Abstract
AbstractTaking the traveling salesman problem as an example of a combinatorial optimization problem that can be solved by neural networks with symmetric connections (Hopfield neural networks), the asymptotic stability and instability conditions of solutions satisfying the constraints of the problem, and instability conditions of nonsolutions which do not satisfy those constraints are presented. From the results, it is shown that network properties such as the limitations of networks with multilinear energy function (wii = 0) and many other phenomena can be explained theoretically. Furthermore, from simulation it is confirmed that the optimal solution for the optimization problem can be obtained with high probability by setting the coefficients of the constraints and the optimization requirements so that they satisfy the presented conditions.
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