Improving local minima of columnar competitive model for TSPs

The columnar competitive model (CCM) has been recently proposed to solve the traveling salesman problem. This method performs much better than the original Hopfield network in terms of both the number and the quality of valid solutions. However, the local minima is still an open unsolved issue. This paper studies the performance of the CCM and aims to improve its local minima problem. The contributions of this paper are: 1) it proves by mathematics that the CCM is hardly to escape from local minimum states in general; 2) an alternate CCM is presented based on a modified energy function so as to enhance the capability of the original CCM; 3) a new algorithm is proposed by combining the alternative CCM with the original one, which enables the network to have lower energy level when trapped in local minima, this makes the network to reach the optimal or near-optimal state quickly; 4) Simulations are carried out to illustrate the performance of the proposed method