Search performance for solving combinatorial optimization problems by a Hopfield network with applying iterative partial constraints

Abstract

A Hopfield network is one of the famous neural network models proposed in 1980s, and it is known as a good tool for solving combinatorial optimization problems. Its working mechanismis quite easy to understand, because its state transition is carried out to reduce the energy defined in advance. But it is true that there are some drawbacks. One is the existence of local energyminima corresponding to spurious solutions. Another is a size of the given task. Generally speaking, it is said that a large-scale network shows poor performance compared with a small-scale one, because the number of combinations for all possibilities are larger. In order to overcome the latter issue, an idea of partitioning applied constraints is tried in this study. Its key aspect is as follows: i) all constraints are divided into several groups, and ii) some of them are applied iteratively while the Hopfield network is searching an optimal solution. As a result of some computer simulations, it is found that the proposed method shows a better score than the conventional method.