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.

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.

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 Integers Continuous Constraints Nonz. Submitter Group Objective Tags
pb-market-split8-70-4 open 71 71 0 0 17 1113 Gleb Belov pb- no_solution binary feasibility knapsack mixed_binary
d20200 open 4000 4000 0 0 1502 189389 COR@L test set 12240* binary decomposition set_partitioning invariant_knapsack knapsack
neos-876808 easy 87268 87268 0 0 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 0 0 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 0 0 42620 307320 M. Winkler 280* 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}
}

Last Update Mar 04, 2024 by Julian Manns
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