Comparison of Artificial Neural Network Architectures and Training Algorithms for Solving the Knight's Tours

This paper compares known architectures and training algorithms of multi-layered artificial neural networks (ANNs) and their ability to solve one specific type of chess problem (the Hamiltonian Cycles known as the Knight's Tours). The networks used here are trained to solve tours starting from the center of a five-by- five chessboard. The ANN architectures focused on are the function approximation feedforward architecture; the classification feedforward architecture; and two customized variations of the function approximation feedforward architecture. The training algorithms compared include Levenberg-Marquardt; variable learning (adaptive) gradient descent; resilient backpropagation; the Fletcher-Reeves conjugate gradient; and the Broyden-Fletcher-Goldfarb-Shanno Quasi-Newton algorithm. These five training algorithms are used for each of the four architectures. The real world application of this research is limited only by the functions given and the parameters used to define the environment. This can be expanded to include a variety of chess pieces (functions) in a variety of environments (any m-by-n sized board or even multidimensional problem solving). The practical limitation on the application is the software necessary to run extremely large neural networks.