net12

benchmark decomposition benchmark_suitable precedence set_packing cardinality invariant_knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
P. Belotti	14115	14021	4.06172e-04	easy	–	214	net12.mps.gz

Network design instance 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	14115	14115
Constraints	14021	14021
Binaries	1603	1603
Integers	0	0
Continuous	12512	12512
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000406172	0.000406172
Nonzeroes	80384	80384

Constraint Classification Properties
	Original	Presolved
Total	14021	14021
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	10	10
Variable Bound	0	0
Set Partitioning	10	0
Set Packing	391	391
Set Covering	2	0
Cardinality	542	552
Invariant Knapsack	0	12
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	13066	13056
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	1.397940
Constraint %		0.156907	4.00500	4.17231	4.17231
Variable %		0.276302	4.16667	4.33581	4.33581
Score	0.919589

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	214	214	0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.
1	214	214	0	0	0	-	2018-10-12	Solution imported from MIPLIB2010.

Similar instances in collection

The following instances are most similar to net12 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
istanbul-no-cutoff	easy	5282	30	5252	20346	71477	Utz-Uwe Haus	–	204.08170701	benchmark benchmark_suitable aggregations variable_bound knapsack mixed_binary
neos-691058	easy	3006	1755	1251	2667	30837	NEOS Server Submission	neos-pseudoapplication-110	296.999999999986	benchmark_suitable set_partitioning cardinality mixed_binary
snip10x10-35r1budget17	hard	47611	63	47548	213801	475334	Utz-Uwe Haus	–	72.30862035707088	aggregations variable_bound invariant_knapsack mixed_binary
loopha13	easy	19356	18150	1206	23758	41809	Hamideh	–	6.40233	benchmark_suitable aggregations precedence variable_bound invariant_knapsack mixed_binary
neos-4477313-unzha	easy	2193	2016	177	4174	30400	Jeff Linderoth	neos-pseudoapplication-110	Unbounded	numerics set_partitioning mixed_binary

Reference

@inproceedings{BelottiMalucelli2003,
 author = {P. Belotti and F. Malucelli},
 booktitle = {Proceedings of the 2003 International Network Optimization
Conference},
 instance = {net12},
 language = {English},
 pages = {72--77},
 title = {A {L}agrangian relaxation approach for the design of networks
with shared protection},
 year = {2003}
}

@article{FischettiLodi2003,
 author = {Fischetti, Matteo and Lodi, Andrea},
 issn = {0025-5610},
 issue = {1},
 journal = {Mathematical Programming},
 keyword = {Mathematics and Statistics},
 pages = {23-47},
 publisher = {Springer},
 title = {Local branching},
 volume = {98},
 year = {2003}
}