Fuzzy scheduling of the parameters in Hopfield neural networks

In this paper, we propose fuzzy control that leads to an ideal scheduling of changing the parameters in Hopfield´s neural network. When a combinatorial optimization problem, such as the traveling salesman problem, is solved by Hopfield´s neural network, it is efficient to change intentionally the parameters of the energy function and sigmoid function. By changing the parameters on purpose, this network can avoid being trapped at a local minima. However, it is difficult to determine how to change these parameters because there exists a complex relation among these parameters. First, we investigate a bad scheduling to change parameters by simple experiments and find several rules that may lead to a good scheduling. The rules extracted from the experimental results are then realized by fuzzy control. By using fuzzy control, we can judge bad scheduling from vague network´s stages and correct the relation among the parameters. The traveling salesman problem is considered as an example to demonstrate its validity by computer simulations.