RESUMO
The Sudoku problem is a well-known logic-based puzzle of combinatorial number-placement. It consists in filling a n(2) × n(2) grid, composed of n columns, n rows, and n subgrids, each one containing distinct integers from 1 to n(2). 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.
Assuntos
Algoritmos , Inteligência Artificial , Teoria dos Jogos , Resolução de Problemas , Software , HumanosRESUMO
The Sudoku is a famous logic-placement game, originally popularized in Japan and today widely employed as pastime and as testbed for search algorithms. The classic Sudoku consists in filling a 9 × 9 grid, divided into nine 3 × 3 regions, so that each column, row, and region contains different digits from 1 to 9. This game is known to be NP-complete, with existing various complete and incomplete search algorithms able to solve different instances of it. In this paper, we present a new cuckoo search algorithm for solving Sudoku puzzles combining prefiltering phases and geometric operations. The geometric operators allow one to correctly move toward promising regions of the combinatorial space, while the prefiltering phases are able to previously delete from domains the values that do not conduct to any feasible solution. This integration leads to a more efficient domain filtering and as a consequence to a faster solving process. We illustrate encouraging experimental results where our approach noticeably competes with the best approximate methods reported in the literature.