Realization of low sensitivity in the Hopfield model for optimal-solution search

The mutually coupled Hopfield model can determine the local minimum of the energy function in a short time by the steepest descent of the energy funct ion surface [1]. To use its high speed, analog implementation of the Hopfie ld model by an analog circuit is considered. On the other hand, no thorough study of various problems in the analog circuit, such as the sensitivity o f the parameters to deviations of the element values, has been presented. F rom this viewpoint, this paper attempts a sensitivity analysis of the Hopfi eld model for the circuit parameters when the model is implemented on an an alog circuit. Sensitivity analysis means in this paper a procedure in which error is provided by a normal random variable to a parameter that may be a ffected by the circuit implementation, and the effect on the solution is ex amined. It is seen that the Hopfield model is highly sensitive to error In other words, the realization of low sensitivity is very important in implem enting the Hopfield model as an analog circuit. This paper proposes a metho d where the diagonal element of the coupling weight matrix is set to a nonz ero value and reports that the sensitivity to error can be reduced by this approach. The property is verified by a numerical simulation for the travel ing salesman problem (TSP). (C) 1999 Scripta Technica.