On the stability of the travelling salesman problem algorithm of Hopfield and Tank
Biological Cybernetics
Neural feature abstraction from judgements of similarity
Neural Computation
An Efficient Multivalued Hopfield Network for the Traveling Salesman Problem
Neural Processing Letters
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Hopfield's (analog) neural net algorithm shows very different characteristics when the net is allowed to evolve while the gain factor of the neural response is gradually increased. The study of the new approach (called quasi stationary flow) yields that (1) The net converges if the weights are symmetric and the strength of inhibitory self connection is less than the slope of the transfer function (i.e., -w"a","a 0). This approach has been successful in solving very large optimization problems. The quasi stationary approach is applied to the Hopfield and Tank's algorithm to solve the Traveling Salesman Problem (TSP). Besides the method of approaching the stable state, modifications are also suggested in (i) the energy function; (ii) the method of determining the energy coefficients: and (iii) the connectivity of the network. Results are reported of experiments with the Hamiltonian Cycle Problem (HCP or discrete TSP) on graphs of up to 500 nodes. The result of experiments with the well known 318 city TSP is also reported and compared with its best known solution computed by linear programming.