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

Philipp Leise | 76068 | 38484 | 1.32986e-04 | open | dws | 140473.60932083728* | dws012-03.mps.gz |

MILP for designing a decentralized water supply system for drinking water in skyscrapers. The nonlinear characteristics of pumps are integrated with the help of an aggregated convex combination. The instances vary in the total number of floors and load scenarios for water demand. First stage variables represent the layout decisions, second stage variables represent the operational parameters, such as the continuous rotating speed of pumps or binary switching decisions.

Detailed explanation of the following tables can be found here.

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

Variables | 76068 | 76061 |

Constraints | 38484 | 38362 |

Binaries | 44616 | 44612 |

Integers | 0 | 0 |

Continuous | 31452 | 31449 |

Implicit Integers | 0 | 0 |

Fixed Variables | 0 | 0 |

Nonzero Density | 0.000132986 | 0.000133341 |

Nonzeroes | 389304 | 389070 |

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

Total | 38484 | 38362 |

Empty | 0 | 0 |

Free | 0 | 0 |

Singleton | 102 | 0 |

Aggregations | 0 | 0 |

Precedence | 990 | 987 |

Variable Bound | 2904 | 2895 |

Set Partitioning | 660 | 660 |

Set Packing | 66 | 66 |

Set Covering | 198 | 0 |

Cardinality | 0 | 0 |

Invariant Knapsack | 0 | 198 |

Equation Knapsack | 0 | 0 |

Bin Packing | 0 | 0 |

Knapsack | 0 | 0 |

Integer Knapsack | 0 | 0 |

Mixed Binary | 33564 | 33556 |

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 | 2.127105 | ||||

Constraint % | 0.00261 | 0.0941957 | 0.0521349 | 0.187686 | |

Variable % | 0.00394 | 0.4553290 | 0.0170906 | 0.913692 | |

Score | 0.124156 |

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 | 140473.6 | 140473.6 | 0e+00 | 1e-06 | 0 | Edward Rothberg | 2020-09-14 | Found with Gurobi |

1 | 148877.4 | 148877.4 | 3e-07 | 0e+00 | 0 | - | 2018-10-12 | Solution found during MIPLIB2017 problem selection. |

The following instances are most similar to dws012-03 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 |
---|---|---|---|---|---|---|---|---|---|---|---|

dws012-02 | open | 51108 | 30096 | 0 | 21012 | 26382 | 261120 | Philipp Leise | dws | 121112.055928511* | aggregations precedence variable_bound set_partitioning set_packing invariant_knapsack mixed_binary |

dws008-03 | hard | 32280 | 18928 | 0 | 13352 | 16344 | 165168 | Philipp Leise | dws | 62831.7633546923 | decomposition precedence variable_bound set_partitioning set_packing invariant_knapsack mixed_binary |

dws012-01 | open | 26148 | 15576 | 0 | 10572 | 14280 | 132936 | Philipp Leise | dws | 82030.53014261134* | decomposition precedence variable_bound set_partitioning set_packing mixed_binary |

dws008-01 | easy | 11096 | 6608 | 0 | 4488 | 6064 | 56400 | Philipp Leise | dws | 37412.60458794508 | benchmark decomposition benchmark_suitable precedence variable_bound set_partitioning set_packing mixed_binary |

uccase10 | open | 110818 | 16800 | 0 | 94018 | 196498 | 787045 | Daniel Espinoza | uccase | 39133.6229762502* | aggregations precedence variable_bound mixed_binary |

```
@inproceedings{AltherrPelzIREC2016,
author = "Altherr, Lena C. and Wolf, Jan and Ederer, Thorsten and Leise, Philipp and Pelz, Peter F.",
title="Algorithmic Design of an Optimal Water Supply System with TOR",
year="2016",
booktitle={3rd International Rotating Equipment Conference}
}
```

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