Improved algorithm of transient chaotic neural network with combinatorial optimization

Transiently chaotic neural network (TCNN) and its improved versions have been proven to have search abilities for combinatorial optimization problem (COP). However, the TCNN may be able to maintain its solving ability while the chaotic dynamics are cut. In this paper, the mechanism of the continuous-time Hopfield neural network (CHNN) and the TCNN for COP are analyzed qualitatively from the view of the energy function. It is believed that the "annealing" progress, i.e., the dynamic relaxation of the energy function, helps the improvement of the TCNN over the CHNN. Another Hopfield network with a linear activation function and annealing strategy for the COP is proposed in this paper. Simulations on the TSP show that the improved network performs as well as TCNN but is much more efficient. The performance of the TCNN is improved when linear activation functions are used. Compared with the traditional sigmoid activation function, the improved network is more suitable for hardware implementation.