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Elements of dynamic programming in local improvement constructions for heuristic solutions of routing problems with constraints

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Abstract

We consider methods for solving routing problems with precedence constraints that use iterative modes based on Bellman insertions while recomputing precedence constraints of the original problem; we assume that the dimension of the latter is sufficiently large, which does not let us, due to complexity of computations, immediately apply dynamic programming in the “global” version.

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References

  1. Melamed, I.I., Sergeev, S.I., and Sigal, I.Kh., The Traveling Salesman Problem. Issues in Theory, Autom. Remote Control, 1989, vol. 50, no. 9, pp. 1147–1173.

    MathSciNet  MATH  Google Scholar 

  2. Melamed, I.I., Sergeev, S.I., and Sigal, I.Kh., The Traveling Salesman’s Problem. Exact Methods, Autom. Remote Control, 1989, vol. 50, no. 10, pp. 1303–1324.

    MathSciNet  MATH  Google Scholar 

  3. Melamed, I.I., Sergeev, S.I., and Sigal, I.Kh., The Traveling Salesman Problem. Approximate Algorithms, Autom. Remote Control, 1989, vol. 50, no. 11, pp. 1459–1479.

    MathSciNet  MATH  Google Scholar 

  4. Petunin, A.A., On Some Strategies for Constructing the Tool’s Route in the Development of Controlling Programs for Thermal Cutting Machines, Vestn. UGATU, Ser. Upravlen., Vychisl. Tekh. Informatika, 2009, vol. 13, no. 2(35), pp. 280–286.

    Google Scholar 

  5. Petunin, A.A., Chentsov, A.G., and Chentsov, P.A., On Routing the Movement of the Tool in Sheet Cutting Machines with Digital Program Control, Nauch.-Tekhn. Vedomosti SPbGPU, Ser. Informatika. Telekommunikatsii. Upravlen., 2013, no. 2 (169), pp. 103–111.

    Google Scholar 

  6. Chentsov, A.G., Ekstremal’nye zadachi marshrutizatsii i raspredeleniya zadanii: voprosy teorii (Extremal Problems of Routing and Task Distribution: Theoretical Fundamentals), Moscow–Izhevsk: RKhD, 2008.

    Google Scholar 

  7. Chentsov, A.G., Dynamic Programming in Extremal Problems of Routing with Constraints, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2010, no. 3, pp. 61–73.

    Google Scholar 

  8. Chentsov, A.G., On Routing Complexes of Jobs, Vestn. UdGU, Mat. Mekh. Komp’yut. Igry, 2013, no. 1, pp. 58–82.

    Google Scholar 

  9. Chentsov, A.G. and Chentsov, A.A., Dynamic Programming in Routing Problem with Constraints and Costs Depending on the List of Tasks, Dokl. Akad. Nauk, 2013, vol. 453, no. 1, pp. 20–23.

    MathSciNet  MATH  Google Scholar 

  10. Litl, Dzh., Murti, K., Suini, D., and Kerel, K., Algorithm for the Traveling Salesman Problem, Ekon. Mat. Metod., 1965, vol. 1, no. 1, pp. 94–107.

    Google Scholar 

  11. Gutin, G. and Punnen, A., The Traveling Salesman Problem and Its Variations, Berlin: Springer, 2002.

    MATH  Google Scholar 

  12. Escudero, L., An Inexact Algorithm for the Sequential Ordering Problem, Eur. J. Oper. Res., 1988, vol. 37, no. 2, pp. 236–249.

    Article  MathSciNet  MATH  Google Scholar 

  13. Sigal, I.Kh., The Decomposition Approach to Solving Traveling Salesman Problem in High Dimensions and Some of Its Applications, Izv. Akad. Nauk SSSR, Tekhn. Kibern., 1990, no. 6, pp. 143–155.

    Google Scholar 

  14. Frolovskii, V.D., Automating the Design of Controlling Programs for Heat Metal Cutting on Equipment with Digital Program Control, Inform. Tekhnol. Proektirovan. Proizvod., 2005, no. 4, pp. 63–66.

    Google Scholar 

  15. Chentsov, A.G., Problem of Successive Megalopolis Traversal with the Precedence Conditions, Autom. Remote Control, 2014, vol. 75, no. 4, pp. 728–744.

    Article  MathSciNet  MATH  Google Scholar 

  16. Chentsov, A.G., On a Parallel Procedure for Constructing the Bellman Function in the Generalized Problem of Courier with Internal Jobs, Autom. Remote Control, 2012, vol. 73, no. 3, pp. 532–546.

    Article  MathSciNet  MATH  Google Scholar 

  17. Kuratowski, K. and Mostowski, A., Set Theory, Amsterdam: North-Holland, 1967. Translated under the title Teoriya mnozhestv (Set Theory), Moscow: Mir, 1970.

    MATH  Google Scholar 

  18. Kormen, T., Leizerson, Ch., and Rivest, R., Algoritmy: Postroenie and Analiz, Moscow: MTsNMO. 1990.

    Google Scholar 

  19. Chentsov, A.A. and Chentsov, A.G., The Problem of Sequential Megalopolis Traversal, Vest. Tambov. Univ., Ser. Estestvenn. Tekh. Nauki, 2014, vol. 5, no. 2, pp. 454–475.

    MATH  Google Scholar 

  20. Petunin, A.A., Chentsov, A.G., and Chentsov, P.A., Local Insertions Based on Dynamic Programming in the Routing Problem with Constraints, Vestn. UdGU, Mat. Mekh. Komp’yut. Igry, 2014, no. 2, pp. 56–75.

    MATH  Google Scholar 

  21. Chentsov, A.A., Chentsov, A.G., and Chentsov, P.A., Method of Iterations in the Routing Problem with Internal Losses, Tr. Inst. Mat. Mekh. UrO RAN, 2009, vol. 15, no. 4, pp. 270–289.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Ural Federal University, Yekaterinburg, Russia

    A. A. Petunin, A. G. Chentsov & P. A. Chentsov

  2. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia

    A. A. Chentsov, A. G. Chentsov & P. A. Chentsov

Authors
  1. A. A. Petunin
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  2. A. A. Chentsov
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  3. A. G. Chentsov
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  4. P. A. Chentsov
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Corresponding author

Correspondence to A. A. Petunin.

Additional information

Original Russian Text © A.A. Petunin, A.A. Chentsov, A.G. Chentsov, P.A. Chentsov, 2017, published in Avtomatika i Telemekhanika, 2017, No. 4, pp. 106–125.

This paper was recommended for publication by A.A. Lazarev, a member of the Editorial Board

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Petunin, A.A., Chentsov, A.A., Chentsov, A.G. et al. Elements of dynamic programming in local improvement constructions for heuristic solutions of routing problems with constraints. Autom Remote Control 78, 666–681 (2017). https://doi.org/10.1134/S0005117917040087

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  • DOI: https://doi.org/10.1134/S0005117917040087

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