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

Paul Rubin | 20644 | 57346 | 1.44508e-04 | open | -- | 124.999999999967* | stockholm.mps.gz |

Toll booth placement problem

Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

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

Variables | 20644 | 20644 |

Constraints | 57346 | 57346 |

Binaries | 962 | 962 |

Integers | 0 | 0 |

Continuous | 19682 | 19682 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000144508 | 0.000144508 |

Nonzeroes | 171076 | 171076 |

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

Total | 57346 | 57346 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 962 | 962 |

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 | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 56384 | 56384 |

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 % | 98.3225 | 98.3225 | 98.3225 | 98.3225 | |

Variable % | 95.3401 | 95.3401 | 95.3401 | 95.3401 | |

Score | 0.045818 |

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 | 2 | 125 | 0 | 0 | 0 | Robert Ashford and Alkis Vazacopoulus | 2019-12-18 | Found using ODH|CPlex | |

1 | 1 | 126 | 0 | 0 | 0 | 0 | - | 2018-10-11 | Solution found during MIPLIB2017 problem selection. |

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

neos-3754224-navua | open | 150228 | 3574 | 0 | 146654 | 232387 | 652974 | Jeff Linderoth | neos-pseudoapplication-83 | 280713.579943285* | numerics aggregations precedence variable_bound set_partitioning mixed_binary |

eva1aprime5x5opt | open | 1712 | 400 | 0 | 1312 | 11929 | 57162 | Yoshihiro Kanno | evaprime | -17.52487708854096* | aggregations variable_bound set_packing mixed_binary |

neos-619167 | easy | 3452 | 400 | 0 | 3052 | 6800 | 20020 | NEOS Server Submission | neos-pseudoapplication-83 | 1.66489361858996 | decomposition numerics precedence variable_bound mixed_binary |

eva1aprime6x6opt | open | 3514 | 836 | 0 | 2678 | 34872 | 161558 | Yoshihiro Kanno | evaprime | -12.885929039705424* | aggregations variable_bound set_packing mixed_binary |

neos-5018451-chiese | easy | 265713 | 1222 | 244 | 264247 | 170175 | 1249955 | Jeff Linderoth | neos-pseudoapplication-69 | -147988824.81 | numerics aggregations variable_bound mixed_binary general_linear |

```
@article{BaiRubin2009,
author = {Lihui Bai and Paul A. Rubin},
journal = {Operations Research},
number = {6},
pages = {1510--1522},
title = {Combinatorial {B}enders Cuts for the Minimum Tollbooth Problem},
volume = {57},
year = {2009}
}
@inproceedings{BaiStampsHarwoodKollmann2006,
author = {Lihui Bai and Matthew T. Stamps and R. Corban Harwood and
Christopher J. Kollmann},
booktitle = {Proceedings of the 2006 Meeting of the Decision Sciences
Institute},
title = {A Genetic Algorithm for the Minimum Tollbooth Problem},
year = {2006}
}
```

Last Update Mai 20, 2021 by Philipp Wellner

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