Solving large scale puzzles with neural networks

The n-queens problem is solved with Boltzmann machines and a depth-first search (DFS) algorithm. In large-scale problems, the Boltzmann machines found a solution much faster than the DFS. The 1000-queens problem was solved using an energy minimization technique. The polyomino puzzles were also solved with Boltzman machines and a DFS algorithm. In small-scale problems, the DFS solved these puzzles faster than Boltzmann machines. Using Gaussian machines, large-size polyomino puzzles were solved successfully. For example, 36 unique solutions were obtained for the 1000-queens problem, and 5×8, 6×10, and 8×8 sized difficult polyomino puzzles were solved