ex1010-pi

binary set_covering

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
M. Winkler	25200	1468	2.76032e-03	open	–	233.0*	ex1010-pi.mps.gz

Logic synthesis problem from the 2010 SAT conference pseudo-Boolean competition 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	25200	25200
Constraints	1468	1468
Binaries	25200	25200
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.00276032	0.00276032
Nonzeroes	102114	102114

Constraint Classification Properties
	Original	Presolved
Total	1468	1468
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	0	0
Set Partitioning	0	0
Set Packing	0	0
Set Covering	1468	1468
Cardinality	0	0
Invariant Knapsack	0	0
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	0	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	0.30103
Constraint %		100	100	100	100
Variable %		100	100	100	100
Score	0.00000

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
6	233	233	Davletshin Mars	2023-10-10	The method is based on combination of methods from our paper “On variables selection in Neural Diving” with local search.
5	234	234	Davletshin Mars	2023-06-22	Found with a method based on Machine Learning.
4	234	234	Yuya Hattori	2023-01-09	This solution is computed by local search based on the paper, M. Yagiura, M. Kishida and T. Ibaraki, “A 3-Flip Neighborhood Local Search for the Set Covering Problem”, European Journal of Operational Research, 172 (2006) 472-499.
3	235	235	Edward Rothberg	2020-06-11	Obtained with Gurobi 9.0 using the solution improvement heuristic
2	236		Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
1	239	239	-	2018-10-10	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to ex1010-pi 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	Constraints	Nonz.	Submitter	Group	Objective	Tags
ramos3	open	2187	2187	2187	32805	F. Ramos	–	186.0*	binary set_covering
seymour	easy	1372	1372	4944	33549	W. Cook, P. Seymour	–	423	benchmark binary benchmark_suitable variable_bound set_covering
fast0507	easy	63009	63009	507	409349	MIPLIB submission pool	–	174	benchmark binary benchmark_suitable variable_bound set_covering
iis-glass-cov	easy	214	214	5375	56133	Marc Pfetsch	iis	20.99999999999999	binary benchmark_suitable set_covering
glass-sc	easy	214	214	6119	63918	Marc Pfetsch	maxfeassub	23	benchmark binary benchmark_suitable set_covering

Reference

@misc{pseudoboolean,
 key = {pseudoboolean},
 note = {http://www.cril.univ-artois.fr/PB10/},
 title = {{P}seudo-{B}oolean {C}ompetition 2010},
 year = {2010}
}