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 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 article 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.