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.

Location of instance in collection

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.

Nonzero entries of original problem

Nonzero entries after trivial presolving

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving (dec-file)

	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	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
core2536-691	easy	15293	15284	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	9	4287	245121	A. Caprara, M. Fischetti, P. Toth	core	1062.0*	binary variable_bound set_covering invariant_knapsack
core4872-1529	open	24656	24645	11	4875	218762	A. Caprara, M. Fischetti, P. Toth	core	1530.0*	binary variable_bound set_covering invariant_knapsack
core2586-950	open	13226	13215	11	2589	104678	A. Caprara, M. Fischetti, P. Toth	core	944.0*	binary variable_bound set_covering invariant_knapsack
fast0507	easy	63009	63009	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}
}