Neural network implementation for the optimal path problem (Q1282576)

The problem of searching an optimal path in a problem environment with marked obstacles and obligatorily visited points is deeply rooted in the past. The authors use the approach of \textit{R. Durbin} and \textit{D. J. Wilshaw} [``An analogous approach to the traveling salesman problem using an elastic net method'', Nature, No. 326 (1987)], but instead of the elastic neural networks method they propose to use an ANZA neurocomputer and simulations on PCs. The idea is that for a given map of the problem environment the coordinates of the starting point and of the termination point are connected by a broken line and that the length of the broken line is minimized by a shift of the breaks of the line taking into account the inclusion of the coordinates of the visited points and the avoidance of zones with obstacles. The problem is formulated rigorously. So far, so good. But the implementation of the problem in the neural networks application formalism is given only in schematic diagrams. It is not clear at all how one can learn in the sense of hierarchical nets. From the very short sketch of the results it is very difficult to recognize what kind of nets were in fact exploited. Besides, only the situation when the number of obligatory visited points is two, is presented. But one knows that the situation is going to be very complicated with an increasing number of such points -- an analogy to the famous traveling salesman problem. The authors state that the relevance of the proposed solution was investigated by computer simulation on a PC and the neurocomputer ANZA. Let us mention that the so-called neurocomputer ANZA has been unsuccessful and is not selling any more. Besides it is not clear what kind of simulations were used on a PC, what kind of neural networks were used, and so on. One can conclude that the proposed neural network implementation of the famous problem of finding an optimal path, presented in the paper, is rather vague and the requirement of the independence of the dimension of the map from the problem environment, from the number of obstacles, and from points to be visited seems not to be granted by the method proposed by the authors.