Hopfield-style neural networks and the TSP

We describe the results of our travelling salesman problem (TSP) neural model, using a linearization of the Hopfield model and an orthogonal projection onto the feasible subspace, including the definition of a region of parameter space that ensures exclusive convergence to tours. Our TSP results are relatively good for up to 30 cities, achieving a large number of optimal tours, but scaling remains a problem. For a particular 100 city problem the results are not very good, giving tours that are 80-90% longer than the optimal tour. We compare the performance of the network to the sequential nearest city algorithm, and provide several ideas for improving the performance of the network, including a divide and conquer approach. The relationship of TSP networks to lateral inhibition networks is also described.<
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