勾配加速形ホップフィールドニューラルネットによる

抄録

Hopfield has shown that the combinatorial optimization problem can be solved on an artificial neural network system minimizing the quadratic energy function. One of the difficulties in applying the network to actual problems is that the network converges to local minimum solutions very slowly because the sigmoidal function is used for an input-output function of the neuron. In order to overcome this difficulty, we propose an accelerated Hopfield neural network which can control the speed of convergence near the local minima by an acceleration parameter. Computational results for the combinatorial problems with two and twenty-five variables show that: (1) the proposed model converges to the local minima more quickly than the conventional model, (2) that the acceleration of convergence makes the attraction region of each local minimum change and makes the accuracy of the solution worse, (3) that if an initial point is selected around the center of unit hyper cube, the proposed network converges to a local minimum very quickly with high accuracy, and these good properties keep unchanged by the acceleration parameter.