sorrell7

binary variable_bound

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Toni Sorrell	2048	78848	9.76562e-04	open	independentset	-198.0*	sorrell7.mps.gz

These instances are based on Neil Sloane’s Challenge problems: Independent Sets in Graphs.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	2048	2048
Constraints	78848	78848
Binaries	2048	2048
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000976562	0.000976562
Nonzeroes	157696	157696

Constraint Classification Properties
	Original	Presolved
Total	78848	78848
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	78848	78848
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.

## Warning in lapply(df["exactobjval"], as.numeric): NAs introduced by coercion

ID	Objective	Exact	Submitter	Date	Description
8	-198	-198	Mars Davletshin	2023-10-25	It was obtained with Huawei OptVerse solver using neural heuristic.
7	-197	-197	Peng Lin, Shaowei Cai, Mengchuan Zou, Jinkun Lin	2023-05-03	Computed by local search based on the paper Peng Lin, Shaowei Cai, Mengchuan Zou, and Jinkun Lin. “New Characterizations and Efficient Local Search for General Integer Linear Programming”, arXiv preprint arXiv:2305.00188 (2023).
6	-196	-196	Shunsuke Kamiya	2020-05-17	Computed with weighting local search with exploiting variable associations (WLS) ([1]) [1] Umetani, Shunji. “Exploiting variable associations to configure efficient local search algorithms in large-scale binary integer programs.” European Journal of Operational Research 263.1 (2017): 72-81.
5	-196	-196	Edward Rothberg	2020-04-22	Obtained with Gurobi 9.0 using the solution improvement heuristic
4	-194	-194	Frederic Didier	2020-02-24	Obtained with Google OR-tools through generating subproblems by fixing part of the current solution and trying to solve them with a sub CP-SAT solver
3	-192		Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
2	-187		Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	-185	-185	-	2018-10-11	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to sorrell7 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
sorrell3	easy	1024	1024	0	169162	338324	Toni Sorrell	independentset	-16	benchmark binary benchmark_suitable variable_bound
sorrell8	easy	2046	2046	0	18944	37888	Toni Sorrell	independentset	-350	binary decomposition variable_bound
sorrell4	hard	2048	2048	0	504451	1008902	Toni Sorrell	independentset	-24	binary variable_bound
z26	open	17937	17937	0	850513	1715613	Daniel Bienstock	–	-1195.0*	binary variable_bound set_packing
manna81	easy	3321	18	3303	6480	12960	MIPLIB submission pool	–	-13164	variable_bound

Reference

No bibliographic information available