Abstract
A famous problem is that of finding the optimal route passing through each
of a collection of N locations given by their coordinates and/or with their
mutual distances, or travel times, exactly once and ending in the starting
point. Even under the additional restriction that distances respectively
travel times are symmetric, this is a very challenging problem already for
moderate N. Since this problem has far more applications than the name
suggests, many efforts were made to effectively solve it or
even to solve certain instances at all. At present one of the smallest unsolved
problems has N=1577. We will show several approaches to its solution
and it will become clear that continuous methods are crucial for solving this
discrete problem efficiently. (An earlier version of this talk was given 4/97)
