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 | 460156810.2 | 0.125 | 460,249,210 | 0.157 | 460647316.2 | 0.25 |
P2 | 461928500.6 | 0.109 | 462,025,737 | 0.154 | 462422695.2 | 0.187 |
P3 | 460184521.6 | 0.094 | 460,277,847 | 0.118 | 460670115.5 | 0.188 |
P4 | 458523854.3 | 0.109 | 458,623,812 | 0.154 | 459015839.3 | 0.188 |
P5 | 461210372.4 | 0.109 | 461,310,363 | 0.146 | 461695917.4 | 0.172 |
P6 | 466736925.2 | 0.109 | 466,839,421 | 0.134 | 467227158.5 | 0.188 |
P7 | 465040652.4 | 0.109 | 465,135,474 | 0.160 | 465533649.4 | 0.188 |
P8 | 465,711,634 | 0.11 | 465,806,825 | 0.132 | 466203952.5 | 0.188 |
P9 | 462,663,898 | 0.093 | 462,758,652 | 0.118 | 463143978.5 | 0.171 |
P10 | 461994675.3 | 0.11 | 462,089,430 | 0.155 | 462501565.4 | 0.188 |
P11 | 463137094.7 | 0.11 | 463,237,318 | 0.158 | 463654765.4 | 0.187 |
P12 | 460644100.8 | 0.11 | 460,736,460 | 0.149 | 461147401.4 | 0.187 |
P13 | 459979852.8 | 0.109 | 460,080,404 | 0.144 | 460480501.1 | 0.172 |
P14 | 465645551.9 | 0.125 | 465,743,431 | 0.180 | 466,147,369 | 0.171 |
P15 | 459540857.4 | 0.109 | 459,641,773 | 0.143 | 460034510.6 | 0.172 |
P16 | 457524145.7 | 0.094 | 457,617,435 | 0.116 | 458003132.4 | 0.187 |
P17 | 463560066.4 | 0.094 | 463,658,619 | 0.129 | 464066716.1 | 0.172 |
P18 | 461800417.3 | 0.125 | 461,896,010 | 0.169 | 462290440.1 | 0.187 |
P19 | 461310140.9 | 0.094 | 461,402,864 | 0.132 | 461809878.3 | 0.172 |
P20 | 463826134.1 | 0.109 | 463,921,172 | 0.137 | 464324355.3 | 0.188 |
P21 | 461729092.8 | 0.125 | 461,826,795 | 0.158 | 462207481.3 | 0.172 |
P22 | 459986245.2 | 0.109 | 460,084,636 | 0.148 | 460465903.5 | 0.187 |
P23 | 466476622.5 | 0.094 | 466,576,728 | 0.126 | 466958243.4 | 0.219 |
P24 | 461750643.4 | 0.094 | 461,844,887 | 0.114 | 462241797.1 | 0.172 |
P25 | 461884416.2 | 0.11 | 461,978,687 | 0.149 | 462377121.9 | 0.172 |
P26 | 462809272.1 | 0.11 | 462,905,999 | 0.162 | 463300162.2 | 0.188 |
P27 | 462,954,846 | 0.109 | 463,050,076 | 0.140 | 463446331.4 | 0.172 |
P28 | 462717628.6 | 0.11 | 462,814,105 | 0.157 | 463207321.1 | 0.172 |
P29 | 461110049.8 | 0.109 | 461,211,171 | 0.160 | 461601038.8 | 0.187 |
P30 | 461842013.8 | 0.125 | 461,938,493 | 0.170 | 462355526.8 | 0.187 |