queens-30

binary knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Ashutosh Mahajan	900	960	1.08148e-01	hard	–	-40	queens-30.mps.gz

Models the problem of placing as many queens on a 30 by 30 chess board as possible so that each queen threatens at most one other queen. 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	900	900
Constraints	960	960
Binaries	900	900
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.108148	0.108148
Nonzeroes	93440	93440

Constraint Classification Properties
	Original	Presolved
Total	960	960
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	0	0
Set Partitioning	0	0
Set Packing	0	0
Set Covering	0	0
Cardinality	0	0
Invariant Knapsack	0	0
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	960	960
Integer Knapsack	0	0
Mixed Binary	0	0
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	0.30103
Constraint %		57.5	57.5	57.5	57.5
Variable %		100.0	100.0	100.0	100.0
Score	0.00000

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
1	-39	-39	0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to queens-30 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	Constraints	Nonz.	Submitter	Group	Objective	Tags
pb-market-split8-70-4	hard	71	71	17	1113	Gleb Belov	pb-	0.0	binary feasibility knapsack mixed_binary
d20200	open	4000	4000	1502	189389	COR@L test set	–	12237.0*	binary decomposition set_partitioning invariant_knapsack knapsack
neos-876808	easy	87268	87268	85808	682376	NEOS Server Submission	neos-pseudoapplication-62	169795.259907	binary decomposition benchmark_suitable aggregations set_packing set_covering invariant_knapsack knapsack mixed_binary
neos-4954274-beardy	hard	12865	12865	17359	140082	Jeff Linderoth	neos-pseudoapplication-62	20946.48	binary decomposition variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack binpacking knapsack
circ10-3	open	2700	2700	42620	307320	M. Winkler	–	256.0*	binary decomposition precedence variable_bound set_partitioning set_packing invariant_knapsack knapsack mixed_binary

Reference

@misc{queenschallenge,
 key = {zzz queens},
 note = {http://domino.research.ibm.com/comm/wwwr_ponder.nsf/challenges/August2008.html},
 title = {{IBM} {P}onder {T}his -- {A}ugust 2008},
 year = {2008}
}