Tabu search for solving optimization problems on Hopfield neural networks

Over the past few decades, numerous attempts have been made to solve combinatorial optimization problems that are NP-complete or NP-hard in a heuristic approach. A Hopfield-type neural network is a method that is often used to solve problems such as the traveling salesman problem. However, it is difficult to find an optimal solution because it is based on gradient descent and its energy function has many local minima. Therefore, many attempts have been made to find ways of escaping from local minima and to find better solutions. T. Tanaka et al. (1996) succeeded in improving the solutions by controlling the coefficient of the energy function. However, their results were not completely satisfying in terms of the quality of the solutions and the computation time. In order to find better solutions in a short time, we introduced a method called tabu search into a Hopfield-type neural network. Tabu search is a simple and flexible method for obtaining good solutions quickly and has been applied to NP-complete problems. Through computer simulations, better solutions were obtained than those obtained by using an ordinary model. Moreover, the computation time was reduced