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

Toni Sorrell | 2048 | 78848 | 9.76562e-04 | open | independentset | -196.0* | sorrell7.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 | 78848 | 78848 |

Binaries | 2048 | 2048 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000976562 | 0.000976562 |

Nonzeroes | 157696 | 157696 |

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

Total | 78848 | 78848 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 78848 | 78848 |

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.

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

2 | 5 | -196 | -196 | 0 | 0 | 0 | Edward Rothberg | 2020-04-22 | Obtained with Gurobi 9.0 using the solution improvement heuristic |

4 | 6 | -196 | -196 | 0 | 0 | 0 | Shunsuke Kamiya | 2020-05-17 | Computed with weighting local search with exploiting variable associations (WLS) ([1]) [1] Umetani, Shunji. "Exploiting variable associations to configure efficient local search algorithms in large-scale binary integer programs." European Journal of Operational Research 263.1 (2017): 72-81. |

5 | 4 | -194 | -194 | 0 | 0 | 0 | Frederic Didier | 2020-02-24 | Obtained with Google OR-tools through generating subproblems by fixing part of the current solution and trying to solve them with a sub CP-SAT solver |

1 | 3 | -192 | 0 | 0 | 0 | Edward Rothberg | 2019-12-13 | Obtained with Gurobi 9.0 | |

6 | 2 | -187 | 0 | 0 | 0 | Robert Ashford and Alkis Vazacopoulus | 2019-12-18 | Found using ODH|CPlex | |

3 | 1 | -185 | -185 | 0 | 0 | 0 | - | 2018-10-11 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to sorrell7 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 |

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

sorrell4 | open | 2048 | 2048 | 0 | 0 | 504451 | 1008900 | Toni Sorrell | independentset | -24* | binary variable_bound |

z26 | open | 17937 | 17937 | 0 | 0 | 850513 | 1715610 | Daniel Bienstock | -- | -1187.0* | binary variable_bound set_packing |

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

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Last Update Nov 16, 2020 by Philipp Wellner

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