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

Balabhaskar Balasundaram | 200 | 17013 | 3.08032e-02 | hard | – | -70 | 2club200v15p5scn.mps.gz |

Maximum 2-club instance; graph; clique relaxations Solved with Gurobi 8.1 on 24 cores in approx. 23 hours.

Detailed explanation of the following tables can be found here.

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

Variables | 200 | 200 |

Constraints | 17013 | 17013 |

Binaries | 200 | 200 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.0308032 | 0.0308032 |

Nonzeroes | 104811 | 104811 |

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

Total | 17013 | 17013 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 246 | 246 |

Set Partitioning | 0 | 0 |

Set Packing | 0 | 0 |

Set Covering | 0 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 16767 | 16767 |

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 | 0.4771212 | ||||

Constraint % | 0.00588 | 0.722977 | 0.722977 | 1.44008 | |

Variable % | 1.00000 | 39.000000 | 39.000000 | 77.00000 | |

Score | 0.0033700 |

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 | -70 | -70 | 0 | 0 | 0 | Joshua Friedman | 2018-11-30 | Found using Gurobi 8.1 on 24 cores after 23 hours. |

1 | -69 | -69 | 0 | 0 | 0 | - | 2018-10-13 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to 2club200v15p5scn 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

genus-sym-grafo5708-48 | open | 3379 | 3377 | 1 | 1 | 20538 | 72579 | Stephan Beyer | genus | -21* | precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear |

genus-g61-25 | open | 14380 | 14378 | 1 | 1 | 94735 | 332877 | Stephan Beyer | genus | -40.0* | numerics set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear |

genus-sym-g62-2 | open | 12912 | 12910 | 1 | 1 | 78472 | 275855 | Stephan Beyer | genus | -38.0* | precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear |

supportcase21i | easy | 27 | 24 | 3 | 0 | 7540 | 95325 | Michael Winkler | – | 20 | indicator numerics set_covering invariant_knapsack general_linear |

supportcase2 | open | 2912 | 2912 | 0 | 0 | 597385 | 7653928 | Michael Winkler | – | 65* | binary aggregations set_covering invariant_knapsack binpacking |

```
@article{BBFMIVH2club2016,
Author = {F. Mahdavi Pajouh and B. Balasundaram and I. V. Hicks},
Journal = {Operations Research},
Month = {November-December},
Number = {6},
Pages = {1466--1481},
Title = {On the 2-club polytope of graphs},
Volume = {64},
Year = {2016}}
```

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