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

Antonio Frangioni | 10788 | 34529 | 4.7944e-04 | open | polygonpack | -51837707.9503404* | polygonpack4-7.mps.gz |

Given a set P of polygons, not necessarily convex, and a rectangle, we want to find the subset S of P with largest possible total area and a position every p in S so that there are no overlaps and they are all included in the rectangle. We allow a small set of rotations (0, 90, 180, 270 degrees) for every polygon. The problem is simplified w.r.t. the real application because the polygons do not have (fully encircled) "holes", which are supposedly filled-in separately, although they can have "bays". Models are saved as .lp. Instance LpPackingModel

Detailed explanation of the following tables can be found here.

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

Variables | 10788 | 10788 |

Constraints | 34529 | 34508 |

Binaries | 10774 | 10774 |

Integers | 0 | 0 |

Continuous | 14 | 14 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000479440 | 0.000479469 |

Nonzeroes | 178591 | 178493 |

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

Total | 34529 | 34508 |

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 | 7 | 7 |

Set Covering | 0 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 336 | 336 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 34186 | 34165 |

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 | 0.903090 | ||||

Constraint % | 0.0029000 | 0.0029000 | 0.0029000 | 0.0029000 | |

Variable % | 0.0370782 | 0.0370782 | 0.0370782 | 0.0370782 | |

Score | 0.000203 |

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 | -51837708 | -51837708 | 0 | 0 | 0 | - | 2018-10-13 | Solution found during MIPLIB2017 problem selection. |

2 | -51837708 | 0 | 0 | 0 | Robert Ashford and Alkis Vazacopoulus | 2019-12-18 | Found using ODH|CPlex |

The following instances are most similar to polygonpack4-7 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

polygonpack4-10 | open | 20537 | 20517 | 0 | 20 | 65935 | 339036 | Antonio Frangioni | polygonpack | -53594065.703* | numerics set_packing invariant_knapsack mixed_binary |

polygonpack4-15 | open | 44237 | 44207 | 0 | 30 | 144478 | 731949 | Antonio Frangioni | polygonpack | -63613612.41121812* | numerics set_packing invariant_knapsack mixed_binary |

polygonpack3-15 | open | 44237 | 44207 | 0 | 30 | 144478 | 731949 | Antonio Frangioni | polygonpack | -54680307.392604* | numerics precedence variable_bound set_packing invariant_knapsack mixed_binary |

polygonpack5-15 | open | 48163 | 48133 | 0 | 30 | 163429 | 804740 | Antonio Frangioni | polygonpack | -54950356.2656221* | numerics precedence variable_bound set_packing invariant_knapsack mixed_binary |

glass4 | easy | 322 | 302 | 0 | 20 | 396 | 1815 | I. Luzzi | -- | 1200012600 | benchmark benchmark_suitable precedence set_partitioning mixed_binary |

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Last Update Mai 20, 2021 by Philipp Wellner

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