Enumerating knight´s tours using an ant colony algorithm

In this paper, we show how an ant colony optimisation algorithm may be used to enumerate knight´s tours for variously sized chessboards. We have used the algorithm to enumerate all tours on 5×5 and 6×6 boards, and, while the number of tours on an 8×8 board is too large for a full enumeration, our experiments suggest that the algorithm is able to uniformly sample tours at a constant, fast rate for as long as is desired.