Cost coefficient control method for solving optimization problems on Hopfield-type neural networks

When solving optimization problems on a Hopfield-type neural network, a constraint coefficient and cost coefficient of an energy function should be determined appropriately. Until recently, the values of these coefficients were decided based on experience and trial and error. Therefore, solutions that satisfy the constraints could not be obtained and the quality of the solutions was not good. In order to avoid this problem, we propose a method to control cost coefficient values automatically while keeping a constraint coefficient to be constant. We applied this method to the Travelling Salesman Problem, and obtained near-optimal solutions more efficiently than other approaches. The proposed algorithm is very effective especially for the difficult city allocations.