sorrell3

benchmark binary benchmark_suitable variable_bound

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Toni Sorrell	1024	169162	1.95312e-03	easy	independentset	-16	sorrell3.mps.gz

These instances are based on Neil Sloane’s Challenge problems: Independent Sets in Graphs. Solved with COPT 7.0 using up to 12 threads in less than 40 minutes.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	1024	1024
Constraints	169162	169162
Binaries	1024	1024
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.00195312	0.00195312
Nonzeroes	338324	338324

Constraint Classification Properties
	Original	Presolved
Total	169162	169162
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	169162	169162
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	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.

ID	Objective	Exact	Int. Viol	Cons. Viol	Obj. Viol	Submitter	Date	Description
1	-16	-16	0	0	0	Jan Krüger	2023-08-20	Solution as found on https://oeis.org/A265032/a265032.html, reported optimal by James B. Shearer

Similar instances in collection

The following instances are most similar to sorrell3 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
sorrell4	hard	2048	2048	0	504451	1008902	Toni Sorrell	independentset	-24	binary variable_bound
sorrell7	open	2048	2048	0	78848	157696	Toni Sorrell	independentset	-198.0*	binary variable_bound
z26	open	17937	17937	0	850513	1715613	Daniel Bienstock	–	-1195.0*	binary variable_bound set_packing
sorrell8	easy	2046	2046	0	18944	37888	Toni Sorrell	independentset	-350	binary decomposition variable_bound
manna81	easy	3321	18	3303	6480	12960	MIPLIB submission pool	–	-13164	variable_bound

Reference

No bibliographic information available