A Simple Learning Algorithm for the Traveling Salesman Problem

Abstract

We propose a learning algorithm for solving the traveling salesman problem based on a simple strategy of trial and adaptation: i) A tour is selected by choosing cities probabilistically according to the ``synaptic'' strengths between cities. ii) The ``synaptic'' strengths of the links that form the tour are then enhanced (reduced) if the tour length is shorter (longer) than the average result of the previous trials. We perform extensive simulations of the random distance traveling-salesman problem. For sufficiently slow learning rates, near optimal tours can be obtained with the average optimal tour lengths close to the lower bounds for the shortest tour lengths.