The Transient Chaotic Neural Network (TCNN) and the Noisy Chaotic Neural Network (NCNN) have been proved their searching abilities for solving combinatorial optimization problems(COPs). The chaotic dynamics of the TCNN and the NCNN are believed to be important for their searching abilities. However, in this paper, we propose a strategy which cuts off the rich dynamics such as periodic and chaotic attractors in the TCNN and just utilizes the nonchaotic converge dynamics of the TCNN to save the time needed for computation. The strategy is named as nonchaotic simulated annealing (NCSA). Experiments on the traveling salesman problems exibit the effectiveness of NCSA. The NCSA saves over half of the time needed for the computation while maintaining the searching ability of the TCNN.