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

S. Weider | 157591 | 2116 | 6.53589e-03 | hard | ivu | 481.0068 | ivu52.mps.gz |

Set partitioning instance resulting from a column generation algorithm used for duty scheduling in public transportation. Solved in June 2014 using CPLEX 12.6 with 48 threads in about 25 days. Imported from MIPLIB2010.

Detailed explanation of the following tables can be found here.

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

Variables | 157591 | 157591 |

Constraints | 2116 | 2116 |

Binaries | 157591 | 157591 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.00653589 | 0.00653589 |

Nonzeroes | 2179480 | 2179480 |

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

Total | 2116 | 2116 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 0 | 0 |

Variable Bound | 0 | 0 |

Set Partitioning | 2110 | 2110 |

Set Packing | 0 | 0 |

Set Covering | 0 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 1 | 1 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 1 | 3 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 4 | 2 |

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 % | 0.047259 | 0.047259 | 0.047259 | 0.047259 | |

Variable % | 0.324257 | 0.324257 | 0.324257 | 0.324257 | |

Score | 0.000471 |

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 |
---|---|---|---|---|---|---|---|---|

1 | 481.3141 | 2e-07 | 2e-07 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to ivu52 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

square37 | easy | 49320 | 49284 | 36 | 0 | 33150 | 9475672 | Sascha Kurz | square | 14.9999997973 | benchmark_suitable set_partitioning general_linear |

square31 | easy | 28860 | 28830 | 30 | 0 | 19435 | 3937200 | Sascha Kurz | square | 15 | benchmark_suitable set_partitioning general_linear |

square41 | easy | 62234 | 62197 | 37 | 0 | 40160 | 13566426 | Sascha Kurz | square | 15 | benchmark benchmark_suitable set_partitioning general_linear |

rvb-sub | hard | 33765 | 33763 | 0 | 2 | 225 | 984143 | S. Weider | – | 16.08499802 | binary set_partitioning knapsack |

square23 | easy | 11660 | 11638 | 22 | 0 | 7887 | 898813 | Sascha Kurz | square | 13 | benchmark_suitable set_partitioning general_linear |

```
@inproceedings{BorndoerferLoebelWeider2008,
author = {Ralf Bornd{\"o}rfer and Andreas L{\"o}bel and Steffen
Weider},
booktitle = {Computer-aided Systems in Public Transport},
editor = {Mark Hickman and Pitu Mirchandani and Stefan Voß},
pages = {3--24},
series = {Lecture Notes in Economics and Mathematical Systems},
title = {A Bundle Method for Integrated Multi-Depot Vehicle and
Duty Scheduling in Public Transit},
volume = {600},
year = {2008}
}
@phdthesis{Weider2007,
author = {Steffen Weider},
school = {Technische Universit{\"a}t Berlin},
title = {Integration of Vehicle and Duty Scheduling in Public
Transport},
year = {2007}
}
```

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