sorrell8

binary decomposition variable_bound

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Toni Sorrell	2046	18944	9.77517e-04	easy	independentset	-350	sorrell8.mps.gz

These instances are based on Neil Sloane’s Challenge problems: Independent Sets in Graphs. Solved in 3489s on 8 cores using Gurobi 9.0. Disclaimer: On https://oeis.org/A265032/a265032.html the optimal solution for sorell8 is reported as -352 because the original instance apparently contains two isolated vertices that were removed when creating the instance. Solved in 3489s on 8 cores using Gurobi 9.0

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	2046	2046
Constraints	18944	18944
Binaries	2046	2046
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000977517	0.000977517
Nonzeroes	37888	37888

Constraint Classification Properties
	Original	Presolved
Total	18944	18944
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	18944	18944
Set Partitioning	0	0
Set Packing	0	0
Set Covering	0	0
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	1.041393
Constraint %		0.100296	10	6.27111	25.9396
Variable %		0.537634	10	8.06452	22.5806
Score	0.819115

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	Int. Viol	Cons. Viol	Obj. Viol	Submitter	Date	Description
2	-350		0	0	0	Edward Rothberg	2019-12-18	Optimal solution found with Gurobi 9.0 in 3489s on 8 cores
1	-350	-350	0	0	0	-	2018-10-11	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to sorrell8 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	Integers	Constraints	Nonz.	Submitter	Group	Objective	Tags
sorrell7	open	2048	2048	0	78848	157696	Toni Sorrell	independentset	-198.0*	binary variable_bound
sorrell3	easy	1024	1024	0	169162	338324	Toni Sorrell	independentset	-16	benchmark binary benchmark_suitable variable_bound
z26	open	17937	17937	0	850513	1715613	Daniel Bienstock	–	-1195.0*	binary variable_bound set_packing
sorrell4	hard	2048	2048	0	504451	1008902	Toni Sorrell	independentset	-24	binary variable_bound
manna81	easy	3321	18	3303	6480	12960	MIPLIB submission pool	–	-13164	variable_bound

Reference

No bibliographic information available