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

A. Caprara, M. Fischetti, P. Toth | 24656 | 4875 | 1.82001e-03 | open | core | 1530.0* | core4872-1529.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 | 24656 | 24588 |

Constraints | 4875 | 4696 |

Binaries | 24645 | 24588 |

Integers | 0 | 0 |

Continuous | 11 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.00182001 | 0.00164748 |

Nonzeroes | 218762 | 190227 |

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

Total | 4875 | 4696 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 59 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 64 | 53 |

Set Partitioning | 0 | 0 |

Set Packing | 0 | 0 |

Set Covering | 4749 | 4642 |

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 | 0.602060 | ||||

Constraint % | 0.362010 | 33.3262 | 4.19506 | 95.4216 | |

Variable % | 0.133934 | 33.2643 | 3.54316 | 96.1159 | |

Score | 0.081142 |

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

1 | 3 | 1530 | 1530 | 0 | 0 | 0 | Edward Rothberg | 2020-04-22 | Obtained with Gurobi 9.0 using the solution improvement heuristic |

3 | 2 | 1532 | 0 | 0 | 0 | Edward Rothberg | 2019-12-13 | Obtained with Gurobi 9.0 | |

2 | 1 | 1537 | 1537 | 0 | 0 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to core4872-1529 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 | 1063.0* | binary variable_bound set_covering invariant_knapsack |

core2586-950 | open | 13226 | 13215 | 0 | 11 | 2589 | 104678 | A. Caprara, M. Fischetti, P. Toth | core | 946.0* | binary variable_bound set_covering invariant_knapsack |

core2536-691 | easy | 15293 | 15284 | 0 | 9 | 2539 | 177739 | A. Caprara, M. Fischetti, P. Toth | core | 689 | binary benchmark_suitable 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 |

ex1010-pi | open | 25200 | 25200 | 0 | 0 | 1468 | 102114 | M. Winkler | -- | 235* | binary 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}
}
```

Last Update Nov 16, 2020 by Philipp Wellner

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