Submitter | Variables | Constraints | Density | Status | Group | Objective | MPS File |
---|---|---|---|---|---|---|---|

Daniel Bienstock | 17937 | 850513 | 1.12458e-04 | open | – | -1195.0* | z26.mps.gz |

Set packing problem arising from the ongoing “Frequency Spectrum Auction” in the U.S. Work is collaboration with Ion Media Networks, Inc.

Detailed explanation of the following tables can be found here.

Original | Presolved | |
---|---|---|

Variables | 17937 | 17936 |

Constraints | 850513 | 850473 |

Binaries | 17937 | 17936 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000112458 | 0.000112467 |

Nonzeroes | 1715610 | 1715590 |

Original | Presolved | |
---|---|---|

Total | 850513 | 850473 |

Empty | 14 | 0 |

Free | 0 | 0 |

Singleton | 26 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 848857 | 848857 |

Set Partitioning | 0 | 0 |

Set Packing | 1616 | 1616 |

Set Covering | 0 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 0 | 0 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 0 | 0 |

General Linear | 0 | 0 |

Indicator | 0 | 0 |

Available nonzero structure and decomposition information. Further information can be found here.

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving (dec-file)

value | min | median | mean | max | |
---|---|---|---|---|---|

Components | 1.973128 | ||||

Constraint % | 0.0002350 | 1.07323 | 0.0007050 | 88.1868 | |

Variable % | 0.0111501 | 1.06442 | 0.0167252 | 77.6830 | |

Score | 0.308955 |

Find solutions below. Download the archive containing all solutions from the Download page.

`## Warning in lapply(df["exactobjval"], as.numeric): NAs introduced by coercion`

ID | Objective | Exact | Int. Viol | Cons. Viol | Obj. Viol | Submitter | Date | Description |
---|---|---|---|---|---|---|---|---|

7 | -1195 | -1195 | 0 | 0 | 0 | Mars Davletshin | 2023-11-23 | It was obtained with Huawei OptVerse solver using neural heuristic and a neighborhood search. |

6 | -1194 | -1194 | 0 | 0 | 0 | Ed Rothberg | 2023-05-19 | Found with the NoRel heuristic. |

5 | -1192 | -1192 | 0 | 0 | 0 | Edward Rothberg | 2020-09-14 | Found with Gurobi |

4 | -1187 | -1187 | 0 | 0 | 0 | Edward Rothberg | 2020-05-15 | Obtained with Gurobi 9.0 using the solution improvement heuristic |

3 | -1186 | 0 | 0 | 0 | Edward Rothberg | 2019-12-13 | Obtained with Gurobi 9.0 | |

2 | -1184 | 0 | 0 | 0 | Robert Ashford and Alkis Vazacopoulus | 2019-12-18 | Found using ODH|CPlex | |

1 | -1101 | -1101 | 0 | 0 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to z26 in the collection. This similarity analysis is based on 100 scaled instance features describing properties of the variables, objective function, bounds, constraints, and right hand sides.

Instance | Status | Variables | Binaries | Integers | Continuous | Constraints | Nonz. | Submitter | Group | Objective | Tags |
---|---|---|---|---|---|---|---|---|---|---|---|

sorrell4 | hard | 2048 | 2048 | 0 | 0 | 504451 | 1008902 | Toni Sorrell | independentset | -24 | binary variable_bound |

sorrell3 | easy | 1024 | 1024 | 0 | 0 | 169162 | 338324 | Toni Sorrell | independentset | -16 | benchmark binary benchmark_suitable variable_bound |

sorrell7 | open | 2048 | 2048 | 0 | 0 | 78848 | 157696 | Toni Sorrell | independentset | -198.0* | binary variable_bound |

sorrell8 | easy | 2046 | 2046 | 0 | 0 | 18944 | 37888 | Toni Sorrell | independentset | -350 | binary decomposition variable_bound |

manna81 | easy | 3321 | 18 | 3303 | 0 | 6480 | 12960 | MIPLIB submission pool | – | -13164 | variable_bound |

`No bibliographic information available`

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