TY - CHAP

T1 - An extremal routing problem with constraints and complicated cost functions

AU - Chentsov, Alexander V.

AU - Chentsov, A. G.

AU - Sesekin, A. N.

PY - 2024

Y1 - 2024

N2 - One routing problem with precedence conditions and complicated cost functions is considered. The natural application can be connected with the engineering problem of dismantling of radiation sources. We must choose starting point, route (index permutation), and concrete trajectory of process. In addition, our index permutation defines the sequence of task. The concrete trajectory must be coordinated with this permutation. In addition, different constraints arise. In particular, the choice of the above-mentioned permutation must satisfy to precedence conditions. For introduction of these conditions, the corresponding system of ordered pairs is specified. These ordered pairs are called address. In our mathematical setting, additive criterion is used. This criterion is formed with employment of cost functions with the task list dependence. In the large, the investigated problem can be considered as a control problem with discrete time for that admissible solutions have the hierarchical structure. In this article, we focus on engineering problem connected with dismantling of finite system of radiation sources; for this problem, the above-mentioned task list dependence has the following nature. Namely, in every time, the corresponding executor is affected to those and only those sources that were not dismantled at this time. For solving this applied problem, the widely understood dynamic programming is used. On this foundation, optimal algorithm for PC is constructed. The computing experiment was realized.

AB - One routing problem with precedence conditions and complicated cost functions is considered. The natural application can be connected with the engineering problem of dismantling of radiation sources. We must choose starting point, route (index permutation), and concrete trajectory of process. In addition, our index permutation defines the sequence of task. The concrete trajectory must be coordinated with this permutation. In addition, different constraints arise. In particular, the choice of the above-mentioned permutation must satisfy to precedence conditions. For introduction of these conditions, the corresponding system of ordered pairs is specified. These ordered pairs are called address. In our mathematical setting, additive criterion is used. This criterion is formed with employment of cost functions with the task list dependence. In the large, the investigated problem can be considered as a control problem with discrete time for that admissible solutions have the hierarchical structure. In this article, we focus on engineering problem connected with dismantling of finite system of radiation sources; for this problem, the above-mentioned task list dependence has the following nature. Namely, in every time, the corresponding executor is affected to those and only those sources that were not dismantled at this time. For solving this applied problem, the widely understood dynamic programming is used. On this foundation, optimal algorithm for PC is constructed. The computing experiment was realized.

UR - http://www.scopus.com/inward/record.url?partnerID=8YFLogxK&scp=85128837339

M3 - Chapter

SN - 978-877022340-9

SN - 978-877022341-6

SP - 21

EP - 52

BT - Advanced Control Systems: Theory and Applications

PB - River Publishers

ER -