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

Daniel Espinoza | 10800 | 319508 | 2.10212e-04 | hard | opm2 | -58540 | opm2-z12-s8.mps.gz |

Problems coming from precedence constrained knapsacks arising in mining applications. These are one-period problems with integer data but large root LP GAP

Imported from the MIPLIB2010 submissions. Solved with CPLEX 12.8, optimal objective confirmed with Gurobi and XPRESS.

Detailed explanation of the following tables can be found here.

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

Variables | 10800 | 10409 |

Constraints | 319508 | 300349 |

Binaries | 10800 | 10409 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000210212 | 0.000218765 |

Nonzeroes | 725377 | 683931 |

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

Total | 319508 | 300349 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 0 | 0 |

Aggregations | 0 | 0 |

Precedence | 319500 | 300341 |

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 | 8 | 8 |

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 % | 99.998 | 99.998 | 99.998 | 99.998 | |

Variable % | 100.000 | 100.000 | 100.000 | 100.000 | |

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

2 | 2 | -58540 | -58540 | 0 | 0 | 0 | Gregor Hendel | 2019-02-27 | Found with CPLEX 12.8 using 8 threads in 14 hours and 22802 B&B nodes. |

1 | 1 | -58395 | -58395 | 0 | 0 | 0 | - | 2018-10-13 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to opm2-z12-s8 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

opm2-z10-s4 | hard | 6250 | 6250 | 0 | 0 | 160633 | 371240 | Daniel Espinoza | opm2 | -33269 | benchmark binary benchmark_suitable precedence knapsack |

opm2-z8-s0 | easy | 3200 | 3200 | 0 | 0 | 63608 | 152793 | Daniel Espinoza | opm2 | -15775 | binary benchmark_suitable precedence knapsack |

rmine13 | open | 23980 | 23980 | 0 | 0 | 197155 | 485784 | Daniel Espinoza | rmine | -3495.3706624382535* | binary precedence mixed_binary |

rmine15 | open | 42438 | 42438 | 0 | 0 | 358395 | 879732 | Daniel Espinoza | rmine | -5018.819990999996* | binary precedence mixed_binary |

opm2-z7-s8 | easy | 2023 | 2023 | 0 | 0 | 31798 | 79756 | Daniel Espinoza | opm2 | -11242 | binary benchmark_suitable precedence knapsack |

`No bibliographic information available`

Last Update Mai 20, 2021 by Philipp Wellner

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