On Non-Uniform Rational B-Splines Surface Neural Networks |
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Authors: | Ming-Yang Cheng Hung-Wen Wu Alvin Wen-Yu Su |
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Affiliation: | (1) Electrical Engineering and Computer Science Department, The University of Toledo, Toledo, OH 43606, USA |
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Abstract: | This article presents a simulation study for validation of an adaptation methodology for learning weights of a Hopfield neural
network configured as a static optimizer. The quadratic Liapunov function associated with the Hopfield network dynamics is
leveraged to map the set of constraints associated with a static optimization problem. This approach leads to a set of constraint-specific
penalty or weighting coefficients whose values need to be defined. The methodology leverages a learning-based approach to
define values of constraint weighting coefficients through adaptation. These values are in turn used to compute values of
network weights, effectively eliminating the guesswork in defining weight values for a given static optimization problem,
which has been a long-standing challenge in artificial neural networks. The simulation study is performed using the Traveling
Salesman problem from the domain of combinatorial optimization. Simulation results indicate that the adaptation procedure
is able to guide the Hopfield network towards solutions of the problem starting with random values for weights and constraint
weighting coefficients. At the conclusion of the adaptation phase, the Hopfield network acquires weight values which readily
position the network to search for local minimum solutions. The demonstrated successful application of the adaptation procedure
eliminates the need to guess or predetermine the values for weights of the Hopfield network. |
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Keywords: | Hopfield neural network Static optimization Combinatorial Weights Adaptation Learning Training Traveling salesman problem Computational complexity Gradient descent Liapunov function |
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