Problem instance number | Weak bound (relaxed formulation I) | Hybrid formulation bound (relaxed weak formulation with most promising strong linking constraints added) | Strong bound (relaxed formulation II) | |||
Value | CPU time | Value | CPU time | Value | CPU time | |
P1 | 1,347,812,101 | 0.984 | 1,348,043,655 | 1.099 | 1,348,824,104 | 1.437 |
P2 | 1,353,943,093 | 0.875 | 1,354,165,275 | 1.037 | 1,354,916,518 | 1.5 |
P3 | 1,353,589,922 | 0.797 | 1,353,818,814 | 0.918 | 1,354,572,437 | 1.406 |
P4 | 1,348,651,591 | 0.875 | 1,348,874,253 | 0.988 | 1,349,651,010 | 1.438 |
P5 | 1,353,236,978 | 0.859 | 1,353,454,443 | 0.970 | 1,354,223,675 | 1.422 |
P6 | 1,345,291,759 | 0.859 | 1,345,512,522 | 0.954 | 1,346,286,225 | 1.5 |
P7 | 1,354,089,798 | 0.875 | 1,354,306,453 | 0.976 | 1,355,101,717 | 1.578 |
P8 | 1,350,526,131 | 0.89 | 1,350,746,131 | 1.032 | 1,351,547,781 | 1.562 |
P9 | 1,347,779,924 | 0.844 | 1,348,003,925 | 0.939 | 1,348,783,579 | 1.563 |
P10 | 1,352,052,432 | 0.968 | 1,352,282,416 | 1.141 | 1,353,075,218 | 1.547 |
P11 | 1,348,474,977 | 0.875 | 1,348,704,892 | 0.998 | 1,349,452,863 | 1.531 |
P12 | 1,358,050,071 | 0.859 | 1,358,285,014 | 1.010 | 1,358,999,314 | 1.61 |
P13 | 1,360,492,873 | 0.875 | 1,360,727,422 | 0.989 | 1,361,471,188 | 1.563 |
P14 | 1,347,055,192 | 0.86 | 1,347,287,155 | 0.949 | 1,348,053,275 | 1.578 |
P15 | 1,346,813,104 | 0.86 | 1,347,032,769 | 0.957 | 1,347,825,533 | 1.409 |
P16 | 1,351,598,681 | 0.859 | 1,351,818,451 | 0.990 | 1,352,597,768 | 1.556 |
P17 | 1,352,634,141 | 0.844 | 1,352,873,693 | 0.938 | 1,353,614,996 | 1.438 |
P18 | 1,347,143,013 | 0.828 | 1,347,368,659 | 0.928 | 1,348,101,467 | 1.422 |
P19 | 1,347,578,203 | 0.844 | 1,347,811,739 | 0.996 | 1,348,549,057 | 1.375 |
P20 | 1,354,172,979 | 0.86 | 1,354,405,219 | 1.024 | 1,355,188,299 | 1.407 |
P21 | 1,353,131,970 | 0.844 | 1,353,350,636 | 0.974 | 1,354,106,286 | 1.407 |
P22 | 1,352,195,677 | 0.875 | 1,352,423,658 | 1.000 | 1,353,198,611 | 1.437 |
P23 | 1,354,067,995 | 0.875 | 1,354,309,967 | 1.036 | 1,355,054,115 | 1.532 |
P24 | 1,348,354,628 | 0.828 | 1,348,587,758 | 0.950 | 1,349,338,895 | 1.478 |
P25 | 1,348,863,378 | 0.86 | 1,349,093,359 | 1.030 | 1,349,868,041 | 1.578 |
P26 | 1,350,507,863 | 0.984 | 1,350,725,025 | 1.156 | 1,351,509,090 | 1.516 |
P27 | 1,351,696,314 | 1 | 1,351,938,538 | 1.191 | 1,352,686,083 | 1.453 |
P28 | 1,348,216,115 | 1 | 1,348,458,524 | 1.139 | 1,349,190,279 | 1.469 |
P29 | 1,349,155,465 | 0.969 | 1,349,378,346 | 1.123 | 1,350,167,144 | 1.406 |
P30 | 1,355,404,108 | 0.968 | 1,355,636,560 | 1.078 | 1,356,383,297 | 1.422 |