  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.
