Abstract:
Inspired by the architecture of the biological brain, artificial neural networks were designed to provide solutions for computationally demanding problems. Neural network architectures are
based on wide-scale parallel computing, a feature that promises an increased computational power.
In this project, we implement a Boltzmann Machine neural network for solving the Traveling
Salesperson Problem (TSP), a constrained optimization problem. We also implement a Kohonen's
Self-Organizing Map for solving the Character Recognition Problem, a pattern recognition
problem. The same problem is also solved by implementing an Adaptive Resonance Theory network. Experimental results show that the execution time of a Boltzmann Machine network for
solving the TSP problem increases at a high rate as the number of cities increases. Moreover,
penalty and bonus parameter values have shown a limited effect on the network performance as
long as the penalty parameter is greater than the· bonus parameter. Experiments also show that
higher initial temperature values decrease the probability of the network converging to a feasible
solution.
Experimental work done on Kohonen's Self-Organizing Map for character recognition
shows that using problem-related initial weight vectors rather than random values improves the
ability of the network to recognize characters accurately. Moreover, the topology of the cluster units and the radius of learning also play key role in the network performance. In Adaptive
Resonance Theory network, experimental results demonstrate the ability of the user to control the
degree of similarity that allows patterns to be clustered on the same unit. Moreover, the order of the input patterns and the number of output cluster units also proved to have an effect on the network's
output.
