Probability Selection for Solving Sudoku with Ant Colony optimization Algorithm

Abstract

Bringing together popular and loved games with artificial learning methods are the most effective way to increase both motivation to work and skills in understanding and solving problems. In this context, especially Japanese puzzles have been tried to be solved with metaheuristic algorithms by researchers in recent years. Among the Japanese puzzles, one of the most popular games all over the world is Sudoku. Since the traditional methods used to solve the problem in the Sudoku puzzle are quite complex, a different method was sought and this study focused on the solving Sudoku puzzle with Ant Colony optimization. In addition, since probability selection is very important in the ant colony algorithm, the effect of Roulette Wheel and Rank Based probability selection methods and the number of colonies on the solution of the Sudoku puzzle was also compared. For the results with the number of colonies, operations were carried out according to 9, 36 and 81 ants. For the study, 15 Sudoku puzzles, easy, medium and difficult, were solved with an ant colony and the time complexity of their solution was evaluated separately for each probability selection. In the results, it was seen that the Rank Based probability selection increased the time complexity of the algorithm by approximately, and it was observed that the increase in the number of ants decreased the working speed but did not affect the result.