Dynamic programming in the routing problem with constraints and costs depending on a list of tasks

Abstract

637 We study the problem of visiting cities with ante� cedence conditions and traveling costs depending on a list of tasks. The formulation of the problem is associ� ated with the dismantling of a shut down nuclear power unit and is a generalization of that considered in (1). Conceptually, the problem under study goes back to the wellknown traveling salesman problem (2-4), but differs from the latter in having several important features. The solution method used follows (5-7) but admits a higher degree of generality in defining the cost functions. Specifically, in contrast to (1), it is assumed that the arrival and departure points in visited cities can be different, which is important for the abovementioned application. As was noted, the cost functions (traveling and internal operation) can depend on the list of tasks that have not been per� formed by the current moment. This kind of depen� dence was not considered in (5-7). This work deals with qualitative issues. A version of the dynamic programming method (DPM) is pro� posed that takes into account the above features (including the antecedence constraints) and is imple� mented without constructing the entire array of Bell� man function values. Additionally, we suggest an iter� ation method based on an equivalent transformation of the original problem to a simpler form.