pigeon-10

benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Sam Allen	490	931	1.78654e-02	easy	pigeon	-9000	pigeon-10.mps.gz

Instance of 3D packing (container loading) problem 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	490	400
Constraints	931	930
Binaries	400	370
Integers	0	0
Continuous	90	30
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.0178654	0.0218817
Nonzeroes	8150	8140

Constraint Classification Properties
	Original	Presolved
Total	931	930
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	0	0
Set Partitioning	0	10
Set Packing	0	0
Set Covering	0	0
Cardinality	60	50
Invariant Knapsack	270	270
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	1	0
Integer Knapsack	0	0
Mixed Binary	600	600
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	0.602060
Constraint %		21.5054	21.5054	21.5054	21.5054
Variable %		32.5000	32.5000	32.5000	32.5000
Score	0.435484

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	-9000	-9000	0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.
1	-9000	-9000	0	0	0	-	2018-10-12	Solution imported from MIPLIB2010.

Similar instances in collection

The following instances are most similar to pigeon-10 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
pigeon-08	easy	344	272	72	601	5176	Sam Allen	pigeon	-7000	benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary
pigeon-13	easy	754	637	117	1561	13871	Sam Allen	pigeon	-12000	benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary
pigeon-16	easy	1072	928	144	2353	21104	Sam Allen	pigeon	-15000	benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary
pigeon-20	easy	1580	1400	180	3661	33100	Sam Allen	pigeon	-19000	benchmark_suitable set_partitioning cardinality invariant_knapsack mixed_binary
supportcase41	open	4725	2000	2725	28923	221321	Domenico Salvagnin	–	32.00076832127569*	precedence variable_bound mixed_binary

Reference

@article{AllenBurkeMarecek2010,
 author = {Sam D. Allen and Edmund K. Burke and Jakub Marecek},
 journal = {Technical Report, University of Nottingham},
 title = {A Space-Indexed Formulation of Packing Boxes into a Larger Box},
 year = {2010}
}

@article{AllenBurkeMarecek2011,
 author = {Sam D. Allen and Edmund K. Burke and Jakub Marecek},
 journal = {Oper. Res. Lett.},
 number = {1},
 pages = {20--24},
 title = {A Space-Indexed Formulation of Packing Boxes into a Larger Box},
 volume = {40},
 year = {2012}
}