This paper considers the optimal location of interacting hub facilities. Using the well-known quadratic integer programming formulation of the uncapacitated, single allocation, p-hub median problem (USApHMP), the authors demonstrate a mapping onto a Hopfield neural network which guarantees feasibility of the final solution. They also propose a novel modification to the Hopfield network which enables escape from local minima, thus improving final solution quality. A practical application of the USApHMP-a postal delivery network-is used to demonstrate that the quality of these Hopfield network solutions compares favorably to those obtained using both exact methods and simulated annealing. Well-known data sets from the literature are also tested using the Hopfield network approaches, and provide further evidence that optimal or near-optimal solutions can consistently be obtained. The speed advantages which can be attained when implementing neural networks in hardware make the Hopfield neural network a very attractive potential alternative to the existing solution techniques.
