Sequential reaching of a system of mobile sets ("reachability domain") in a
parameter space is studied; the reachability domains yield the solution of
certain problems on modifying the routes of the routine problem. Stable re
alization of extrema is demonstrated and a relationship between the computa
tion error and loss in quality is derived. Concrete variants of the problem
of sequential reaching of sets under variable margins for the degree of de
viation from the shortest route in solving the routine problem are modeled.