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

J. Goessens, S. v. Hoessel, L. Kroon | 14101 | 1761 | 1.17175e-02 | easy | sp9 | 660705645.759 | sp97ar.mps.gz |

Railway line planning instance. Solved with Gurobi 4.5.1 on a 12-core Linux system in 2678.77 sec. Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

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

Variables | 14101 | 14101 |

Constraints | 1761 | 1739 |

Binaries | 14101 | 14101 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.0117175 | 0.0118648 |

Nonzeroes | 290968 | 290945 |

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

Total | 1761 | 1739 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 22 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 52 | 52 |

Set Partitioning | 0 | 0 |

Set Packing | 1140 | 1140 |

Set Covering | 129 | 130 |

Cardinality | 0 | 0 |

Invariant Knapsack | 0 | 0 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 418 | 417 |

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 | 3.075912 | ||||

Constraint % | 0.0575043 | 0.0576010 | 0.0575043 | 0.172513 | |

Variable % | 0.0141834 | 0.0839025 | 0.0921920 | 0.141834 | |

Score | 0.684877 |

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 | 660705646 | 660705646 | 0 | 0 | 1e-07 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to sp97ar 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

sp98ar | easy | 15085 | 15085 | 0 | 0 | 1435 | 426148 | J. Goessens, S. v. Hoessel, L. Kroon | sp9 | 529740623.2 | benchmark binary benchmark_suitable variable_bound set_packing set_covering mixed_binary |

sp98ic | easy | 10894 | 10894 | 0 | 0 | 825 | 316317 | J. Goessens, S. v. Hoessel, L. Kroon | sp9 | 449144758.4 | binary decomposition benchmark_suitable variable_bound set_packing set_covering mixed_binary |

sp97ic | easy | 12497 | 12497 | 0 | 0 | 1033 | 316629 | J. Goessens, S. v. Hoessel, L. Kroon | sp9 | 427684487.6799999 | binary decomposition benchmark_suitable variable_bound set_packing set_covering mixed_binary |

neos-1516309 | easy | 4500 | 4500 | 0 | 0 | 489 | 30400 | NEOS Server Submission | neos-pseudoapplication-26 | 35954 | binary decomposition set_packing set_covering knapsack |

n3div36 | easy | 22120 | 22120 | 0 | 0 | 4484 | 340740 | R. Meirich | nseq | 130800 | benchmark binary decomposition benchmark_suitable set_packing set_covering mixed_binary |

```
@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}
}
@article{GoossensHoeselKroon2004,
author = {J.-W. Goossens and S. van Hoesel and L. G. Kroon},
journal = {Transportation Science},
language = {English},
number = {3},
pages = {379--393},
title = {A Branch-and-Cut Approach for Solving Railway Line-Planning Problems},
volume = {38},
year = {2004}
}
```

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