相互結合型ニューラルネットによる組合せ問題の近似解法 : 情報ディスプレイ : 無線・光伝送 : 画像通信システム : 画像応用

抄録

Hopfield has shown that the travelling salesman problem (TSP) can be solved on a neural network minimizing the quadratic energy function. The network converges to the steady state with not the global but a local minimum of the function. The best value of r depends on the structure of the TSP and no systematic method for finding such r has been proposed. We call the minimum r satisfying all the constraints the minimum possible r (r*) and propose an algorithmic procedure to find r*. Furthermore, we introduce the augmented penalty function using the Lagrange multipliers to decrease r* and improve the local minimum of the TSP. We analyze the equivalence between the multiplier and the threshold of the neuron and propose a new analytical and rapid scheme for updating the multipliers.