This paper examines the possibility to use neural networks for approximately solving the MiniSum problem, a classic facility location problem. For this we first create a set of realistic MiniSum instances, based on the Bulgarian road network. Two standard neural network approaches – Hopfield networks and Boltzmann machines, are then applied to the instances. Since the quality of solutions is not satisfactory, the reasons for the poor performance are discussed. An improved neural network approach is then proposed. This approach has excellent performance on the MiniSum instances. It always finds solutions just several percent worse than the optimum, and is often able to find the exact optimum.
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