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

Shunji Umetani | 100000 | 2000 | 5e-03 | open | scp | 321.0* | scpk4.mps.gz |

This is a random test instance generator for SCP using the scheme of the following paper, namely the column cost c[j] are integer randomly generated from [1,100]; every column covers at least one row; and every row is covered by at least two columns. see reference: E. Balas and A. Ho, Set covering algorithms using cutting planes, heuristics, and subgradient optimization: A computational study, Mathematical Programming, 12 (1980), 37-60. We have newly generated Classes I-N with the following parameter values, where each class has five instances. We have also generated reduced instances by a standard pricing method in the following paper: S. Umetani and M. Yagiura, Relaxation heuristics for the set covering problem, Journal of the Operations Research Society of Japan, 50 (2007), 350-375. You can obtain the instance generator program from the following web site. https://sites.google.com/site/shunjiumetani/benchmark

Detailed explanation of the following tables can be found here.

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

Variables | 1e+05 | 1e+05 |

Constraints | 2000 | 2000 |

Binaries | 1e+05 | 1e+05 |

Integers | 0 | 0 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.005 | 0.005 |

Nonzeroes | 1e+06 | 1e+06 |

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

Total | 2000 | 2000 |

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 | 0 | 0 |

Set Covering | 2000 | 2000 |

Cardinality | 0 | 0 |

Invariant Knapsack | 0 | 0 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

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 % | 100 | 100 | 100 | 100 | |

Variable % | 100 | 100 | 100 | 100 | |

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

3 | 4 | 321 | 321 | 0 | 0 | 0 | Shunsuke Kamiya | 2020-05-17 | Computed with weighting local search with exploiting variable associations (WLS) ([1]) [1] Umetani, Shunji. "Exploiting variable associations to configure efficient local search algorithms in large-scale binary integer programs." European Journal of Operational Research 263.1 (2017): 72-81. |

1 | 3 | 323 | 323 | 0 | 0 | 0 | Edward Rothberg | 2020-04-22 | Obtained with Gurobi 9.0 using the solution improvement heuristic |

4 | 2 | 325 | 0 | 0 | 0 | Edward Rothberg | 2019-12-13 | Obtained with Gurobi 9.0 | |

2 | 1 | 327 | 327 | 0 | 0 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to scpk4 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

scpj4scip | open | 99947 | 99947 | 0 | 0 | 1000 | 999893 | Shunji Umetani | scp | 128.0* | binary set_covering |

scpl4 | open | 200000 | 200000 | 0 | 0 | 2000 | 2000000 | Shunji Umetani | scp | 262.0* | binary set_covering |

scpm1 | open | 500000 | 500000 | 0 | 0 | 5000 | 6250000 | Shunji Umetani | scp | 557.0* | binary set_covering |

scpn2 | open | 1000000 | 1000000 | 0 | 0 | 5000 | 12500000 | Shunji Umetani | scp | 516.0* | binary set_covering |

ex1010-pi | open | 25200 | 25200 | 0 | 0 | 1468 | 102114 | M. Winkler | -- | 235* | binary set_covering |

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Last Update Nov 16, 2020 by Philipp Wellner

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