Optimization of the start point in the GTSP with the precedence conditions

The paper is devoted to the routing problem with constraints and cost functions that can depend on the list of tasks. It is assumed that the initial condition for the process with discrete time can be selected within a metric space that satisfies the condition of complete boundedness. It is supposed that the problem includes a visiting of a finite system of megalopolises (non-empty finite sets) with the fulfillment of some works. The cost of these works each time depend on the point of arrival and the point of departure. The costs of movement and work are aggregated additively. For the problem solution widely understood dynamic programming method providing $\varepsilon$-optimal solution for any $\varepsilon>0$ is used.