On solution of the problem of successive round of sets by the ‘nonclosed’ travelling salesman problem

Consideration was given to an iterative method of solution of the problem of successive round of a set using a model of the auxiliary travelling salesman problem with a reconstructible system of ‘towns’. A possible deviation from the global extremum was estimated at each step of iterations which were assumed to cease as soon as the desired – in terms of this estimate – accuracy was attained. Computer experiment demonstrated, however, that the iterative procedure stabilized after several steps, although the global extremum was not necessarily attained. Yet, stabilization of the iterative procedure itself is related with very interesting modes of solving the route problem that deserve independent study.