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 | 464761657.8 | 0.172 | 464,856,004 | 0.193 | 465252234.1 | 0.203 |
P2 | 465982540.6 | 0.141 | 466,077,974 | 0.160 | 466,479,602 | 0.203 |
P3 | 463307328.6 | 0.141 | 463,406,152 | 0.153 | 463794110.6 | 0.203 |
P4 | 463827848.1 | 0.14 | 463,921,356 | 0.159 | 464328797.5 | 0.187 |
P5 | 462125994.6 | 0.141 | 462,227,246 | 0.156 | 462614855.4 | 0.203 |
P6 | 464303782.3 | 0.141 | 464,405,186 | 0.158 | 464812299.2 | 0.203 |
P7 | 466278050.8 | 0.140 | 466,375,689 | 0.158 | 466787603.6 | 0.203 |
P8 | 463635528.2 | 0.141 | 463,730,203 | 0.152 | 464,121,359 | 0.187 |
P9 | 463313848.7 | 0.141 | 463,413,322 | 0.156 | 463809058.1 | 0.187 |
P10 | 464,843,759 | 0.109 | 464,937,239 | 0.120 | 465335659.3 | 0.187 |
P11 | 464899247.3 | 0.110 | 464,993,389 | 0.119 | 465404355.6 | 0.203 |
P12 | 463364638.6 | 0.109 | 463,457,636 | 0.122 | 463851905.1 | 0.203 |
P13 | 464718283.4 | 0.125 | 464,815,642 | 0.135 | 465205666.3 | 0.203 |
P14 | 461971206.5 | 0.125 | 462,068,220 | 0.142 | 462461413.5 | 0.203 |
P15 | 466460412.4 | 0.109 | 466,557,763 | 0.124 | 466968490.2 | 0.187 |
P16 | 466,121,646 | 0.125 | 466,215,197 | 0.140 | 466623984.1 | 0.203 |
P17 | 466,613,596 | 0.109 | 466,708,832 | 0.118 | 467117668.5 | 0.187 |
P18 | 457,455,118 | 0.125 | 457,547,981 | 0.141 | 457,942,972 | 0.203 |
P19 | 465677481.6 | 0.125 | 465,778,580 | 0.141 | 466196407.9 | 0.203 |
P20 | 464276924.6 | 0.125 | 464,370,012 | 0.142 | 464,767,951 | 0.203 |
P21 | 462941205.5 | 0.125 | 463,035,738 | 0.140 | 463438858.3 | 0.203 |
P22 | 461101747.4 | 0.125 | 461,195,628 | 0.136 | 461599000.9 | 0.203 |
P23 | 465161010.4 | 0.125 | 465,258,415 | 0.135 | 465650542.7 | 0.203 |
P24 | 461900311.9 | 0.125 | 461,998,743 | 0.135 | 462396333.7 | 0.203 |
P25 | 463755031.4 | 0.125 | 463,856,362 | 0.141 | 464258661.5 | 0.203 |
P26 | 459684460.9 | 0.125 | 459,780,121 | 0.134 | 460163496.2 | 0.235 |
P27 | 466716094.5 | 0.110 | 466,811,865 | 0.125 | 467213751.9 | 0.219 |
P28 | 465410474.9 | 0.109 | 465,503,929 | 0.123 | 465913015.5 | 0.203 |
P29 | 465,546,559 | 0.125 | 465,645,488 | 0.141 | 466045992.9 | 0.219 |
P30 | 459281474.2 | 0.141 | 459,377,556 | 0.156 | 459785502.4 | 0.203 |