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

Toni Sorrell | 2046 | 18944 | 9.77517e-04 | easy | independentset | -350 | sorrell8.mps.gz |

These instances are based on Neil Sloane’s Challenge problems: Independent Sets in Graphs. Solved in 3489s on 8 cores using Gurobi 9.0. Disclaimer: On https://oeis.org/A265032/a265032.html the optimal solution for sorell8 is reported as -352 because the original instance apparently contains two isolated vertices that were removed when creating the instance. Solved in 3489s on 8 cores using Gurobi 9.0

Detailed explanation of the following tables can be found here.

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

Variables | 2046 | 2046 |

Constraints | 18944 | 18944 |

Binaries | 2046 | 2046 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000977517 | 0.000977517 |

Nonzeroes | 37888 | 37888 |

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

Total | 18944 | 18944 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 18944 | 18944 |

Set Partitioning | 0 | 0 |

Set Packing | 0 | 0 |

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 | 1.041393 | ||||

Constraint % | 0.100296 | 10 | 6.27111 | 25.9396 | |

Variable % | 0.537634 | 10 | 8.06452 | 22.5806 | |

Score | 0.819115 |

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 |
---|---|---|---|---|---|---|---|---|

2 | -350 | 0 | 0 | 0 | Edward Rothberg | 2019-12-18 | Optimal solution found with Gurobi 9.0 in 3489s on 8 cores | |

1 | -350 | -350 | 0 | 0 | 0 | - | 2018-10-11 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to sorrell8 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

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

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

z26 | open | 17937 | 17937 | 0 | 0 | 850513 | 1715613 | Daniel Bienstock | – | -1195.0* | binary variable_bound set_packing |

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

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

`No bibliographic information available`

Last Update 2024 by Julian Manns

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