msc98-ip

numerics aggregations precedence variable_bound set_partitioning cardinality invariant_knapsack knapsack integer_knapsack mixed_binary general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
E-Plus, D. Bienstock, A. Bley, R. Wessäly	21143	15850	2.77271e-04	easy	–	19839497.0058743	msc98-ip.mps.gz

Min-cost network dimensioning problems with a finite set of link capacities for each bidirected link, unsplittable shortest path routing, path restoration for single node failures, and routing path length restrictions 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	21143	13262
Constraints	15850	15653
Binaries	20237	12359
Integers	53	75
Continuous	853	828
Implicit Integers	0	23
Fixed Variables	0	0
Nonzero Density	0.000277271	0.000399802
Nonzeroes	92918	82995

Constraint Classification Properties
	Original	Presolved
Total	15850	15653
Empty	1	0
Free	0	0
Singleton	81	0
Aggregations	280	291
Precedence	0	1
Variable Bound	1739	1888
Set Partitioning	586	738
Set Packing	0	0
Set Covering	0	0
Cardinality	3331	3168
Invariant Knapsack	5210	5194
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	473	442
Integer Knapsack	1	2
Mixed Binary	4069	3828
General Linear	79	101
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	2.448706
Constraint %		0.0063900	0.198073	0.0063900	53.6200
Variable %		0.0150727	0.165289	0.0226091	40.5758
Score	0.337033

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	19839497	19839497	0	0	4e-06	-	2018-10-12	Solution found during MIPLIB2017 problem selection.
1	19839497	19839497	0	0	0e+00	-	2018-10-12	Solution imported from MIPLIB2010.

Similar instances in collection

The following instances are most similar to msc98-ip 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
atlanta-ip	easy	48738	46667	106	1965	21732	257532	E-Plus, D. Bienstock, A. Bley, R. Wessäly	–	90.009878614	benchmark benchmark_suitable aggregations precedence variable_bound set_partitioning set_covering cardinality invariant_knapsack binpacking knapsack integer_knapsack mixed_binary general_linear
lr1dr02vc05v8a-t360	open	20810	12174	6471	2165	7560	58950	Dimitri Papageorgiou	maritime	123046.8149370308*	aggregations variable_bound set_partitioning set_packing cardinality mixed_binary general_linear
neos-4358725-tagus	open	11494	4898	0	6596	22777	59925	Jeff Linderoth	neos-pseudoapplication-57	4206.140099965*	numerics aggregations precedence variable_bound set_partitioning invariant_knapsack mixed_binary general_linear
neos-3068746-nene	open	4890	3815	1075	0	4664	29515	Jeff Linderoth	neos-pseudoapplication-45	61910283.68794999*	numerics precedence set_partitioning set_packing integer_knapsack general_linear
neos-1067731	easy	8779	6330	0	2449	3423	30998	NEOS Server Submission	neos-pseudoapplication-11	1025102	benchmark_suitable aggregations set_partitioning mixed_binary

Reference

@techreport{BleyKoch2002,
 author = {Andreas Bley and Thorsten Koch},
 institution = {Zuse Institute Berlin},
 language = {English},
 number = {ZR 02-41},
 title = {Integer programming approaches to access and backbone {IP}-network planning},
 year = {2002}
}