Study of Traveling Salesman Problem by Self-Organizing Maps

Abstract

The traveling salesman problem has long been studied as an optimization problem that connects multiple cities with the shortest path. Angeniol published the method of SOM for the first time in 1988. Usually, a ring-shaped one-dimensional SOM is used to solve the problem. In Japan, Fujimura et al. and other researchers have studied the problem by SOM and attempted to shorten the calculation time. They developed inertial terms, eliminating intersections and learning rate functions, etc. to get shorter path and to shorten the calculation time. In this research, we applied these ideas to the traveling salesman problem while maintaining the prototype of SOM as much as possible. The subjects were att48 and att532, for which the shortest distance was already known. In the att48, the shortest path was obtained by SOM. We will show the advantages and disadvantages of the SOM method.