An almost perfect heuristic for the N nonattacking queens problem

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Abstract

We present a heuristic technique for finding solutions to the N nonattacking queens problem that is almost perfect in the sense that it finds a first solution without any backtracks in most cases. In addition to previously known variable-ordering heuristics and their extensions, it uses a value-ordering heuristic, which contributes dramatically to its success. Using these heuristics, solutions have been found for all values of N between 4 and 1000.

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    Brute-force algorithms try to find all the solutions by checking all these arrangements, but this is unpractical for large values of n. Thus several different approaches have been proposed in literatures to solve the n-queens problem without listing technique. Some of these are as follows: using of backtracking search (Bitner and Reingold, 1975), local search and conflict minimization techniques (Sosic and Gu, 1994), neural networks (Onomi et al., 2011; Bharitkar and Mendel, 2000), search heuristic methods (Kale, 1990), probabilistic local search algorithms (Sosic and Gu, 1991) and integer programming (Foulds and Johnston, 1984). The n-queens Problem, a generalization of the original 8-queens problem, asks whether n nonattacking queens can be placed on an n × n chessboard in such a way that no queen can attack another, i.e., so that no two queens are placed in the same row or column or on the same diagonal.

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