There has been much interest in using optics to implement computer interconnection networks. However, there has been little discussion of any routing methodologies besides those already used in electronics. In this paper, a neural network routing methodology is proposed that can generate control bits for an optical multistage interconnection network (OMIN). Though we present no optical implementation of this methodology, we illustrate its control for an optical interconnection network. These OMINs may be used as communication media for shared memory, distributed computing systems.The routing methodology makes use of an Artificial Neural Network (ANN) that functions as a parallel computer for generating the routes. The neural network routing scheme may be applied to electrical as well as optical interconnection networks.However, since the ANN can be implemented using optics, this routing approach is especially appealing for an optical computing environment. The parallel nature of the ANN computation may make this routing scheme faster than conventional routing approaches, especially for OMINs that are irregular. Furthermore, the neural network routing scheme is fault-tolerant. Results are shown for generating routes in a 16 times 16, 3 stage OMIN. (Also cross-referenced as UMIACS-TR-94-21.)