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A Hybrid alldifferent-Tabu Search Algorithm for Solving Sudoku Puzzles.

Ricardo Soto1, Broderick Crawford2, Cristian Galleguillos3

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This study introduces a novel hybrid algorithm combining tabu search and the alldifferent constraint for solving Sudoku puzzles more efficiently. The new method significantly outperforms existing hybrid and approximate approaches for this NP-complete problem.

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Area of Science:

  • Artificial Intelligence
  • Computer Science
  • Operations Research

Background:

  • Sudoku is a logic-based combinatorial number-placement puzzle on an n(2)×n(2) grid.
  • Sudoku puzzles are classified as NP-complete, requiring efficient solving algorithms.
  • Existing methods include diverse exact and approximate approaches.

Purpose of the Study:

  • To propose a new hybrid algorithm for solving Sudoku puzzles.
  • To enhance the efficiency and robustness of Sudoku solving methods.

Main Methods:

  • A novel hybrid algorithm is developed, integrating classic tabu search with the alldifferent global constraint from constraint programming.
  • The alldifferent constraint efficiently filters domains for pairwise distinct integers, crucial for Sudoku constraints.
  • This integration alleviates the computational load on the tabu search component.

Main Results:

  • The proposed hybrid algorithm demonstrates superior performance compared to existing methods.
  • Experimental results show faster and more robust Sudoku solving capabilities.
  • The algorithm outperforms previously reported best results from hybrid and approximate methods.

Conclusions:

  • The combination of tabu search and the alldifferent constraint offers a powerful approach to Sudoku solving.
  • This hybrid method significantly improves efficiency and robustness for NP-complete combinatorial problems.
  • The findings suggest potential for broader applications of this hybrid technique in constraint satisfaction problems.