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

T. Achterberg | 2728 | 1442 | 1.7243e-03 | easy | aflow | 1168 | aflow40b.mps.gz |

Arborescence flow problem on a graph with 40 nodes and edge density 0.9 Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

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

Variables | 2728 | 2728 |

Constraints | 1442 | 1442 |

Binaries | 1364 | 1364 |

Integers | 0 | 0 |

Continuous | 1364 | 1364 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.0017243 | 0.0017243 |

Nonzeroes | 6783 | 6783 |

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

Total | 1442 | 1442 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 1364 | 1364 |

Set Partitioning | 39 | 39 |

Set Packing | 0 | 0 |

Set Covering | 0 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 0 | 0 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 39 | 39 |

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 | 1.602060 | ||||

Constraint % | 2.14979 | 2.49475 | 2.49653 | 2.70458 | |

Variable % | 2.19941 | 2.56410 | 2.56598 | 2.78592 | |

Score | 0.947936 |

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 | 1168 | 1168 | 0 | 0 | 0 | - | 2018-10-10 | Solution imported from MIPLIB2010. |

1 | 1168 | 1168 | 0 | 0 | 0 | - | 2018-10-10 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to aflow40b 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

aflow30a | easy | 842 | 421 | 0 | 421 | 479 | 2091 | T. Achterberg | aflow | 1158 | decomposition benchmark_suitable variable_bound set_partitioning mixed_binary |

h50x2450 | easy | 4900 | 2450 | 0 | 2450 | 2549 | 12152 | MIPLIB submission pool | fixed-cost-network-flow | 32906.880834 | decomposition benchmark_suitable variable_bound set_partitioning mixed_binary |

n370b | open | 10000 | 5000 | 0 | 5000 | 5150 | 20000 | J. Aronson | n37 | 1220708.0* | decomposition variable_bound mixed_binary |

n3707 | open | 10000 | 5000 | 0 | 5000 | 5150 | 20000 | J. Aronson | n37 | 1186691.0* | decomposition variable_bound mixed_binary |

n3700 | open | 10000 | 5000 | 0 | 5000 | 5150 | 20000 | J. Aronson | n37 | 1218974.9999999998* | decomposition variable_bound mixed_binary |

```
@mastersthesis{Pfender2000,
author = {T. Pfender},
instance = {aflow50},
language = {German},
school = {Technische {Universit\"at} Berlin},
title = {{Arboreszenz-Fl\"usse} in {G}raphen: polyedrische {U}ntersuchungen},
type = {Diploma thesis},
year = {2000}
}
```

Last Update 2024 by Julian Manns

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