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Computational Intelligence and Neuroscience
Volume 2015, Article ID 286354, 10 pages
http://dx.doi.org/10.1155/2015/286354
Research Article

A Hybrid alldifferent-Tabu Search Algorithm for Solving Sudoku Puzzles

1Pontificia Universidad Católica de Valparaíso, 2362807 Valparaíso, Chile
2Universidad Autónoma de Chile, 7500138 Santiago, Chile
3Universidad Cientifica del Sur, Lima 18 Lima, Peru
4Universidad Central de Chile, 8370178 Santiago, Chile
5Universidad San Sebastián, 8420524 Santiago, Chile
6Escuela de Ingeniería Industrial, Universidad Diego Portales, 8370109 Santiago, Chile
7Facultad de Ingeniería, Universidad Santo Tomás, 2561694 Viña del Mar, Chile

Received 7 January 2015; Accepted 24 April 2015

Academic Editor: Christian W. Dawson

Copyright © 2015 Ricardo Soto et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Sudoku problem is a well-known logic-based puzzle of combinatorial number-placement. It consists in filling a grid, composed of columns, rows, and subgrids, each one containing distinct integers from 1 to . Such a puzzle belongs to the NP-complete collection of problems, to which there exist diverse exact and approximate methods able to solve it. In this paper, we propose a new hybrid algorithm that smartly combines a classic tabu search procedure with the alldifferent global constraint from the constraint programming world. The alldifferent constraint is known to be efficient for domain filtering in the presence of constraints that must be pairwise different, which are exactly the kind of constraints that Sudokus own. This ability clearly alleviates the work of the tabu search, resulting in a faster and more robust approach for solving Sudokus. We illustrate interesting experimental results where our proposed algorithm outperforms the best results previously reported by hybrids and approximate methods.