core2536-691

binary benchmark_suitable variable_bound set_covering invariant_knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
A. Caprara, M. Fischetti, P. Toth	15293	2539	4.57749e-03	easy	core	689	core2536-691.mps.gz

Set covering instance coming from Italian railway models 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	15293	15278
Constraints	2539	2505
Binaries	15284	15278
Integers	0	0
Continuous	9	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.00457749	0.00417727
Nonzeroes	177739	159870

Constraint Classification Properties
	Original	Presolved
Total	2539	2505
Empty	0	0
Free	0	0
Singleton	5	0
Aggregations	0	0
Precedence	0	0
Variable Bound	4	1
Set Partitioning	0	0
Set Packing	0	0
Set Covering	2527	2503
Cardinality	0	0
Invariant Knapsack	1	1
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	2	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 %		0.0399202	0.0399202	0.0399202	0.0399202
Variable %		0.0130864	0.0130864	0.0130864	0.0130864
Score	0.000399

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	689	689	0	0	0	-	2018-10-29	Solution found during MIPLIB2017 problem selection.
1	689	689	0	0	0	-	2018-10-13	Solution imported from MIPLIB2010.

Similar instances in collection

The following instances are most similar to core2536-691 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
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
rail507	easy	63019	63009	10	509	468878	A. Caprara, M. Fischetti, P. Toth	–	174	benchmark binary benchmark_suitable 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}
}