A 4×4 Sudoku Solving Model Based on Multi-layer Perceptron

Abstract

Sudoku is a very popular mathematical and logical curiosity with abundant variations. Many artificial intelligence (AI) programs that imitate human expertise have been developed to solve sudoku puzzles. However, most popular methods, such as Recurrent Relational Networks and Double Q-learning, are primarily reinforcement learning (RL) algorithms. These algorithms are rather complex since they consist of two or more fundamental models for achieving high accuracy. To circumvent this drawback, this paper proposes a simple Multi-Layer Perceptron (MLP) model that not only produces correct results but is easy enough for implementation as well. Since the MLP model is a supervised learning method and is widely used in classification problems, this paper first discusses how the training data is generated. It then demonstrates a coding method that can be used to convert 4 × 4 sudoku puzzles to classification problems. Afterward, it shows the MLP settings and how the predictions from the model can be transformed into legal solutions. This model has been thoroughly tested on sudoku puzzles with various levels of difficulty, and the resulting data illustrate that its accuracy is no worse than those reinforcement learning methods and other non-AI algorithms. Moreover, with slight modification, the MLP model can be utilized on larger scales, such as 9 × 9 sudoku puzzles, or even harder ones.