2club200v15p5scn

binary variable_bound invariant_knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Balabhaskar Balasundaram	200	17013	3.08032e-02	hard	–	-70	2club200v15p5scn.mps.gz

Maximum 2-club instance; graph; clique relaxations Solved with Gurobi 8.1 on 24 cores in approx. 23 hours.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	200	200
Constraints	17013	17013
Binaries	200	200
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.0308032	0.0308032
Nonzeroes	104811	104811

Constraint Classification Properties
	Original	Presolved
Total	17013	17013
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	246	246
Set Partitioning	0	0
Set Packing	0	0
Set Covering	0	0
Cardinality	0	0
Invariant Knapsack	16767	16767
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	0.4771212
Constraint %		0.00588	0.722977	0.722977	1.44008
Variable %		1.00000	39.000000	39.000000	77.00000
Score	0.0033700

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
2	-70	-70	0	0	0	Joshua Friedman	2018-11-30	Found using Gurobi 8.1 on 24 cores after 23 hours.
1	-69	-69	0	0	0	-	2018-10-13	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to 2club200v15p5scn 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	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
genus-sym-grafo5708-48	open	3379	3377	1	1	20538	72579	Stephan Beyer	genus	-21*	precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear
genus-g61-25	open	14380	14378	1	1	94735	332877	Stephan Beyer	genus	-40.0*	numerics set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear
genus-sym-g62-2	open	12912	12910	1	1	78472	275855	Stephan Beyer	genus	-38.0*	precedence set_partitioning set_covering cardinality invariant_knapsack knapsack general_linear
supportcase21i	easy	27	24	3	0	7540	95325	Michael Winkler	–	20	indicator numerics set_covering invariant_knapsack general_linear
supportcase2	open	2912	2912	0	0	597385	7653928	Michael Winkler	–	65*	binary aggregations set_covering invariant_knapsack binpacking

Reference

@article{BBFMIVH2club2016,
    Author = {F. Mahdavi Pajouh and B. Balasundaram and I. V. Hicks},
    Journal = {Operations Research},
    Month = {November-December},
    Number = {6},
    Pages = {1466--1481},
    Title = {On the 2-club polytope of graphs},
    Volume = {64},
    Year = {2016}}