On the stability of the travelling salesman problem algorithm of Hopfield and Tank
Biological Cybernetics
The guilty net for the traveling salesman problem
Computers and Operations Research - Special issue on neural networks and operations research
A new family of multivalued networks
Neural Networks
Self-organizing maps
An Efficient Multivalued Hopfield Network for the Traveling Salesman Problem
Neural Processing Letters
An Associative Multivalued Recurrent Network
IBERAMIA 2002 Proceedings of the 8th Ibero-American Conference on AI: Advances in Artificial Intelligence
A Recurrent Multivalued Neural Network for the N-Queens Problem
IWANN '01 Proceedings of the 6th International Work-Conference on Artificial and Natural Neural Networks: Connectionist Models of Neurons, Learning Processes and Artificial Intelligence-Part I
IEEE Transactions on Neural Networks
On equilibria, stability, and instability of Hopfield neural networks
IEEE Transactions on Neural Networks
A selective approach to parallelise Bees Swarm Optimisation metaheuristic: application to MAX-W-SAT
International Journal of Innovative Computing and Applications
International Journal of Innovative Computing and Applications
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In this paper, a new family of multivalued recurrent neural networks (MREM) is proposed. Its architecture, some computational properties and convergence is shown. We also have generalized the function of energy of the Hopfield model by a new function of the outputs of neurons that we named "function of similarity" as it measures the resemblance between their outputs. When the function of similarity is the product function, the model proposed is identical to the binary Hopfield one. This network shows a great versatility to represent, in an effective way, most of the combinatorial optimization problem [14-17] due to it usually incorporates some or all the restrictions of the problem generating only feasible states and avoiding the presence of parameters in the energy function, as other models do. When this interesting property is obtained, it also avoids the time-consuming task of fine tuning of parameters. In order to prove its suitability, we have used as benchmark the symmetric Travelling Salesman Problem (TSP). The versatility of MREM allows to define some different updating rules based on effective heuristic algorithms that cannot be incorporated into others Hopfield models.