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

A. Caprara, M. Fischetti, P. Toth | 63019 | 509 | 1.46174e-02 | easy | – | 174 | rail507.mps.gz |

Railway crew scheduling Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

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

Variables | 63019 | 63001 |

Constraints | 509 | 490 |

Binaries | 63009 | 63001 |

Integers | 0 | 0 |

Continuous | 10 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.0146174 | 0.0151319 |

Nonzeroes | 468878 | 467130 |

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

Total | 509 | 490 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 8 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 3 | 1 |

Set Partitioning | 0 | 0 |

Set Packing | 0 | 0 |

Set Covering | 496 | 488 |

Cardinality | 0 | 0 |

Invariant Knapsack | 1 | 1 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 1 | 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 % | 0.204082 | 0.204082 | 0.204082 | 0.204082 | |

Variable % | 0.003170 | 0.003170 | 0.003170 | 0.003170 | |

Score | 0.002041 |

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 | 174 | 174 | 0 | 0 | 0 | - | 2018-10-29 | Solution found during MIPLIB2017 problem selection. |

1 | 174 | 174 | 0 | 0 | 0 | - | 2018-10-12 | Solution imported from MIPLIB2010. |

The following instances are most similar to rail507 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

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 |

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 |

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 | 946* | binary 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}
}
@article{FischettiLodi2003,
author = {Fischetti, Matteo and Lodi, Andrea},
issn = {0025-5610},
issue = {1},
journal = {Mathematical Programming},
keyword = {Mathematics and Statistics},
pages = {23-47},
publisher = {Springer},
title = {Local branching},
volume = {98},
year = {2003}
}
```

Last Update Mar 04, 2024 by Julian Manns

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