AbstractIn solving optimization problems on Hopfield‐type neural networks, a constraint coefficient and a cost coefficient of an energy function should be appropriately determined. Until recently, the values of these coefficients were decided on the basis of experience and trial and error. As a result, 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 the constraint coefficient constant. In this method, the constraint condition for a solution is changed gradually, when the last constraint condition is satisfied, the solution is obtained. Under each constraint condition, the maximum value of cost coefficient is calculated, leading the Traveling Salesman Problem (TSP) for 10 to 30 cities, and obtained near‐optimal solutions more efficiently than an ordinary TSP algorithm. The computation time was reduced 10‐fold, compared with an ordinary TSP algo