Journal ArticleDOI
An investigation into the improvement of local minima of the Hopfield network
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TLDR
Experiments on travelling salesman problems show that the local minima of large-scale networks can be greatly improved by the NPA algorithm, however, the global minima are still difficult to achieve.About:
This article is published in Neural Networks.The article was published on 1996-10-01. It has received 71 citations till now. The article focuses on the topics: Hopfield network & Maxima and minima.read more
Citations
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Journal ArticleDOI
The co-adaptive neural network approach to the Euclidean travelling salesman problem
E. M. Cochrane,John E. Beasley +1 more
TL;DR: A new Self-Organising NN approach, called the Co-Adaptive Net, which involves not just unsupervised learning to train neurons, but also allows neurons to co-operate and compete amongst themselves depending on their situation.
Journal ArticleDOI
A review of Hopfield neural networks for solving mathematical programming problems
TL;DR: The Hopfield neural network (HNN) is one major neural network for solving optimization or mathematical programming (MP) problems and utilizes three common methods, penalty functions, Lagrange multipliers, and primal and dual methods to construct an energy function.
Journal ArticleDOI
A neural network algorithm for the traveling salesman problem with backhauls
Hassan Ghaziri,Ibrahim H. Osman +1 more
TL;DR: In this paper, a new heuristic based on Kohonen's self-organizing feature map for the traveling salesman problem with backhauls (TSPB) is introduced.
Journal ArticleDOI
An Efficient Multivalued Hopfield Network for the Traveling Salesman Problem
TL;DR: Simulation results for Euclidean Traveling Salesman Problems taken from the data library TSPLIB indicate that this multivalued neural approach is superior to the best neural network currently reported for this problem.
Journal ArticleDOI
PWR fuel management optimization using neural networks
TL;DR: In this paper, the authors presented a new method to solve the problem of finding the best configuration of fuel assemblies in a pressurized water reactor (PWR) core by using continuous Hopfield neural network accompanied by simulated annealing method.
References
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Journal ArticleDOI
Optimization by Simulated Annealing
TL;DR: There is a deep and useful connection between statistical mechanics and multivariate or combinatorial optimization (finding the minimum of a given function depending on many parameters), and a detailed analogy with annealing in solids provides a framework for optimization of very large and complex systems.
Journal ArticleDOI
Neural computation of decisions in optimization problems
John J. Hopfield,David W. Tank +1 more
TL;DR: Results of computer simulations of a network designed to solve a difficult but well-defined optimization problem-the Traveling-Salesman Problem-are presented and used to illustrate the computational power of the networks.
Journal ArticleDOI
On the stability of the travelling salesman problem algorithm of Hopfield and Tank
Greg Wilson,G. S. Pawley +1 more
TL;DR: The application of the method of Hopfield and Tank to the Travelling Salesman Problem has been re-examined in an effort to find a procedure for scaling to system sizes of real interest, but no satisfactory refinement was found and the reasons for algorithm failure have been identified.
Journal ArticleDOI
A theoretical investigation into the performance of the Hopfield model
TL;DR: In this paper, the behavior of the Hopfield model as a content-addressable memory and as a method of solving the traveling salesman problem (TSP) is analyzed based on the geometry of the subspace set up by the degenerate eigenvalues of the connection matrix.
Proceedings ArticleDOI
Theories on the Hopfield neural networks
TL;DR: In this article, the authors show that Hopfield neural networks are well suited to solving large-scale optimization problems, but their convergence characteristics are not theoretically known, by an eigenvalue analysis, conditions for converging to a vertex, a point on the edge or an interior point of the hypercube.
Related Papers (5)
On the stability of the travelling salesman problem algorithm of Hopfield and Tank
Greg Wilson,G. S. Pawley +1 more