Product Geometric Crossover for the Sudoku Puzzle

Moraglio, Alberto; Togelius, Julian; Lucas, Simon M.

doi:10.1109/cec.2006.1688347

Cited by 50 publications

(58 citation statements)

References 4 publications

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“…In all cases, trees were initialized using uniform growth to depth 7, so that all trees of the initial population of all experiments were complete and had 64 terminals and 64 nonterminals. We used the lattice neighbourhood topology, which has previously been shown to work well with GPSO [15].…”

Section: Methodsmentioning

confidence: 99%

“…The requirements for GPSO to work in a given space is that there is a way of measuring the distance between two points (solutions), that there is a mutation operator that stochastically perturbs a point, and that there is a weighted geometrical crossover operator that given two parent points produces an offspring that lies between them. In a first application to GPSO to discrete spaces, it was shown to perform satisfactorily on the problem of finding solutions to Sudoku puzzles [15].…”

Section: Introductionmentioning

confidence: 99%

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Geometric PSO + GP = Particle Swarm Programming

Togelius

Nardi

Moraglio

2008

2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence)

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Abstract-Geometric particle swarm optimization (GPSO) is a recently introduced formal generalization of traditional particle swarm optimization (PSO) that applies naturally to both continuous and combinatorial spaces. In this paper we apply GPSO to the space of genetic programs represented as expression trees, uniting the paradigms of genetic programming and particle swarm optimization. The result is a particle swarm flying through the space of genetic programs. We present initial experimental results for our new algorithm.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geometric PSO + GP = Particle Swarm Programming

Togelius

Nardi

Moraglio

2008

2008 IEEE Congress on Evolutionary Computation (IEEE World Congress on Computational Intelligence)

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“…There are also approaches based on natural computing as [Moraglio et al 2006] and [Sato and Inoue 2010]. Both works discussed genetic operators to the problem.…”

Section: Related Workmentioning

confidence: 99%

Combining Metaheuristics and CSP Algorithms to Solve Sudoku

Machado

Chaimowicz

2011

2011 Brazilian Symposium on Games and Digital Entertainment

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Sudoku is a very popular puzzle game that is played by millions of people everyday. In spite of that, it is a NP-Hard problem that can be very difficult to solve depending on the initial conditions of the board. In this paper, we propose the combination of metaheuristics with techniques from the Constraint Satisfaction Problem (CSP) domain that speed up the solution's search process by decreasing its search space and its processing time. Experiments performed with boards of size 3, 4 and 5 show that this approach allows the resolution of a greater number of instances when compared to an initial baseline.

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“…Sudoku puzzle ( [1]- [3], [[5]- [7], [15]- [16]) consists of 9*9 grid and 3*3 blocks for all 81 cells. Each puzzle, which has unique solution, has some cells that have already been filled in.…”

Section: A Sudoku Puzzlementioning

confidence: 99%

Solution and Level Identification of Sudoku Using Harmony Search

Mandal¹,

Sadhu²

2013

IJMECS

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Abstract-Different optimization techniques have been used to solve Sudoku. Zong Woo Geem have applied harmony search in Sudoku to get better result. He has taken a Sudoku and time complexity has been optimized by different values of parameters. But, he has not given way of solution in details. He has also not given any idea to recognize the level of Sudoku. In this paper, an algorithm has been proposed based on harmony search to solve and identify the Sudoku efficiently. It has been observed that time complexity i.e. the maximum number of iteration has been reduced by choosing appropriate parameter values. The level of Sudoku has also been identified using probability metric. Finally, the number of iterations has been calculated with different values of parameters and the level of different Sudoku has been identified.

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Product Geometric Crossover for the Sudoku Puzzle

Cited by 50 publications

References 4 publications

Geometric PSO + GP = Particle Swarm Programming

Geometric PSO + GP = Particle Swarm Programming

Combining Metaheuristics and CSP Algorithms to Solve Sudoku

Solution and Level Identification of Sudoku Using Harmony Search

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