22 | 9000 | 7 | 46 | 0.795605 | 8 | 70 | 0.577204 | 6 | 46 | 0.686404 |
| 23 | 9000 | 9 | 45 | 0.218401 | 101 | 357 | 2.090413 | 46 | 150 | 0.873606 |
| 24 | 9000 | 5 | 47 | 0.093601 | 14 | 88 | 0.156001 | 14 | 97 | 0.249602 |
| 25 | 9000 | 9 | 28 | 0.0312 | 40 | 214 | 0.249602 | 8 | 46 | 0.0624 |
| 26 | 9000 | 24 | 102 | 0.327602 | 24 | 100 | 0.249602 | 3 | 24 | 0.0312 |
| 27 | 9000 | 6 | 20 | 0.0312 | 34 | 109 | 0.187201 | 92 | 321 | 0.530403 |
| 28 | 9000 | 13 | 50 | 0.124801 | 20 | 83 | 0.109201 | 23 | 84 | 0.140401 |
| 29 | 9000 | 6 | 36 | 0.0468 | 4 | 21 | 0.0312 | 4 | 21 | 0.0312 |
| 30 | 9000 | 11 | 37 | 0.0624 | 454 | 931 | 1.450809 | 424 | 1346 | 1.747211 |
| 31 | 9000 | 18 | 63 | 0.124801 | 15 | 51 | 0.093601 | 3 | 10 | 0.0312 |
| 32 | 9000 | 18 | 70 | 0.218401 | 23 | 61 | 0.218401 | 3 | 18 | 0.0624 |
| 33 | 9000 | 2 | 5 | 0.000001 | 2 | 5 | 0.0312 | 2 | 5 | 0.000001 |
| 34 | 9000 | 8 | 16 | 0.0312 | 6 | 12 | 0.0312 | 3 | 6 | 0.0312 |
| 35 | 9000 | 4 | 13 | 0.0312 | 4 | 10 | 0.0312 | 3 | 8 | 0.000001 |
| 36 | 9000 | 7 | 23 | 4.602029 | 8 | 28 | 5.569236 | 10 | 47 | 8.673656 |
| 37 | 9000 | 7 | 23 | 0.0624 | 1412 | 2829 | 6.942044 | 2000 | 6021 | 11.356873 |
| 38 | 9000 | 4 | 18 | 0.0312 | 8 | 35 | 0.187201 | 4 | 11 | 0.0312 |
| 39 | 9000 | 5 | 19 | 0.0312 | 28 | 56 | 0.124801 | 3 | 8 | 0.0312 |
| 40 | 9000 | 13 | 43 | 0.561604 | 835 | 2936 | 36.223432 | 9 | 41 | 0.421203 |
| 41 | 9000 | 10 | 32 | 0.0624 | 17 | 41 | 0.093601 | 22 | 81 | 0.124801 |
| 42 | 9000 | 4 | 33 | 0.0624 | 13 | 35 | 0.124801 | 9 | 47 | 0.109201 |
| 43 | 9000 | 16 | 62 | 1.029607 | 16 | 38 | 0.951606 | 13 | 48 | 0.780005 |
| 44 | 9000 | 3 | 17 | 0.156001 | 9 | 50 | 0.624004 | 3 | 17 | 0.187201 |
| 45 | 9000 | 21 | 118 | 1.49761 | 12 | 81 | 0.858006 | 3 | 24 | 0.202801 |
| 46 | 9000 | 20 | 81 | 1.435209 | 209 | 443 | 11.247672 | 110 | 362 | 6.630042 |
| 47 | 9000 | 11 | 37 | 27.066173 | 30 | 97 | 68.64044 | 37 | 112 | 87.220159 |
| 48 | 9000 | 13 | 54 | 9.718862 | 31 | 92 | 18.610919 | 23 | 50 | 11.980877 |
| 49 | 9000 | 11 | 37 | 0.0624 | 478 | 979 | 1.51321 | 504 | 1592 | 1.887612 |
| 50 | 9000 | 11 | 37 | 7.971651 | 472 | 967 | 263.68849 | 444 | 1273 | 299.381519 |
| 51 | 9000 | 6 | 31 | 0.156001 | 7 | 25 | 0.218401 | 3 | 17 | 0.124801 |
| 52 | 9000 | 62 | 186 | 0.998406 | 63 | 195 | 0.842405 | 4 | 21 | 0.0624 |
| 53 | 9000 | 10 | 32 | 0.0312 | 2000 | 4059 | 7.72205 | 1865 | 5618 | 7.971651 |
| 54 | 9000 | 4 | 11 | 0.0312 | 21 | 79 | 0.156001 | 17 | 79 | 0.124801 |
| 55 | 9000 | 10 | 24 | 3.010819 | 7 | 25 | 3.213621 | 3 | 10 | 1.076407 |
| 56 | 9000 | 7 | 21 | 0.0156 | 2000 | 4003 | 6.489642 | 1390 | 4107 | 5.335234 |
| 57 | 9000 | 5 | 39 | 0.358802 | 67 | 220 | 4.024826 | 3 | 24 | 0.202801 |
| 58 | 9000 | 5 | 24 | 0.343202 | 114 | 282 | 6.411641 | 82 | 315 | 5.257234 |
| 59 | 9000 | 5 | 39 | 0.343202 | 68 | 310 | 4.72683 | 3 | 23 | 0.171601 |
| 60 | 9000 | 18 | 74 | 1.294808 | 206 | 437 | 11.107271 | 119 | 363 | 6.957645 |
| 61 | 9000 | 5 | 39 | 0.358802 | 85 | 247 | 4.929632 | 3 | 24 | 0.218401 |
| 62 | 9000 | 4 | 32 | 0.234001 | 4 | 32 | 0.249602 | 3 | 22 | 0.187201 |
| 63 | 9000 | 3 | 22 | 0.187201 | 3 | 22 | 0.187201 | 3 | 22 | 0.187201 |
| 64 | 9000 | 5 | 39 | 0.343202 | 23 | 147 | 1.747211 | 3 | 23 | 0.218401 |
| 65 | 9000 | 12 | 59 | 15.334898 | 14 | 51 | 14.944896 | 7 | 21 | 6.130839 |
| 66 | 9000 | 3 | 9 | 1.62241 | 2000 | 4022 | 1114.767546 | 529 | 2196 | 443.526443 |
| 67 | 9000 | 5 | 28 | 0.093601 | 15 | 58 | 0.280802 | 3 | 23 | 0.0312 |
| 68 | 9000 | 13 | 55 | 0.109201 | 11 | 27 | 0.0624 | 9 | 25 | 0.0624 |
| 69 | 9000 | 16 | 73 | 0.218401 | 24 | 55 | 0.187201 | 20 | 70 | 0.171601 |
| 70 | 9000 | 4 | 13 | 2.542816 | 41 | 203 | 36.332633 | 35 | 231 | 37.783442 |
| 71 | 9000 | 11 | 35 | 0.093601 | 2000 | 4014 | 6.708043 | 1491 | 4631 | 5.600436 |
| 72 | 9000 | 9 | 30 | 21.85574 | 1089 | 3897 | 2675.588751 | 287 | 1015 | 704.391315 |
| 73 | 9000 | 19 | 65 | 0.093601 | 607 | 1269 | 1.856412 | 669 | 2062 | 2.293215 |