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Chelyabinskiy Fiziko-Matematicheskiy Zhurnal, 2022, Volume 7, Issue 2, Pages 209–233
DOI: https://doi.org/10.47475/2500-0101-2022-17205
(Mi chfmj282)
 

This article is cited in 3 scientific papers (total in 3 papers)

Mathematics

Optimal routing in problems of sequential traversal of megapolises in the presence of constraints

A. A. Petuninab, A. G. Chentsovb, P. A. Chentsovb

a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
b N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
References:
Abstract: The problem of optimal routing of movements is considered with additional constraints such as precedence conditions and cost functions depending on the job list. Dependencies of this kind refer to the so-called dynamic restrictions, in which the value of the objective function at each step of the movement depends on the trajectory (history) of the path traveled and determines the admissibility of the selected movement. The considered statement is focused, first of all, on engineering applications related to the optimization of the route of the tool of CNC machines; other applications are possible. The objects of visit are non-empty finite sets — megacities. As the main problem in this paper, we consider the problem of optimal tool routing for CNC sheet cutting machines, known as the Cutting Path Problem or Tool Path Problem. This problem arises at the stage of development of control programs for the CNC machine, which set the tool path and a number of technological commands. Among the formal restrictions, the precedence conditions are especially distinguished, which are caused by the technological features of sheet cutting on CNC machines and which can be used to reduce the computational complexity of the problem being solved and construct feasible solutions. The main research method is the widely understood dynamic programming (DP), which takes into account the precedence conditions and the dependence of cost functions on the list of tasks. As applied to the problem of routing the tool of sheet cutting machines, the dependence of the objective function on the list of tasks makes it possible to reduce thermal deformations of the material during thermal cutting. The article provides a rigorous mathematical formalization of the problem of constrained movement routing and a description of the exact solution algorithm. In the process of solving, the order of tasks execution, the specific process trajectory and the starting point are optimized. The algorithm is implemented as a PC program; model examples are solved.
Keywords: megalopolises, route, trajectory, dynamic programming, precedence constraints, dynamic constraints, tool path optimization problem, CNC sheet cutting machine, feasible optimal solution.
Funding agency Grant number
Russian Foundation for Basic Research 20-08-00873
The work was carried out with the financial support of the RFBR (grant 20-08-00873).
Received: 13.03.2022
Revised: 29.04.2022
Document Type: Article
UDC: 519.8.А
Language: Russian
Citation: A. A. Petunin, A. G. Chentsov, P. A. Chentsov, “Optimal routing in problems of sequential traversal of megapolises in the presence of constraints”, Chelyab. Fiz.-Mat. Zh., 7:2 (2022), 209–233
Citation in format AMSBIB
\Bibitem{PetCheChe22}
\by A.~A.~Petunin, A.~G.~Chentsov, P.~A.~Chentsov
\paper Optimal routing in problems of sequential traversal of megapolises in the presence of constraints
\jour Chelyab. Fiz.-Mat. Zh.
\yr 2022
\vol 7
\issue 2
\pages 209--233
\mathnet{http://mi.mathnet.ru/chfmj282}
\crossref{https://doi.org/10.47475/2500-0101-2022-17205}
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  • https://www.mathnet.ru/eng/chfmj/v7/i2/p209
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Chelyabinskiy Fiziko-Matematicheskiy Zhurnal
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