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

Ashutosh Mahajan | 900 | 960 | 1.08148e-01 | hard | – | -40 | queens-30.mps.gz |

Models the problem of placing as many queens on a 30 by 30 chess board as possible so that each queen threatens at most one other queen. Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

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

Variables | 900 | 900 |

Constraints | 960 | 960 |

Binaries | 900 | 900 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.108148 | 0.108148 |

Nonzeroes | 93440 | 93440 |

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

Total | 960 | 960 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 0 | 0 |

Set Partitioning | 0 | 0 |

Set Packing | 0 | 0 |

Set Covering | 0 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 0 | 0 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 960 | 960 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 0 | 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 | 0.30103 | ||||

Constraint % | 57.5 | 57.5 | 57.5 | 57.5 | |

Variable % | 100.0 | 100.0 | 100.0 | 100.0 | |

Score | 0.00000 |

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 | -39 | -39 | 0 | 0 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to queens-30 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

pb-market-split8-70-4 | hard | 71 | 71 | 0 | 0 | 17 | 1113 | Gleb Belov | pb- | 0.0 | binary feasibility knapsack mixed_binary |

d20200 | open | 4000 | 4000 | 0 | 0 | 1502 | 189389 | COR@L test set | – | 12239.0* | binary decomposition set_partitioning invariant_knapsack knapsack |

neos-876808 | easy | 87268 | 87268 | 0 | 0 | 85808 | 682376 | NEOS Server Submission | neos-pseudoapplication-62 | 169795.259907 | binary decomposition benchmark_suitable aggregations set_packing set_covering invariant_knapsack knapsack mixed_binary |

neos-4954274-beardy | hard | 12865 | 12865 | 0 | 0 | 17359 | 140082 | Jeff Linderoth | neos-pseudoapplication-62 | 20946.48 | binary decomposition variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack binpacking knapsack |

circ10-3 | open | 2700 | 2700 | 0 | 0 | 42620 | 307320 | M. Winkler | – | 280* | binary decomposition precedence variable_bound set_partitioning set_packing invariant_knapsack knapsack mixed_binary |

```
@misc{queenschallenge,
key = {zzz queens},
note = {http://domino.research.ibm.com/comm/wwwr_ponder.nsf/challenges/August2008.html},
title = {{IBM} {P}onder {T}his -- {A}ugust 2008},
year = {2008}
}
```

Last Update 2024 by Julian Manns

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