Comparison of Heuristic Algorithms for the N-Queen Problem

Martinjak, Ivica; Golub, Marin

doi:10.1109/iti.2007.4283867

Cited by 32 publications

(20 citation statements)

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“…K. D. Crawford in [2], applied Genetic Algorithm and have discussed two ways to solve n-Queen problem. Ivica et al provided a comparison of different heuristic techniques in [1]. The techniques include Simulated Annealing, Tabu Search and Genetic Algorithm.…”

Section: Related Workmentioning

confidence: 99%

Solving N Queen Problem using Genetic Algorithm

Farhan¹,

Tareq²,

Awad³

2015

IJCA

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Section: Related Workmentioning

confidence: 99%

Solving N Queen Problem using Genetic Algorithm

Farhan¹,

Tareq²,

Awad³

2015

IJCA

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“…Heuristic algorithms have been presented and compared, using such techniques as simulated annealing, tabu search, and genetic algorithms [4]. Recent methods involve particle swarm optimization, dynamic load distribution, ant colony optimization, gravitational search algorithms, and other recently developed techniques [5].…”

Section: Fig 1 One Solution For the Non-attacking N-queens Problem mentioning

confidence: 99%

Swapping algorithm and meta-heuristic solutions for combinatorial optimization n-queens problem

Vaughan

2015

2015 Science and Information Conference (SAI)

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Abstract-This research proposes the swapping algorithm a new algorithm for solving the n-queens problem, and provides data from experimental performance results of this new algorithm. A summary is also provided of various meta-heuristic approaches which have been used to solve the n-queens problem including neural networks, evolutionary algorithms, genetic programming, and recently Imperialist Competitive Algorithm (ICA). Currently the Cooperative PSO algorithm is the best algorithm in the literature for finding the first valid solution. Also the research looks into the effect of the number of hidden nodes and layers within neural networks and the effect on the time taken to find a solution. This paper proposes a new swapping algorithm which swaps the position of queens.

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“…A witnessing solution can be constructed easily (Bell & Stevens, 2009) but note that the witness (a set of n queens) requires n log n bits to specify but this is not polynomial in the size of the input, which is only log n bits. The n-Queens problem has often been incorrectly called NP-hard, even in well-cited papers (Mandziuk, 1995;Martinjak & Golub, 2007;ShahHosseini, 2009;Nakaguchi, Kenya, & Tanaka, 1999, each with at least 29 citations). The counting version of the problem, i.e.…”

Section: Introductionmentioning

confidence: 99%

Complexity of n-Queens Completion

Gent

Jefferson

Nightingale

2017

jair

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The n-Queens problem is to place n chess queens on an n by n chessboard so that no two queens are on the same row, column or diagonal. The n-Queens Completion problem is a variant, dating to 1850, in which some queens are already placed and the solver is asked to place the rest, if possible. We show that n-Queens Completion is both NP-Complete and #P-Complete. A corollary is that any non-attacking arrangement of queens can be included as a part of a solution to a larger n-Queens problem. We introduce generators of random instances for n-Queens Completion and the closely related Blocked n-Queens and Excluded Diagonals Problem. We describe three solvers for these problems, and empirically analyse the hardness of randomly generated instances. For Blocked n-Queens and the Excluded Diagonals Problem, we show the existence of a phase transition associated with hard instances as has been seen in other NP-Complete problems, but a natural generator for n-Queens Completion did not generate consistently hard instances. The significance of this work is that the n-Queens problem has been very widely used as a benchmark in Artificial Intelligence, but conclusions on it are often disputable because of the simple complexity of the decision problem. Our results give alternative benchmarks which are hard theoretically and empirically, but for which solving techniques designed for n-Queens need minimal or no change.

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Comparison of Heuristic Algorithms for the N-Queen Problem

Cited by 32 publications

References 1 publication

Solving N Queen Problem using Genetic Algorithm

Solving N Queen Problem using Genetic Algorithm

Swapping algorithm and meta-heuristic solutions for combinatorial optimization n-queens problem

Complexity of n-Queens Completion

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