Abstract
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.
Highlights
The Sudoku is a logic-based placement puzzle, widely present as pastime game in newspapers and magazines
We propose a new algorithm for the efficient solving of Sudoku instances based on cuckoo search, geometric operators, and prefiltering phases
The cuckoo search is a relatively modern nature-inspired metaheuristic [14,15,16,17,18] to which we introduce geometric operators in order to correctly move to promising regions of a discrete space of solutions
Summary
The Sudoku is a logic-based placement puzzle, widely present as pastime game in newspapers and magazines. We propose a new algorithm for the efficient solving of Sudoku instances based on cuckoo search, geometric operators, and prefiltering phases. The cuckoo search is a relatively modern nature-inspired metaheuristic [14,15,16,17,18] to which we introduce geometric operators in order to correctly move to promising regions of a discrete space of solutions.
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