PSI - Issue 40

Available online at www.sciencedirect.com Available online at www.sciencedirect.com Sci nceDirect StructuralIntegrity Procedia 00 (2022) 000 – 000 Available online at www.sciencedirect.com ScienceDirect StructuralIntegrity Procedia 00 (2022) 000 – 000

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Procedia Structural Integrity 40 (2022) 105–111

© 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics of Materials and Structures. Abstract It is considered the routing problem solution in which the task set is the union of two subsets (zones); one of subsets should be serviced earlier than the second. It is supposed that each task is connected with the visit to a megalopolis (nonempty finite set) and fulfilment of works. The regular succession of task fulfilment should satisfy to precedence conditions realized in each of zones. The cost functions assume a task list dependence; cost aggregation is supposed additive. For solution, the two-stage dynamic programming procedure is used. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. Keywords: Dynamic programming, routing problem, precedence conditions, sheet cutting. Introduction The routing problem with constraints considered in this article has, as prototype, the known hard-to-solve traveling salesman problem (TSP); see [1, 2, 3, 4]. But, essential singularities of numerical and qualitative nature arise. First of all, this is connected with constraints and complicated cost functions. The above-mentioned singularities are motivated by needs of engineering applications. Among them, now we note problems arising in 15th International Conference on Mechanics, Resource and Diagnostics of Materials and Stru tures To the application of two-stage dynamic programming in the problem of sequential visiting of megalopolises A.G. Chentsov a,b , P.A. Chentsov a,b * a Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620108, Russia b Ural Federal U iversity, ul. Mira, 19, Yekat rinburg, 620002, Russia Abstract It is considered the routing problem solution in which the task set is the union of two subsets (zones); one of subsets should be servi ed earli r an the second. It is supp sed that eac task is connected with the vi it to a megalopolis (nonemp y finite set) and fulfilment of works. The regular cces ion of task fulfilment should sat sfy to precedence conditions realized in each of zones. The cost unctions assume ta k list dependence; cost aggregation is supp sed ad itiv . For solution, the two-stage dy amic programming procedur is u ed. © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der re ponsibility of scientific committee of the15th Int rnational Conference o Mechanics, Resource and Diagnostics of Materials and S ructur s. Keywords: Dynamic p ogramming, routing problem, precedence conditions, sheet cutting. Introduction The routing problem with constraints considered in this article has, as prototype, the known hard-to-solve traveling salesman problem (TSP); see [1, 2, 3, 4]. But, essential singularities of num rical and qualit tive natur aris . Fir t of ll, this is connected with constraints and complicated cost functions. The above-m ntioned singularities are motivated by e ds of engineering applications. Among them, now we note pro lems arising in 15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures To the application of two-stage dynamic programming in the problem of sequential visiting of megalopolises A.G. Chentsov a,b , P.A. Chentsov a,b * a Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620108, Russia b Ural Federal University, ul. Mira, 19, Yekaterinburg, 620002, Russia

* Corresponding author. Tel.: +8-922-112-25-86; E-mail address: chentsov@imm.uran.ru; chentsov.p@mail.ru * Corresponding author. Tel.: +8-922-112-25-86; E-mail ad ress: chentsov@imm.uran.ru; chentsov.p@mail.ru

2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures. 2452-3216 © 2022 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review u der re ponsibility of scientific committe of the15th Int rnational C ference o Mechanics, Resource and Diagnostics of Mate ials and Structures.

2452-3216 © 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of the scientific committee of the15th International Conference on Mechanics, Resources and Diagnostics

of Materials and Structures. 10.1016/j.prostr.2022.04.013