"Conscientious" neural nets for tour construction in the traveling salesman problem: the vigilant net

Abstract Previous research has established the feasibility of applying adaptive neural network approaches to the traveling salesman problem. Such methods (unlike the Hopfield network) gradually adjust a ring of nodes until the nodes correspond to actual data points, making them comparable to tour construction heuristics. However, they typically require a few thousand iterations and may not yield “node separation”—a one-to-one correspondence between nodes and cities—in a reasonable processing time. The vigilant net addresses these shortcomings by utilizing a hardware implementable mechanism-that of vigilance, from adaptive resonance theory networks—to help separate nodes without excessive processing. Further, for these solution methods to be truly viable, they must not demand fine-tuning of various parameters, as presently they do. Finally, an advantage to using these methods must be established. Results from previous research and new insights help determine appropriate parameter settings and strategies for the algorithm. Two strategies for selecting the important vigilance parameter are investigated here. In one, feedback from the network helps to adjust vigilance. Results indicate that the vigilant network can yield acceptable results in very short processing times, and the two strategies perform virtually.identically. Comparisons with conventional heuristics yield further insights.