Finding knight's tours on an M×N chessboard with O(MN) hysteresis McCulloch-Pitts neurons
Kuo-Chun Lee, Yoshiyasu Takefuji · IEEE Transactions on Systems Man and Cybernetics · 1994
How can a knight be moved on a chessboard so that the knight visits each square once and only once and goes back to the starting square? The earliest serious attempt to find a knight's tour on the chessboard was made by L. Euler in 1759 /spl lsqb/1/spl rsqb/. In this correspondence, a parallel algorithm based on the hysteresis McCulloch-Pitts neurons is proposed to solve the knight's tour problem. The relation between the traveling salesman problem and the knight's tour problem is also discussed. A large number of simulation runs were performed to investigate the behavior of the hysteresis McCulloch-Pitts neural model. The purpose of this correspondence is to present a case study/spl minus/how to successfully represent the combinatorial optimization problems by means of neural network.>