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 Variables Binaries Integers Continuous Constraints Nonz. Submitter Group Status Objective
pb-market-split8-70-4 71 71 0 0 17 1113 Gleb Belov pb- open
d20200 4000 4000 0 0 1502 189389 COR@L test set open 12252*
neos-876808 87268 87268 0 0 85808 682376 NEOS Server Submission neos-pseudoapplication-62 easy 169795.259907
neos-4954274-beardy 12865 12865 0 0 17359 140082 Jeff Linderoth neos-pseudoapplication-62 hard 20946.48
circ10-3 2700 2700 0 0 42620 307320 M. Winkler open 378*

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 Nov 09, 2018 by Gregor Hendel
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