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2018 | OriginalPaper | Chapter

Chasing First Queens by Integer Programming

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Abstract

The n-queens puzzle is a well-known combinatorial problem that requires to place n queens on an \(n\times n\) chessboard so that no two queens can attack each other. Since the 19th century, this problem was studied by many mathematicians and computer scientists. While finding any solution to the n-queens puzzle is rather straightforward, it is very challenging to find the lexicographically first (or smallest) feasible solution. Solutions for this type are known in the literature for \(n\le 55\), while for some larger chessboards only partial solutions are known. The present paper was motivated by the question of whether Integer Linear Programming (ILP) can be used to compute solutions for some open instances. We describe alternative ILP-based solution approaches, and show that they are indeed able to compute (sometimes in unexpectedly-short computing times) many new lexicographically optimal solutions for n ranging from 56 to 115.

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Appendix
Available only for authorised users
Footnotes
1
Alternatively, one could fix \(x_{ij}=1\), check the resulting model for feasibility, and then move to the next position.
 
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Metadata
Title
Chasing First Queens by Integer Programming
Authors
Matteo Fischetti
Domenico Salvagnin
Copyright Year
2018
DOI
https://doi.org/10.1007/978-3-319-93031-2_16

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