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

P. Belotti | 14115 | 14021 | 4.06172e-04 | easy | – | 214 | net12.mps.gz |

Network design instance Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

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

Variables | 14115 | 14115 |

Constraints | 14021 | 14021 |

Binaries | 1603 | 1603 |

Integers | 0 | 0 |

Continuous | 12512 | 12512 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000406172 | 0.000406172 |

Nonzeroes | 80384 | 80384 |

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

Total | 14021 | 14021 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 10 | 10 |

Variable Bound | 0 | 0 |

Set Partitioning | 10 | 0 |

Set Packing | 391 | 391 |

Set Covering | 2 | 0 |

Cardinality | 542 | 552 |

Invariant Knapsack | 0 | 12 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 13066 | 13056 |

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 | 1.397940 | ||||

Constraint % | 0.156907 | 4.00500 | 4.17231 | 4.17231 | |

Variable % | 0.276302 | 4.16667 | 4.33581 | 4.33581 | |

Score | 0.919589 |

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 | 214 | 214 | 0 | 0 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

1 | 214 | 214 | 0 | 0 | 0 | - | 2018-10-12 | Solution imported from MIPLIB2010. |

The following instances are most similar to net12 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

istanbul-no-cutoff | easy | 5282 | 30 | 0 | 5252 | 20346 | 71477 | Utz-Uwe Haus | – | 204.08170701 | benchmark benchmark_suitable aggregations variable_bound knapsack mixed_binary |

neos-691058 | easy | 3006 | 1755 | 0 | 1251 | 2667 | 30837 | NEOS Server Submission | neos-pseudoapplication-110 | 296.999999999986 | benchmark_suitable set_partitioning cardinality mixed_binary |

snip10x10-35r1budget17 | hard | 47611 | 63 | 0 | 47548 | 213801 | 475334 | Utz-Uwe Haus | – | 72.30862035707088 | aggregations variable_bound invariant_knapsack mixed_binary |

loopha13 | easy | 19356 | 18150 | 0 | 1206 | 23758 | 41809 | Hamideh | – | 6.40233 | benchmark_suitable aggregations precedence variable_bound invariant_knapsack mixed_binary |

neos-4477313-unzha | easy | 2193 | 2016 | 0 | 177 | 4174 | 30400 | Jeff Linderoth | neos-pseudoapplication-110 | Unbounded | numerics set_partitioning mixed_binary |

```
@inproceedings{BelottiMalucelli2003,
author = {P. Belotti and F. Malucelli},
booktitle = {Proceedings of the 2003 International Network Optimization
Conference},
instance = {net12},
language = {English},
pages = {72--77},
title = {A {L}agrangian relaxation approach for the design of networks
with shared protection},
year = {2003}
}
@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}
}
```

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