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

Toni Sorrell | 2048 | 504451 | 9.76562e-04 | hard | independentset | -24 | sorrell4.mps.gz |

These instances are based on Neil Sloane’s Challenge problems: Independent Sets in Graphs.

Detailed explanation of the following tables can be found here.

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

Variables | 2048 | 2048 |

Constraints | 504451 | 504451 |

Binaries | 2048 | 2048 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000976562 | 0.000976562 |

Nonzeroes | 1008900 | 1008900 |

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

Total | 504451 | 504451 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 504451 | 504451 |

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 | 0.30103 | ||||

Constraint % | 100 | 100 | 100 | 100 | |

Variable % | 100 | 100 | 100 | 100 | |

Score | 0.00000 |

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

3 | -24 | -24 | 0 | 0 | 0 | Jan Krüger | 2023-08-20 | Solution as found on https://oeis.org/A265032/a265032.html, reported optimal by Pablo San Segundo |

2 | -24 | 0 | 0 | 0 | Edward Rothberg | 2019-12-13 | Obtained with Gurobi 9.0 | |

1 | -23 | -23 | 0 | 0 | 0 | - | 2018-10-11 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to sorrell4 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

sorrell3 | hard | 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 | – | -1194.0* | binary variable_bound set_packing |

sorrell7 | open | 2048 | 2048 | 0 | 0 | 78848 | 157696 | Toni Sorrell | independentset | -197.0* | 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`

Last Update Mar 04, 2024 by Julian Manns

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