Handling Sudoku puzzles with irregular learning cellular automata

Abstract

The use of Cellular Automata (CA) in combination with Learning Automata (LA) has demonstrated effectiveness in handling hard-to-be-solved problems. Due to their capacity to learn and adapt, as well as their inherent parallelism, they can expedite the problem-solving process for a range of problems, such as challenging logic puzzles. One such puzzle is Sudoku, which poses a combinatorial optimization challenge of great difficulty and complexity. In this study, a Sudoku puzzle was represented as an Irregular Learning Cellular Automaton (ILCA), using a reward and penalty algorithm to resolve it. Simulations for an amount of 400 puzzles were performed, while the results demonstrate that the proposed algorithm operates effectively, highlighting the concurrent and learning capabilities of the ILCA structure. Furthermore, two different performance enhancement methods are investigated, namely learning rates method and selective probability reset rule, which are able to increase the initial performance by 26.8%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$26.8\\%$$\\end{document} and to achieve an overall 99.3%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$99.3\\%$$\\end{document} resolution rate.