Solving Sudoku Puzzles by using Hopfield Neural Networks
نویسندگان
چکیده
In this paper two different approaches to solve Sudoku puzzles with neural networks are presented. The first approach is proposed by J.J. Hopfield. He tries to solve the Sudoku puzzle with help of a Hopfield network and treated the problem as an integer optimization problem that is also used for the solution of the well known Traveling Salesmen Problem (TSP). Second solution uses the Hopfield network with an extension, called co-processor. Since neural networks can exactly solve linear programming problems, such a network can be used as co-processor to improve the performance of the Hopfield network. Combination of both networks, where the Hopfield network was used first, was able to solve a lot of puzzles. Key-Words: Sudoku puzzle, Sudoku problem, Neural Networks, Hopfield Neural Network, Traveling Salesmen Problem (TSP), Linear programming problems
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