Abstract :
The Hopfield neural networks are well suited to solving large-scale optimization problems, but their convergence characteristics are not theoretically known. The author clarifies, by an eigenvalue analysis, conditions for converging to a vertex, a point on the edge, or an interior point of the hypercube. Taking the traveling salesman problem as an example, the author shows how to determine the weighting factors of the constraints and the objective function in the energy. Numerical calculations demonstrate that optimal or near-optimal solutions are obtained for 6, 10, and 13 cities.<>
Keywords :
convergence of numerical methods; eigenvalues and eigenfunctions; neural nets; optimisation; Hopfield neural networks; convergence; eigenvalue analysis; objective function; optimization; traveling salesman problem; weighting factors; Convergence of numerical methods; Eigenvalues and eigenfunctions; Neural networks; Optimization methods;
