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

Hsiang-Yun WU | 4537 | 7719 | 7.69764e-04 | open | – | 8263.099999999999* | tokyometro.mps.gz |

The layout model for Tokyo Metro Map

Detailed explanation of the following tables can be found here.

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

Variables | 4537 | 4157 |

Constraints | 7719 | 7367 |

Binaries | 2496 | 2148 |

Integers | 2041 | 2009 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 593 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000769764 | 0.000822051 |

Nonzeroes | 26958 | 25175 |

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

Total | 7719 | 7367 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 28 | 0 |

Aggregations | 150 | 289 |

Precedence | 0 | 171 |

Variable Bound | 622 | 488 |

Set Partitioning | 386 | 265 |

Set Packing | 0 | 0 |

Set Covering | 0 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 0 | 0 |

Equation Knapsack | 0 | 3 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 0 | 2 |

General Linear | 6533 | 6149 |

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 | 2.733197 | ||||

Constraint % | 0.0135740 | 0.0393647 | 0.0135740 | 0.814443 | |

Variable % | 0.0467181 | 0.0997950 | 0.0934361 | 0.607335 | |

Score | 0.212130 |

Find solutions below. Download the archive containing all solutions from the Download page.

`## Warning in lapply(df["exactobjval"], as.numeric): NAs introduced by coercion`

ID | Objective | Exact | Int. Viol | Cons. Viol | Obj. Viol | Submitter | Date | Description |
---|---|---|---|---|---|---|---|---|

4 | 8263.1 | 8263.1 | 0 | 0 | 0 | Edward Rothberg | 2022-07-12 | Obtained with Gurobi 9.5 using the NoRel heuristic. |

3 | 8329.4 | 0 | 0 | 0 | Edward Rothberg | 2019-12-13 | Obtained with Gurobi 9.0 | |

2 | 8467.6 | 0 | 0 | 0 | Robert Ashford and Alkis Vazacopoulus | 2019-12-18 | Found using ODH|CPlex | |

1 | 8471.9 | 8471.9 | 0 | 0 | 0 | - | 2018-10-10 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to tokyometro 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.

```
@Misc{TokyoMetro:17,
author = {H.-Y. Wu and S. Takahashi},
title = {A MIP Dataset for the Layout of Tokyo Metro},
Year = {2017}
}
@phdthesis{phdwu:13,
author = {H.-Y. Wu},
title = {Constrained Optimization Approaches to Customizing Layout and Annotation for Metro Maps},
school = {The University of Tokyo},
year = {2013},
month = {March},
address = {Chiba, Japan},
}
```

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