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 | 465681644.6 | 0.109 | 465,779,158 | 0.125 | 466164697.7 | 0.188 |
P2 | 457544301.9 | 0.109 | 457,638,693 | 0.128 | 458054151.7 | 0.203 |
P3 | 459974575.7 | 0.093 | 460,067,583 | 0.106 | 460478771.5 | 0.188 |
P4 | 458538365.5 | 0.094 | 458,633,100 | 0.116 | 459024202.6 | 0.187 |
P5 | 460692904.2 | 0.094 | 460,793,612 | 0.111 | 461176844.4 | 0.203 |
P6 | 459,533,942 | 0.094 | 459,626,170 | 0.124 | 460005875.9 | 0.203 |
P7 | 460283567.4 | 0.109 | 460,376,361 | 0.141 | 460778713.3 | 0.187 |
P8 | 461,788,231 | 0.109 | 461,882,251 | 0.131 | 462277760.5 | 0.188 |
P9 | 456723909.6 | 0.125 | 456,816,899 | 0.150 | 457209892.4 | 0.172 |
P10 | 459648712.5 | 0.125 | 459,744,963 | 0.158 | 460163566.7 | 0.172 |
P11 | 456480416.3 | 0.11 | 456,579,336 | 0.127 | 456977922.9 | 0.188 |
P12 | 465421105.4 | 0.109 | 465,520,659 | 0.127 | 465917396.2 | 0.172 |
P13 | 463411618.9 | 0.109 | 463,506,016 | 0.138 | 463903987.7 | 0.188 |
P14 | 462087761.9 | 0.125 | 462,188,543 | 0.160 | 462585844.7 | 0.172 |
P15 | 464393272.7 | 0.109 | 464,494,557 | 0.135 | 464873431.8 | 0.187 |
P16 | 459898122.6 | 0.125 | 459,995,391 | 0.147 | 460381579.4 | 0.172 |
P17 | 460720255.7 | 0.109 | 460,814,657 | 0.145 | 461222610.1 | 0.187 |
P18 | 460516332.1 | 0.125 | 460,613,547 | 0.153 | 461019806.6 | 0.188 |
P19 | 460753982.8 | 0.109 | 460,850,649 | 0.131 | 461254252.7 | 0.187 |
P20 | 459873402.2 | 0.109 | 459,966,067 | 0.144 | 460379360.6 | 0.172 |
P21 | 461661335.6 | 0.125 | 461,757,407 | 0.149 | 462144676.9 | 0.218 |
P22 | 464025496.2 | 0.109 | 464,123,545 | 0.124 | 464,520,012 | 0.172 |
P23 | 456996616.6 | 0.141 | 457,093,226 | 0.184 | 457461190.2 | 0.172 |
P24 | 463178689.2 | 0.125 | 463,280,311 | 0.156 | 463674506.7 | 0.172 |
P25 | 460206278.2 | 0.11 | 460,301,633 | 0.147 | 460708601.5 | 0.188 |
P26 | 462363155.8 | 0.11 | 462,459,743 | 0.130 | 462850313.3 | 0.172 |
P27 | 464172352.1 | 0.11 | 464,268,389 | 0.137 | 464682393.6 | 0.203 |
P28 | 457850163.7 | 0.11 | 457,942,192 | 0.135 | 458357345.2 | 0.188 |
P29 | 462003319.6 | 0.125 | 462,098,030 | 0.148 | 462497026.1 | 0.172 |
P30 | 460635912.7 | 0.11 | 460,733,936 | 0.133 | 461120649.7 | 0.187 |