Abstract:
This thesis addresses both the theoretical and practical issues arising from the use of the Hopfield Net in a variety of engineering applications. The study examines a number of such applications which may be solved with this neural network. Its distinctive features are also described. The purpose of the study is basically two-fold. It seeks firstly to develop new applications with the Hopfield Net. Secondly, this study also aims to improve upon the fundamental design of such neural network models to overcome some of the difficulties in using them. However, these two goals cannot be achieved without a thorough understanding and appreciation of some of the problems associated with this approach. Therefore, the thesis also seeks to provide a comprehensive examination of the model as used in two major areas. Original contributions to both the understanding and applications of the Hopfield Net will be presented. Comparisons with some of the existing methods are also provided. Key developments are supported by way of detailed analysis and validated through simulations. The investigation begins by examining the role of neural networks in the field of combinatorial optimization. The study of neural networks is maturing rapidly, but the technology cannot be fully appreciated without a retrospective Iook at its origins. A brief historical perspective of neural networks, tracing their evolution into their present form is presented. A review of some of these networks with particular reference to their system architecture and primary applications will also be given. While the discrete Hopfield Net may be used as a Content-Addressable Memory, the continuous version may be used to solve combinatorial optimization problems. The properties and performance of both models are examined by detailed analysis and extensive computer simulations. Comparisons with some of the existing techniques are also made. An inherent problem with the continuous model involves determining the best set of network parameters so that good solutions are produced. Several existing techniques to find good parameter sets have been examined and in the light of the results, two new approaches are presented. The performance of the Hopfield Net for the two-dimensional assignment problem is also examined and improvements suggested. Although neural network approaches to solve the standard cell placement problem have been suggested, they have not made use of the special characteristics of the problem. A significantly different new approach is proposed. Unlike the current neural network approaches, this new approach has embedded some of the unique characteristics of the problem. This gives it the ability to extend its search for the global minimum into areas which were previously inaccessible. In order that the network may solve inequality constraint problems, modifications have to be made to the basic network architecture. This consists of having extra neurons whose main purpose is to provide an extra degree of flexibility. Such a network is used to solve a new problem of this class. Another major application of the Hopfield Net comes in the form of the problem involving the channel assignment for a cellular communication network. Conventional approaches to solve this problem involve heuristics based on the degree of difficulty of assignment. Simulation results obtained from both the neural network approach and a heuristic technique will be presented. Finally, key aspects of this work which are suitable for further study will be identified.