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 | 462154595.8 | 0.125 | 462,252,526 | 0.168 | 462647776.5 | 0.203 |
P2 | 463922755.7 | 0.125 | 464,021,386 | 0.172 | 464424535.6 | 0.219 |
P3 | 454902314.7 | 0.094 | 454,995,979 | 0.130 | 455391806.2 | 0.234 |
P4 | 462729689.5 | 0.11 | 462,824,549 | 0.156 | 463237509.7 | 0.203 |
P5 | 463264246.2 | 0.109 | 463,357,548 | 0.159 | 463756427.2 | 0.203 |
P6 | 459871109.2 | 0.109 | 459,967,544 | 0.149 | 460359595.1 | 0.203 |
P7 | 463005259.3 | 0.109 | 463,102,583 | 0.150 | 463499775.1 | 0.203 |
P8 | 461,750,540 | 0.11 | 461,846,630 | 0.154 | 462250609.3 | 0.203 |
P9 | 462513368.3 | 0.109 | 462,607,027 | 0.142 | 463008757.8 | 0.203 |
P10 | 464652116.8 | 0.109 | 464,746,116 | 0.157 | 465,123,264 | 0.203 |
P11 | 465,808,805 | 0.125 | 465,907,370 | 0.174 | 466,306,867 | 0.25 |
P12 | 466659753.5 | 0.14 | 466,754,205 | 0.181 | 467165643.8 | 0.25 |
P13 | 465859563.6 | 0.141 | 465,953,947 | 0.177 | 466,367,333 | 0.234 |
P14 | 460683422.9 | 0.125 | 460,784,405 | 0.158 | 461175212.4 | 0.234 |
P15 | 459791614.3 | 0.125 | 459,888,906 | 0.174 | 460282546.8 | 0.188 |
P16 | 460724495.9 | 0.109 | 460,819,912 | 0.155 | 461231699.5 | 0.172 |
P17 | 461385093.5 | 0.125 | 461,480,185 | 0.158 | 461887513.4 | 0.203 |
P18 | 463032455.3 | 0.125 | 463,126,358 | 0.173 | 463528485.4 | 0.188 |
P19 | 461040271.5 | 0.109 | 461,141,147 | 0.152 | 461544498.2 | 0.25 |
P20 | 461,943,881 | 0.093 | 462,038,256 | 0.134 | 462455999.9 | 0.187 |
P21 | 461975515.3 | 0.11 | 462,077,104 | 0.139 | 462458306.3 | 0.188 |
P22 | 459544615.7 | 0.109 | 459,645,210 | 0.152 | 460,037,834 | 0.187 |
P23 | 461886169.8 | 0.11 | 461,983,905 | 0.146 | 462402129.2 | 0.203 |
P24 | 459427161.6 | 0.109 | 459,522,677 | 0.147 | 459,901,863 | 0.188 |
P25 | 465536812.4 | 0.125 | 465,631,596 | 0.161 | 466,037,225 | 0.234 |
P26 | 461721331.5 | 0.125 | 461,819,032 | 0.173 | 462220540.5 | 0.25 |
P27 | 460304848.7 | 0.11 | 460,396,956 | 0.148 | 460808541.2 | 0.234 |
P28 | 458865037.7 | 0.125 | 458,963,051 | 0.167 | 459365142.4 | 0.218 |
P29 | 461224194.5 | 0.109 | 461,321,005 | 0.153 | 461736086.6 | 0.203 |
P30 | 462191950.1 | 0.109 | 462,287,670 | 0.149 | 462677404.9 | 0.219 |