A Novel Evolutionary Algorithm with Column and Sub-Block Local Search for Sudoku Puzzles

Sudoku puzzles are not only popular intellectual games but also NP-hard combinatorial problems related to various real-world applications, which have attracted much attention worldwide. Although many efficient tools, such as evolutionary computation (EC) algorithms, have been proposed for solving Sudoku puzzles, they still face great challenges with regard to hard and large instances of Sudoku puzzles. Therefore, to efficiently solve Sudoku puzzles, this paper proposes a genetic algorithm (GA)-based method with a novel local search technology called local search-based GA (LSGA). The LSGA includes three novel design aspects. First, it adopts a matrix coding scheme to represent individuals and designs the corresponding crossover and mutation operations. Second, a novel local search strategy based on column search and sub-block search is proposed to increase the convergence speed of the GA. Third, an elite population learning mechanism is proposed to let the population evolve by learning the historical optimal solution. Based on the above technologies, LSGA can greatly improve the search ability for solving complex Sudoku puzzles. LSGA is compared with some state-of-the-art algorithms at Sudoku puzzles of different difficulty levels and the results show that LSGA performs well in terms of both convergence speed and success rates on the tested Sudoku puzzle instances

SudokuSat - A tool for analyzing difficult sudoku puzzles

Studies in Computational Intelligence16625-3

SUDOKUSAT—A Tool for Analyzing Difficult Sudoku Puzzles

Sudoku puzzles enjoy world-wide popularity, and a large community of puzzlers is hoping for ever more difficult puzzles. A crucial step for generating difficult Sudoku puzzles is the fast assessment of the difficulty of a puzzle. In a study in 2006, it has been shown that SAT solving provides a way to efficiently differentiate between Sudoku puzzles according to their difficulty, by analyzing which resolution technique solves a given puzzle. This paper shows that one of these techniques—unit resolution with failed literal propagation—does not solve a recently published Sudoku puzzle called AI Escargot, claimed to be the world’s most difficult. The technique is also unable to solve any of a list of difficult puzzles published after AI Escargot, whereas it solves all previously studied Sudoku puzzles. We show that the technique can serve as an efficient and reliable computational method for distinguishing the most difficult Sudoku puzzles. As a proof-of-concept for an efficient difficulty checker, we present the tool SUDOKUSAT that categorizes Sudoku puzzles with respect to the resolution technique required for solving them. 1. Sudoku Sudoku puzzles have fascinated puzzle solvers since their invention in 1979. A Sudoku puzzle is a 9 × 9 grid of cells, which is composed of nine 3 × 3 non-overlapping boxes of cells. The objective is to fill the grid with digits from 1 to 9 so that each row, column and box contains any digit at most once. Some cells are already filled with digits; these cells are called hints. To be a proper Sudoku puzzle, the grid must admit a unique way to fill the remaining cells to meet the objective (Uniqueness Property). Figure 1 shows a Sudoku puzzle that can be solved within a few minutes by an experienced puzzler. Whereas precursors of Sudoku—based on magic squares and Latin squares—were known since the late 19 th century