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

George Fonseca | 2893026 | 325547 | 1.38939e-05 | open | timetabling | 1715.0* | kottenpark09.mps.gz |

Educational timetabling problems from several real schools/universities around the world. These instances were originally expressed in the xhstt file format [1] and formulated as Integer Programming models as described at [2].

[1] https://www.sciencedirect.com/science/article/pii/S0377221717302242 [2] https://link.springer.com/article/10.1007/s10479-011-1012-2 Ed Klotz reports the CPLEX Settings which he used to find the current best known solution: “With these settings, you get sufficiently fast node throughput that the tree search and node heuristics have some chance of success. After about 10 hours with 12 threads (and again 512 GB of RAM, although I don’t think that much was required), you start to get solutions with objectives in the 4000-5000 range, and letting it continue for 10 or more hours you eventually get solutions in the 2000-3000 range. I did not really experiment with alternate parameter settings to improve the tree search; that might help, as well as possibly using the attached solution as an advanced start and kicking off the run with the above settings with that solution immediately available.”

CPLEX Parameter File Version 12.9.0.0 - 12.9.0.0 | 2018-12-12 | a167f58ab5

```
CPXPARAM_MIP_Strategy_StartAlgorithm 4
CPXPARAM_MIP_Strategy_SubAlgorithm 4
CPXPARAM_MIP_SubMIP_StartAlg 4
CPXPARAM_MIP_SubMIP_SubAlg 4
CPXPARAM_Barrier_Crossover -1
2208 "submip.prm"
```

And the submip.prm file consists of:

```
CPXPARAM_MIP_SubMIP_StartAlg 4
CPXPARAM_MIP_SubMIP_SubAlg 4
CPXPARAM_Barrier_Crossover -1
```

The undocumented parameter 2208 refers to

```
CPLEX set mip submip _paramfile submip.prm
New value for parameter file for sub-MIPs: submip.prm
```

Detailed explanation of the following tables can be found here.

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

Variables | 2893026 | 1410175 |

Constraints | 325547 | 226913 |

Binaries | 2892333 | 1409482 |

Integers | 693 | 693 |

Continuous | 0 | 0 |

Implicit Integers | 0 | 639 |

Fixed Variables | 0 | 0 |

Nonzero Density | 1.38939e-05 | 2.25252e-05 |

Nonzeroes | 13085500 | 7207770 |

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

Total | 325547 | 226913 |

Empty | 2170 | 0 |

Free | 0 | 0 |

Singleton | 3193 | 0 |

Aggregations | 123838 | 86519 |

Precedence | 13888 | 12462 |

Variable Bound | 17522 | 16077 |

Set Partitioning | 128709 | 87087 |

Set Packing | 10030 | 8764 |

Set Covering | 1283 | 1113 |

Cardinality | 10694 | 5996 |

Invariant Knapsack | 11562 | 7604 |

Equation Knapsack | 362 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 266 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 71 | 18 |

General Linear | 1959 | 1273 |

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 | |||||

Constraint % | |||||

Variable % | |||||

Score |

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

3 | 1715 | 1715 | 0 | 0 | 0 | Edward Rothberg | 2020-07-17 | Obtained with the Gurobi 9.0 solution improvement heuristic |

2 | 2120 | 0 | 0 | 0 | Ed Klotz | 2019-02-27 | Found using CPLEX with customized parameters | |

1 | 4280 | 0 | 0 | 0 | Ed Klotz | 2019-01-28 |

The following instances are most similar to kottenpark09 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.

```
@article{FONSECA201728,
title = "Integer programming techniques for educational timetabling",
journal = "European Journal of Operational Research",
volume = "262",
number = "1",
pages = "28 - 39",
year = "2017",
note = "",
issn = "0377-2217",
doi = "http://dx.doi.org/10.1016/j.ejor.2017.03.020",
url = "http://www.sciencedirect.com/science/article/pii/S0377221717302242",
author = "George H.G. Fonseca and Haroldo G. Santos and Eduardo G. Carrano and Thomas J.R. Stidsen",
keywords = "Timetabling",
keywords = "Integer Programming",
keywords = "Formulation"
}
```

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