On a Nonstationary Route Problem with Constraints

The extremal route problem of permutations under constraints in the form of preceding conditions is investigated. It is supposed that an executer leaves the initial point (the base) after which he visits a system of megalopolises (finite goal sets) and performs some work on each megalopolis. The cost functions for executor permutations and interior works depend on the “visiting moment” that can correspond to the real time or can also correspond to the natural regular succession (the first visiting, the second visiting, and so on). An economic variant of the widely interpreted dynamic programming method (DPM) is constructed. On this basis an optimal computer realized algorithm is constructed. A variant of a greed algorithm is proposed.