Constrained optimal routing

The problem of sequentially traversing sets to precedence constraints is considered. It is assumed that on each sets, some jobs involving expenditures may be completed, total expenditures are formed by the costs of these jobs and those for moving between sets. The trace of traversing the enumerated sets is optimized, after which the regular iteration step of the procedure described is performed. The problem of sequentially traversing megalopolises involving travels between megalopolises and the traveling sales subproblems for cities within each megalopolis. Several theorems are provided to satisfy and prove this formula.