f2000

binary variable_bound set_covering

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
M. Winkler	4000	10500	7.02381e-04	open	–	1810.0*	f2000.mps.gz

Reformulated SAT instance from the 2010 SAT conference pseudo-Boolean competition Imported from MIPLIB2010. First feasible solution found by MemComputing, Inc. (https://memcpu.com/)

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	4000	3995
Constraints	10500	10495
Binaries	4000	3995
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000702381	0.000703357
Nonzeroes	29500	29490

Constraint Classification Properties
	Original	Presolved
Total	10500	10495
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	2000	1995
Set Partitioning	0	0
Set Packing	0	0
Set Covering	8500	8500
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	3.300161
Constraint %		0.0095300	0.0095300	0.0095300	0.0095300
Variable %		0.0500626	0.0500626	0.0500626	0.0500626
Score	0.189995

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	1810	1810	Edward Rothberg	2020-11-25	Found with Gurobi 9.1 NoRel heuristics
3	1811	1811	Fabio Traversa	2020-10-07	Found by MemComputing’s SaaS in a 15 minute run.
2	1835		Edward Rothberg	2020-02-05	Obtained with Gurobi 9.0
1	1846	1846		2019-06-04	found by MemComputing, Inc.

Similar instances in collection

The following instances are most similar to f2000 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
stein45inf	easy	45	45	332	1079	MIPLIB submission pool	stein	Infeasible	infeasible binary variable_bound set_covering invariant_knapsack mixed_binary
stein15inf	easy	15	15	37	135	MIPLIB submission pool	stein	Infeasible	infeasible binary set_covering invariant_knapsack mixed_binary
stein9inf	easy	9	9	14	54	MIPLIB submission pool	stein	Infeasible	infeasible binary set_covering invariant_knapsack mixed_binary
hanoi5	easy	3862	3862	16399	39718	M. Winkler	–	1931	binary variable_bound set_covering
seymour	easy	1372	1372	4944	33549	W. Cook, P. Seymour	–	423	benchmark binary benchmark_suitable variable_bound 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}
}