On one routing problem with non-additive cost aggregation

Abstract

We investigate the problem on sequential round of megalopolises (nonempty finite sets) with preceding conditions and nonadditive aggregation of costs. We suppose that a variant of aggregation with respect to "external" phase (by the estimation of the system of cycles, which are determined every time by the "external" movement and internal jobs) corresponds to the "bottleneck" problem with the correction parameter. At the "internal" phase (within the cycle), an aggregation of costs with respect to external movement and carrying out works can be arbitrary. We construct nonadditive variant of the procedure of dynamic programming (DP) including economical variant, which uses preceding conditions. In the form of a program for a personal computer, we realize the optimal algorithm based on DP for the statement oriented to the problem on control of an autonomous system, which works in aggressive environment and implements a sequential process of dismantling of the sources of exposures (of this environment) to the system. Such a statement can correspond to the engineering problem on sequential dismantling of the sources of radiation under emergency situations on the nuclear power plants in the case of application of the robotic system with electronic equipment, which can work only if tolerances are complied with respect to influence of radiation during entire time interval. For this variant of the general statement, we implement a calculation experiment by means of a personal computer. © 2020 South Ural State University. All rights reserved.