30_70_45_095_100

binary decomposition benchmark_suitable precedence variable_bound set_covering mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
J. Walser	10976	12526	3.39236e-04	easy	30_70	3	30_70_45_095_100.mps.gz

Geographic radar station allocation 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	10976	10975
Constraints	12526	12526
Binaries	10975	10975
Integers	0	0
Continuous	1	0
Implicit Integers	0	0
Fixed Variables	1	0
Nonzero Density	0.000339236	0.000339267
Nonzeroes	46640	46640

Constraint Classification Properties
	Original	Presolved
Total	12526	12526
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	10447	10447
Variable Bound	5	5
Set Partitioning	0	0
Set Packing	0	0
Set Covering	18	18
Cardinality	0	0
Invariant Knapsack	0	0
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	2056	2056
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	2.687529
Constraint %		0.0079800	0.171988	0.191601	1.91601
Variable %		0.0182216	0.205686	0.227770	2.26859
Score	0.833261

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	3	3	0	0	0	-	2018-10-29	Solution imported from MIPLIB2010.
1	3	3	0	0	0	-	2018-10-13	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to 30_70_45_095_100 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
30_70_45_095_98	easy	10990	10989	0	1	12471	46387	J. Walser	30_70	11.99999999999999	binary decomposition benchmark_suitable precedence variable_bound set_covering mixed_binary
30_70_45_05_100	easy	10772	10771	0	1	12050	45889	J. Walser	30_70	9	binary decomposition benchmark_suitable precedence variable_bound set_covering mixed_binary
comp08-2idx	easy	11554	11487	67	0	12536	51608	Matias Sørensen	coursetimetabling	37	decomposition benchmark_suitable precedence variable_bound set_packing cardinality invariant_knapsack mixed_binary general_linear
supportcase40	easy	16440	2000	0	14440	38192	104420	Domenico Salvagnin	–	24256.3122898	benchmark decomposition benchmark_suitable precedence variable_bound set_packing mixed_binary
comp07-2idx	easy	17264	17155	109	0	21235	86577	Matias Sørensen	coursetimetabling	6	benchmark decomposition benchmark_suitable precedence variable_bound set_packing cardinality invariant_knapsack mixed_binary general_linear

Reference

@inproceedings{Walser1997,
 author = {Walser, Joachim P.},
 booktitle = {Proceedings of the 14th national conference on
artificial intelligence and 9th conference on Innovative applications of
artificial intelligence},
 pages = {269--274},
 publisher = {AAAI Press},
 title = {Solving linear pseudo-Boolean constraint problems with local
search},
 year = {1997}
}

@misc{Walser1997b,
 author = {J. P. Walser},
 note = {http://www.ps.uni-saarland.de/~walser/radar/radar.html},
 title = {Radar Surveillance},
 year = {1997}
}