The travelling salesman problem and the Hopfield neural network

The author outlines a simple method of defining and implementing the traveling salesman problem (TSP) by using a Hopfield neural network. The pitfalls and problems encountered during implementation are explained. It is concluded that optimization problems such as the TSP can be better solved by using the Hopfield network than by a computer intensive search of all possible solutions to the problem. By a proper choice of network parameters it is possible to ensure valid solutions to the problem. An illustrative four-city example effectively points out the practical considerations required for a novice in this area to implement this problem successfully. For the example, the solutions obtained for random, normalized intercity distances were always valid. In addition, 90% of the results were optimal solutions. The rest of the results were usually the second best path for the tour.<>