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

A. Caprara, M. Fischetti, P. Toth | 15293 | 2539 | 4.57749e-03 | easy | core | 689 | core2536-691.mps.gz |

Set covering instance coming from Italian railway models Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

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

Variables | 15293 | 15278 |

Constraints | 2539 | 2505 |

Binaries | 15284 | 15278 |

Integers | 0 | 0 |

Continuous | 9 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.00457749 | 0.00417727 |

Nonzeroes | 177739 | 159870 |

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

Total | 2539 | 2505 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 5 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 4 | 1 |

Set Partitioning | 0 | 0 |

Set Packing | 0 | 0 |

Set Covering | 2527 | 2503 |

Cardinality | 0 | 0 |

Invariant Knapsack | 1 | 1 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 2 | 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 | 0.301030 | ||||

Constraint % | 0.0399202 | 0.0399202 | 0.0399202 | 0.0399202 | |

Variable % | 0.0130864 | 0.0130864 | 0.0130864 | 0.0130864 | |

Score | 0.000399 |

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 | 689 | 689 | 0 | 0 | 0 | - | 2018-10-29 | Solution found during MIPLIB2017 problem selection. |

1 | 689 | 689 | 0 | 0 | 0 | - | 2018-10-13 | Solution imported from MIPLIB2010. |

The following instances are most similar to core2536-691 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

core4284-1064 | open | 21714 | 21705 | 0 | 9 | 4287 | 245121 | A. Caprara, M. Fischetti, P. Toth | core | 1062.0* | binary variable_bound set_covering invariant_knapsack |

core4872-1529 | open | 24656 | 24645 | 0 | 11 | 4875 | 218762 | A. Caprara, M. Fischetti, P. Toth | core | 1530.0* | binary variable_bound set_covering invariant_knapsack |

core2586-950 | open | 13226 | 13215 | 0 | 11 | 2589 | 104678 | A. Caprara, M. Fischetti, P. Toth | core | 944.0* | binary variable_bound set_covering invariant_knapsack |

rail507 | easy | 63019 | 63009 | 0 | 10 | 509 | 468878 | A. Caprara, M. Fischetti, P. Toth | – | 174 | benchmark binary benchmark_suitable variable_bound set_covering invariant_knapsack |

fast0507 | easy | 63009 | 63009 | 0 | 0 | 507 | 409349 | MIPLIB submission pool | – | 174 | benchmark binary benchmark_suitable variable_bound set_covering |

```
@article{CapraraFischettiToth1999,
author = {A. Caprara and M. Fischetti and P. Toth},
instance = {core4872-1529},
journal = {Operations Research},
language = {English},
pages = {730--743},
title = {A heuristic method for the set covering problem},
volume = {47},
year = {1999}
}
```

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