core4872-1529

binary variable_bound set_covering invariant_knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
A. Caprara, M. Fischetti, P. Toth	24656	4875	1.82001e-03	open	core	1530.0*	core4872-1529.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	24656	24588
Constraints	4875	4696
Binaries	24645	24588
Integers	0	0
Continuous	11	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.00182001	0.00164748
Nonzeroes	218762	190227

Constraint Classification Properties
	Original	Presolved
Total	4875	4696
Empty	0	0
Free	0	0
Singleton	59	0
Aggregations	0	0
Precedence	0	0
Variable Bound	64	53
Set Partitioning	0	0
Set Packing	0	0
Set Covering	4749	4642
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	0.602060
Constraint %		0.362010	33.3262	4.19506	95.4216
Variable %		0.133934	33.2643	3.54316	96.1159
Score	0.081142

Best Known Solution(s)

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	Submitter	Date	Description
3	1530	1530	Edward Rothberg	2020-04-22	Obtained with Gurobi 9.0 using the solution improvement heuristic
2	1532		Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
1	1537	1537	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to core4872-1529 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
core2586-950	open	13226	13215	11	2589	104678	A. Caprara, M. Fischetti, P. Toth	core	944.0*	binary variable_bound set_covering invariant_knapsack
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
rail507	easy	63019	63009	10	509	468878	A. Caprara, M. Fischetti, P. Toth	–	174	benchmark binary benchmark_suitable variable_bound set_covering invariant_knapsack
ex1010-pi	open	25200	25200	0	1468	102114	M. Winkler	–	233.0*	binary 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}
}