ART/SOFM: a hybrid approach to the TSP

We present a new method of solving large scale travelling salesman problem (TSP) instances using a combination of adaptive resonance theory (ART) and self organizing feature maps (SOFM). We divide our algorithm into three phases: phase one uses ART to form clusters of cities; phase two uses a novel modification of the traditional SOFM algorithm to solve a slight variant of the TSP in each cluster of cities; and phase three uses another version of the SOFM to link all the clusters. The experimental results show that our algorithm finds approximate solutions which are about 13% longer than those reported by the chained Lin Kernighan method for problem sizes of 14,000 cities