aflow40b

decomposition benchmark_suitable variable_bound set_partitioning mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
T. Achterberg	2728	1442	1.7243e-03	easy	aflow	1168	aflow40b.mps.gz

Arborescence flow problem on a graph with 40 nodes and edge density 0.9 Imported from MIPLIB2010.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	2728	2728
Constraints	1442	1442
Binaries	1364	1364
Integers	0	0
Continuous	1364	1364
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.0017243	0.0017243
Nonzeroes	6783	6783

Constraint Classification Properties
	Original	Presolved
Total	1442	1442
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	1364	1364
Set Partitioning	39	39
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	39	39
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	1.602060
Constraint %		2.14979	2.49475	2.49653	2.70458
Variable %		2.19941	2.56410	2.56598	2.78592
Score	0.947936

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	1168	1168	0	0	0	-	2018-10-10	Solution imported from MIPLIB2010.
1	1168	1168	0	0	0	-	2018-10-10	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to aflow40b 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	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
aflow30a	easy	842	421	421	479	2091	T. Achterberg	aflow	1158	decomposition benchmark_suitable variable_bound set_partitioning mixed_binary
h50x2450	easy	4900	2450	2450	2549	12152	MIPLIB submission pool	fixed-cost-network-flow	32906.880834	decomposition benchmark_suitable variable_bound set_partitioning mixed_binary
n370b	open	10000	5000	5000	5150	20000	J. Aronson	n37	1220708.0*	decomposition variable_bound mixed_binary
n3707	open	10000	5000	5000	5150	20000	J. Aronson	n37	1186691.0*	decomposition variable_bound mixed_binary
n3700	open	10000	5000	5000	5150	20000	J. Aronson	n37	1218974.9999999998*	decomposition variable_bound mixed_binary

Reference

@mastersthesis{Pfender2000,
 author = {T. Pfender},
 instance = {aflow50},
 language = {German},
 school = {Technische {Universit\"at} Berlin},
 title = {{Arboreszenz-Fl\"usse} in {G}raphen: polyedrische {U}ntersuchungen},
 type = {Diploma thesis},
 year = {2000}
}