Simplifying neural networks by soft weight-sharing
Neural Computation
Keeping the neural networks simple by minimizing the description length of the weights
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Neural Networks for Optimization and Signal Processing
Neural Networks for Optimization and Signal Processing
Continuous-time symmetric Hopfield nets are computationally universal
Neural Computation
Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research
INFORMS Journal on Computing
Mathematics and Computers in Simulation
ICANN/ICONIP'03 Proceedings of the 2003 joint international conference on Artificial neural networks and neural information processing
Convergence acceleration of the Hopfield neural network by optimizing integration step sizes
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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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.