An integrated self-organizing map for the traveling salesman problem

Abstract

As a representative combinatorial optimization problem, the Traveling Salesman Problem (TSP) has attracted extensive research. In this paper, we develop a new Self-Organizing Map (SOM) network for the TSP and call it the Integrated SOM (ISOM) network. Its learning rule embodies the effective mechanisms of three typical learning rules. In its single learning activity, the excited neuron first is dragged close to the input city, and then is expanded towards the convex-hull of the TSP, and finally, it is drawn close to the middle point of its two neighbor neurons. The elaborate cooperation among these three learning mechanisms is evolved by a genetic algorithm. The simulation results show that the finally established ISOM can generate more promising solutions, with similar computation time, than other neural networks like the SOM network, the Expanded SOM, and the Convex Elastic Net.