Neural methods for the traveling salesman problem: Insights from operations research

Abstract

Adaptive neural approaches to the traveling salesman problem appear to hold great promise, as evidenced by the work of Angeniol et al., among others. An adaptive approach based on self-organizing feature maps with conscience—the guilty net—has also exhibited the ability to give short tour lengths for the TSP. Neural approaches rarely compare in speed or efficacy, however, with good heuristics from operations research. In this paper, experiments with the guilty net and a new extension, the vigilant net, show that adaptive approaches can benefit from established results in operations research. Specifically, a simple starting position strategy derives from operations research literature, and proves an important force in reducing tour lengths. In addition, operations research yields insights into the kinds of TSP instances that should be studied. Nonuniformly distributed cities pose an important problem, and the guilty and vigilant nets yield tour lengths shorter than even a comparable geometry preserving operations research heuristic. Experimentation also shows the effect of neighborhood size and conscience.