rail507

benchmark binary benchmark_suitable variable_bound set_covering invariant_knapsack

Submitter Variables Constraints Density Status Group Objective MPS File
A. Caprara, M. Fischetti, P. Toth 63019 509 1.46174e-02 easy 174 rail507.mps.gz

Railway crew scheduling

Imported from MIPLIB2010.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 63019 63001
Constraints 509 490
Binaries 63009 63001
Integers 0 0
Continuous 10 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.0146174 0.0151319
Nonzeroes 468878 467130
Constraint Classification Properties
Original Presolved
Total 509 490
Empty 0 0
Free 0 0
Singleton 8 0
Aggregations 0 0
Precedence 0 0
Variable Bound 3 1
Set Partitioning 0 0
Set Packing 0 0
Set Covering 496 488
Cardinality 0 0
Invariant Knapsack 1 1
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 1 0
General Linear 0 0
Indicator 0 0

Structure

Available nonzero structure and decomposition information. Further information can be found here.

value min median mean max
Components 0.301030
Constraint % 0.204082 0.204082 0.204082 0.204082
Variable % 0.003170 0.003170 0.003170 0.003170
Score 0.002041

Best Known Solution(s)

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
2 174 174 0 0 0 - 2018-10-29 Solution found during MIPLIB2017 problem selection.
1 174 174 0 0 0 - 2018-10-12 Solution imported from MIPLIB2010.

Similar instances in collection

The following instances are most similar to rail507 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
core2536-691 easy 15293 15284 0 9 2539 177739 A. Caprara, M. Fischetti, P. Toth core 689 binary benchmark_suitable variable_bound set_covering invariant_knapsack
core4284-1064 open 21714 21705 0 9 4287 245121 A. Caprara, M. Fischetti, P. Toth core 1067* binary variable_bound set_covering invariant_knapsack
core4872-1529 open 24656 24645 0 11 4875 218762 A. Caprara, M. Fischetti, P. Toth core 1537* binary variable_bound set_covering invariant_knapsack
core2586-950 open 13226 13215 0 11 2589 104678 A. Caprara, M. Fischetti, P. Toth core 950* binary variable_bound set_covering invariant_knapsack
fast0507 easy 63009 63009 0 0 507 409349 MIPLIB submission pool 174 benchmark binary benchmark_suitable variable_bound set_covering

Reference

@article{CapraraFischettiToth1999,
 author = {A. Caprara and M. Fischetti and P. Toth},
 instance = {core4872-1529},
 journal = {Operations Research},
 language = {English},
 pages = {730--743},
 title = {A heuristic method for the set covering problem},
 volume = {47},
 year = {1999}
}

@article{FischettiLodi2003,
 author = {Fischetti, Matteo and Lodi, Andrea},
 issn = {0025-5610},
 issue = {1},
 journal = {Mathematical Programming},
 keyword = {Mathematics and Statistics},
 pages = {23-47},
 publisher = {Springer},
 title = {Local branching},
 volume = {98},
 year = {2003}
}

Last Update Jun 24, 2019 by Gregor Hendel
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