Integer programming, including a Gomory-cut variant, yields new lex-first n-queens solutions for n=56-115 and min-max beautiful solutions for n<=176.
Lexicography and degeneracy: can a pure cutting plane algorithm work? Mathematical Programmming, 130:153–176, 2011
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Finding First and Most-Beautiful Queens by Integer Programming
Integer programming, including a Gomory-cut variant, yields new lex-first n-queens solutions for n=56-115 and min-max beautiful solutions for n<=176.