core2586-950

binary variable_bound set_covering invariant_knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
A. Caprara, M. Fischetti, P. Toth	13226	2589	3.057e-03	open	core	944.0*	core2586-950.mps.gz

Set covering instance coming from Italian railway models Imported from the MIPLIB2010 submissions.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	13226	13179
Constraints	2589	2495
Binaries	13215	13179
Integers	0	0
Continuous	11	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.00305700	0.00273831
Nonzeroes	104678	90040

Constraint Classification Properties
	Original	Presolved
Total	2589	2495
Empty	0	0
Free	0	0
Singleton	42	0
Aggregations	0	0
Precedence	0	0
Variable Bound	36	26
Set Partitioning	0	0
Set Packing	0	0
Set Covering	2508	2468
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	0.4771212
Constraint %		1.082160	49.4589	49.4589	97.8357
Variable %		0.597987	49.8637	49.8637	99.1295
Score	0.0192730

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
4	944	944	Mars Davletshin	2023-12-08	The improvement was obtained with Huawei OptVerse solver using solution improvement heuristic.
3	946	946	DeepMind	2020-08-12	Obtained with SCIP using a custom branching rule.
2	948		Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
1	950	950	-	2018-10-11	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to core2586-950 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
core4872-1529	open	24656	24645	11	4875	218762	A. Caprara, M. Fischetti, P. Toth	core	1530.0*	binary 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
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

No bibliographic information available