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

Simon Felix | 160400 | 399096 | 1.87002e-05 | open | schedule | -35.4584* | fhnw-schedule-pairb400.mps.gz |

Continuous-time project scheduling and selection, inspired by an industry use-case. Each project has a value, the sum should be maximized. Each project has a deadline, and an earliest start date. Three formulations of the same problem (“Pair A”, “Pair B” and “Slot”) - we expect “Pair B” to be the best formulation.

Detailed explanation of the following tables can be found here.

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

Variables | 160400 | 92720 |

Constraints | 399096 | 230280 |

Binaries | 160000 | 92416 |

Integers | 0 | 0 |

Continuous | 400 | 304 |

Implicit Integers | 0 | 0 |

Fixed Variables | 96 | 0 |

Nonzero Density | 1.87002e-05 | 3.04499e-05 |

Nonzeroes | 1197100 | 650152 |

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

Total | 399096 | 230280 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 96 | 0 |

Aggregations | 0 | 0 |

Precedence | 159600 | 101973 |

Variable Bound | 0 | 10483 |

Set Partitioning | 0 | 0 |

Set Packing | 0 | 0 |

Set Covering | 79800 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 0 | 46056 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 159600 | 71768 |

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 % | 68.8345 | 68.8345 | 68.8345 | 68.8345 | |

Variable % | 67.7922 | 67.7922 | 67.7922 | 67.7922 | |

Score | 0.221701 |

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 | -35.45840 | -35.45841 | 0 | 8e-07 | 6.1e-06 | Mou Sun, Tao Li, Wotao Yin | 2023-12-22 | Results computed using an adapted CPLEX with a 2-hour limit; details in the report “MindOpt Adapter for CPLEX Benchmarking Performance Analysis” (arXiv preprint: 2312.13527, 2023). |

3 | -35.45718 | -35.45718 | 0 | 0e+00 | 0.0e+00 | Edward Rothberg | 2020-04-22 | Obtained with Gurobi 9.0 using the solution improvement heuristic |

2 | -34.19035 | 0 | 0e+00 | 0.0e+00 | Edward Rothberg | 2019-12-13 | Obtained with Gurobi 9.0 | |

1 | -28.78138 | -28.78138 | 0 | 0e+00 | 0.0e+00 | - | 2018-10-10 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to fhnw-schedule-pairb400 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

fhnw-schedule-pairb200 | open | 40200 | 40000 | 0 | 200 | 99554 | 298554 | Simon Felix | schedule | -19.24094384259708* | precedence variable_bound invariant_knapsack mixed_binary |

ns1828997 | open | 27275 | 27275 | 0 | 0 | 81725 | 190670 | NEOS Server Submission | neos-pseudoapplication-13 | 7.99999999999967* | binary precedence variable_bound cardinality invariant_knapsack |

neos-4300652-rahue | easy | 33003 | 20900 | 0 | 12103 | 76992 | 183616 | Jeff Linderoth | neos-pseudoapplication-13 | 2.1416 | benchmark decomposition benchmark_suitable aggregations precedence variable_bound set_partitioning cardinality knapsack mixed_binary |

neos-3283608-agout | easy | 26256 | 26224 | 0 | 32 | 108649 | 301792 | Jeff Linderoth | neos-pseudoapplication-84 | Unbounded | precedence variable_bound set_partitioning set_covering invariant_knapsack mixed_binary |

neos-3209462-rhin | hard | 56453 | 383 | 0 | 56070 | 170226 | 447473 | Jeff Linderoth | neos-pseudoapplication-98 | 12 | aggregations precedence variable_bound set_partitioning set_covering cardinality invariant_knapsack mixed_binary |

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